From: zulu Date: Wed, 8 Jan 2014 16:32:01 +0000 (+0100) Subject: relecture vlad de 0 a 70 X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/these_gilles.git/commitdiff_plain/7a1f7981654e75ea330b58c7f93620ce69bf13b2?ds=inline relecture vlad de 0 a 70 --- diff --git a/THESE/Chapters/chapter1b/chapter1b.tex b/THESE/Chapters/chapter1b/chapter1b.tex index 1cd0756..c089c24 100644 --- a/THESE/Chapters/chapter1b/chapter1b.tex +++ b/THESE/Chapters/chapter1b/chapter1b.tex @@ -11,14 +11,14 @@ La technologie de fabrication des GPUs étant identique à celle des CPUs, c'est \label{fig-gpucpu1} \end{figure} -Cette spécialisation des circuits GPU a permis d'en améliorer les performances brutes beaucoup plus rapidement que pour les CPUs, au fil des évolutions de la technologie. Il en est allé de même pour les débits mémoire théoriques. Les graphiques de la figure \ref{fig-gpucpu2} comparent les rythmes de ces évolutions pour les GPUs Nvidia\textregistered et pour les CPUs Intel\textregistered. +Cette spécialisation des circuits GPU a permis d'en améliorer les performances brutes beaucoup plus rapidement que pour les CPUs, au fil des évolutions de la technologie. Il en est allé de même pour les débits mémoire théoriques. Les graphiques de la figure \ref{fig-gpucpu2} comparent les rythmes de ces évolutions pour les GPUs Nvidia\textregistered~ et pour les CPUs Intel\textregistered. Les problèmes requérant les capacités de calcul spécifiques des GPUs ne sont cependant pas limités aux questions de rendu graphique, aussi les scientifiques ont-ils très vite cherché à tirer parti de la puissance de calcul croissante des GPUs pour traiter d'autres types de problèmes, faisant sens à l'acronyme GPGPU (General Purpose Graphical Processing Unit). \begin{figure}[h] \centering - \subfigure[Nombre maximum théorique d'opérations en virgule flottante par seconde en fonction de l'année et de l'architecture.]{\includegraphics[height=5cm]{Chapters/chapter1b/img/gpucpu2a.png}}\quad - \subfigure[Bande passante théorique maximale des diverses architectures.]{\includegraphics[height=5cm]{Chapters/chapter1b/img/gpucpu2b.png}} + \subfigure[Nombre maximum théorique d'opérations en virgule flottante par seconde en fonction de l'année et de l'architecture.]{\includegraphics[width=9cm]{Chapters/chapter1b/img/gpucpu2a.png}}\\ + \subfigure[Bande passante théorique maximale des diverses architectures.]{\includegraphics[width=9cm]{Chapters/chapter1b/img/gpucpu2b.png}} \caption{Comparaison des performances des GPUs Nvidia et des CPU Intel (d'après \cite{CUDAPG}).} \label{fig-gpucpu2} \end{figure} @@ -66,7 +66,7 @@ Une petite quantité de mémoire on-chip est présente sur chaque SM et permet l Globale & off-chip &grille&580/80/350 &144 & 6G \\ \bottomrule \end{tabular} - \caption{Caractéristiques des différents types de mémoire disponibles sur le GPU. Pour les mémoires cachées, les latences sont données selon l'accès \textit{sans-cache/L1/L2}. Les mesures ont été obtenues à l'aide des microprogrammes de test de \cite{wong2010demystifying}.} + \caption{Caractéristiques des différents types de mémoire disponibles sur le GPU. Pour les mémoires cachées, les latences sont données selon l'accès \textit{sans-cache/L1/L2} et ont été obtenues à l'aide des microprogrammes de test de \cite{wong2010demystifying}. Les valeurs de débit sont données par le constructeur.} \label{tab-gpu-memoire} \end{table} @@ -102,5 +102,22 @@ Les limitations de l'\textit{occupancy} ont pour origine : Nous verrons que cette notion d'\textit{occupancy}, si elle conserve du sens, peut toutefois être remise en question en optimisant d'autres aspects permettant d'arriver à une réduction de l'effet des latences, comme le parallélisme d'instructions ou l'augmentation du volume des transactions. En effet, ces techniques, et surtout l'utilisation avisée des différents types de mémoire du GPU permettent d'obtenir des performances élevées, parfois inenvisageables en suivant les prescriptions du constructeur. - - +\section{Synthèse des contraintes d'implémentation} +Certaines de ces contraintes ont déjà été évoquées rapidement, mais il nous semble important d'en donner ici une présentation synthétique. +\begin{enumerate} +\item \textbf{Contiguïté}. +Les accès aléatoires à la mémoire globale sont en règle générale très pénalisants. Toutefois, il est possible de tirer parti du cache de niveau 1 (à une dimension) en organisant les données pour que tous les threads d'un même warp accèdent à des données appartenant au même bloc de 128 octets de mémoire. Le non-respect de cette contrainte de contiguïté (\textit{coalescence}) induit des accès réalisés en plusieurs transactions serialisées et donc une perte potentiellement importante de performances. +\item \textbf{Conflits de banques}. +La mémoire partagée, plus rapide que la mémoire globale, peut sembler une solution évidente pour obtenir des performances élevées. Cependant, elle est physiquement organisée en 32 \og banques \fg{} de largeur 32 bits et présente elle aussi une contrainte majeure. Sur architecture Fermi, l'exécution des threads d'un warp est assurée par deux \textit{moteurs d'exécution} qui activent en parallèle chacun des deux demi-warp. +Un \textbf{conflit de banque} se produit lorsque deux threads n'appartenant pas au même demi-warp accèdent à des données localisées dans la même banque de mémoire partagée. La transaction parallèle est alors interrompue et sérialisée. +Ici encore, la perte de performance peut être importante, mais il peut s'avérer très complexe, coûteux, voire impossible d'organiser les données en mémoire partagée de sorte à éviter tout conflit de banque. +\item \textbf{Branches divergentes}. +Toute branche d'exécution divergente entraine une sérialisation des exécution des threads du warp auquel ils appartiennent. Il convient donc d'éviter cette situation et d'organiser les traitements en conséquence en privilégiant le plus souvent un découpage plus fin en plusieurs kernels élémentaires plutôt que des kernels \og lourds \fg{}. +\item \textbf{Transferts GPU$\leftrightarrow$CPU}. +Les transferts de données entre la mémoire globale du GPU et celle de son hôte CPU peuvent représenter l'essentiel du temps de traitement total et doivent donc être optimisées pour en réduire la fréquence et le volume des données à copier. Cela peut parfois être contradictoire avec la multiplication de petits kernels élémentaires. +Il est toutefois possible, lorsque la séquence de traitement le permet, de réaliser des transferts en temps masqué, pendant l'exécution d'un kernel, en créant plusieurs flux d'exécution. +\item \textbf{Partage des ressources d'un SM} +Le paragraphe sur l'\textit{occupancy} a abordé cet aspect par un exemple. Il faut retenir que chaque SM possède des ressources mémoire (registres, mémoire partagée) que les threads des blocs logiques de la grille de calcul se partagent au cours de l'exécution d'un kernel. L'équilibre entre l'utilisation de ces ressources et le dimensionnement de la grille de calcul relève d'un compromis parfois délicat à trouver pour obtenir les meilleures performances possibles. +\item \textbf{Les latences}. L'exécution des kernels subit l'effet de latences d'origines diverses. Les latences d'accès aux mémoires (voir Table \ref{tab-gpu-memoire}), les latences des différentes instructions arithmétiques ou encore les latences crées par l'inter dépendance d'instructions consécutives. Il est impératif de les prendre en considération et de mettre en \oe uvre des techniques adaptées pour les masquer au mieux. +\end{enumerate} +L'ensemble de ces aspects rend difficile la conception d'implémentations GPU rapides car rares sont les transcriptions directes d'un code CPU qui ne se heurtent pas sévèrement à l'une ou l'autre des contraintes que l'on vient d'énumérer. Les performances qui en résultent sont alors très en deça de celles attendues, voire inférieures à celles de l'implémentation CPU. diff --git a/THESE/Chapters/chapter2/chapter2.tex b/THESE/Chapters/chapter2/chapter2.tex index 17dd162..43ceac1 100644 --- a/THESE/Chapters/chapter2/chapter2.tex +++ b/THESE/Chapters/chapter2/chapter2.tex @@ -1,13 +1,13 @@ -L'étendue des techniques applicables aux images numériques est aujourd'hui si vaste qu'il serait illusoire de chercher à les décrire ici de manière exhaustive. Ce chapitre présente plus spécifiquement les algorithmes utilisés en présence d'images (fortement) bruitées, c'est-à-dire présentant des distorsions par rapport à la réalité \og absolue \fg{} qu'elles représentent. +L'étendue des techniques applicables aux images numériques est aujourd'hui si vaste qu'il serait illusoire de chercher à les décrire ici de manière exhaustive. Ce chapitre présente plus spécifiquement les algorithmes utilisés en présence d'images (fortement) bruitées, c'est-à-dire présentant une altération de la réalité \og absolue \fg{} qu'elles représentent. Le bruit rend potentiellement délicate l'extraction des informations utiles contenues dans les images perturbées ou en complique l'interprétation, automatisée ou humaine. L'intuition incite donc à chercher des méthodes efficaces de pré-traitement réduisant la puissance du bruit et permettant ainsi aux traitements de plus haut niveau (comme la segmentation), d'opérer dans de meilleures conditions. -Toutefois, il faut également considérer que les opérations préalables de réduction de bruit génèrent des modifications statistiques et peuvent altérer les caractéristiques que l'on cherche à mettre en évidence grâce au traitement principal. En ce sens, il peut être préférable de chercher à employer des algorithmes de haut niveau travaillant directement sur les images bruitées pour en préserver toute l'information, ce qui est le cadre de notre contribution portant sur l'algorithme du \textit{snake} (chapitre \ref{ch-snake}). +Toutefois, il faut également considérer que les opérations préalables de réduction de bruit génèrent des modifications statistiques et peuvent altérer les caractéristiques que l'on cherche à mettre en évidence grâce au traitement principal. En ce sens, il peut être préférable de chercher à employer des algorithmes de haut niveau travaillant directement sur les images bruitées pour en préserver toute l'information, ce qui est le cadre de notre contribution portant sur un algorithme de segmentation par contour actif polygonal (dit \textit{snake}, voir chapitre \ref{ch-snake}). De plus, toute opération supplémentaire si basique soit elle, réduit le temps de traitement disponible pour l'opération de haut niveau. En effet, lorsque les images à analyser sont de grande taille, procéder à un débruitage préalable peut s'avérer incompatible avec les contraintes de débit. -Les images auxquelles nous nous intéressons sont généralement les images numériques allant des images naturelles telles que définies par Caselles \cite{Caselles99topographicmaps} aux images d'amplitude issues de l'imagerie radar à ouverture synthétique (ROS ou en anglais SAR) \cite{cutrona1990synthetic}, de l'imagerie médicale à ultrasons (échographie) ou de la microscopie électronique. +Les images auxquelles nous nous intéressons sont généralement les images numériques allant des images naturelles telles que définies par Caselles \cite{Caselles99topographicmaps} aux images d'amplitude issues de l'imagerie radar à ouverture synthétique (ROS ou en anglais SAR) \cite{cutrona1990synthetic}, ou de l'imagerie médicale à ultrasons (échographie). Ces dispositifs d'acquisition sont, par essence, générateurs de bruits divers, inhérents aux technologies mises en \oe uvre et qui viennent dégrader l'image idéale de la scène que l'on cherche à représenter ou analyser. On sait aujourd'hui caractériser de manière assez précise ces bruits et la section \ref{sec_bruits} en détaille les origines physiques ainsi que les propriétés statistiques qui en découlent. On peut d'ores et déjà avancer que la connaissance de l'origine d'une image et donc des propriétés des bruits associés qui en corrompent les informations, est un atout permettant de concevoir des techniques de filtrage adaptées à chaque situation. Quant à la recherche d'un filtre universel, bien qu'encore illusoire, elle n'est pas abandonnée, tant les besoins sont nombreux, divers et souvent complexes. diff --git a/THESE/Chapters/chapter2/chapter2b.tex b/THESE/Chapters/chapter2/chapter2b.tex index 106b0f0..5fb1077 100644 --- a/THESE/Chapters/chapter2/chapter2b.tex +++ b/THESE/Chapters/chapter2/chapter2b.tex @@ -1,9 +1,9 @@ \section{Modèle d'image bruitée} -On considère qu'une image observée, de largeur $L$ pixels et de hauteur $H$ pixels, est un ensemble de $N=LH$ observations sur un domaine $\Omega$ à deux dimensions ($\Omega \subset \mathbb{Z}^2$). À chaque élément de $\Omega$, aussi appelé \textit{pixel}, est associé un indice unique $k \in [\![1;N]\!]$, une position $x_k=(i,j)_k \in\Omega$ et une valeur observée $v_k=v(i,j)_k$. +On considère qu'une image observée, de largeur $L$ pixels et de hauteur $H$ pixels, est un ensemble de $N=LH$ observations sur un domaine $\Omega$ à deux dimensions ($\Omega \subset \mathbb{Z}^2$). À chaque élément de $\Omega$, aussi appelé \textit{pixel}, est associé un indice unique $k \in [\![1;N]\!]$, une position $x_k \in\Omega$ et une valeur observée $v_k$. Chaque position $x_k$ peut aussi être représenté par ses coordonnées cartésiennes $(i,j)$. La valeur observée peut, selon les cas, être de dimension $1$ pour les images représentées en niveaux de gris ou de dimension 3 pour les images couleur représentées au format RVB. Les dimensions supérieures, pour la représentation des images hyperspectrales ne sont pas abordées dans ce manuscrit. L'image observée peut ainsi être considérée comme un vecteur à $N$ éléments $\bar{v}= (v_k)_{k\in [\![1;N]\!]}$. Les divers traitements appliqués aux images observées ont souvent pour but d'accéder aux informations contenues dans une image sous-jacente, débarrassée de toute perturbation, dont nous faisons l'hypothèse qu'elle partage le même support $\Omega$ et que nous notons $\bar{u}$. L'estimation de $\bar{u}$ réalisée par ces traitements est notée $\widehat{\bar{u}} = (\widehat{u}_k)_{k\in [\![1;N]\!]}$. -Le lien entre $\bar{u}$ et $\bar{v}$ peut être exprimé par la relation $\bar{v}=\bar{u}+\sigma\epsilon$, où $\epsilon \in \mathbb{R}^N$ représente le modèle de perturbation appliquée à $\bar{u}$ et $\sigma$ représente la puissance de cette perturbation qui a mené à l'observation de $\bar{v}$. +Le lien entre $\bar{u}$ et $\bar{v}$ peut être exprimé, par exemple dans le cas de bruit additif, par la relation $\bar{v}=\bar{u}+\epsilon$, où $\epsilon \in \mathbb{R}^N$, de valeur moyenne nulle et de variance $\epsilon^2$, représente le modèle de perturbation appliquée à $\bar{u}$ et qui a mené à l'observation de $\bar{v}$. Dans le cas général, $\epsilon$ dépend de $\bar{u}$ et est caractérisé par la densité de probabilité (PDF pour Probability Density Function) $p(v|u)$. \section{Modèles de bruit}\label{sec_bruits} @@ -24,9 +24,9 @@ On a alors l'expression suivante, où $\sigma >0$ \[p(v|u)=\frac{1}{\sqrt{2}\pi\sigma}\mathrm{e}^{-\frac{(v-u)^2}{2\sigma^2}}\] \subsection{Le speckle} -En imagerie radar, sonar ou médicale, les surfaces que l'on veut observer sont \og éclairées \fg{} par des sources cohérentes. Les propriétés locales de ces surfaces sont le siège de réflexions multiples qui interfèrent entre elles pour générer un bruit de tavelures, ou speckle, dont l'intensité dépend de l'information contenue dans le signal observé. +En imagerie active radar ou ultrasonore (échographique), les surfaces que l'on veut observer sont \og éclairées \fg{} par des sources cohérentes. Les propriétés locales de ces surfaces sont le siège de réflexions multiples qui interfèrent entre elles pour générer un bruit de tavelures, ou speckle, dont l'intensité est liée, entre autres, à la reflexivité de la scène observée et à l'incidence du signal source. Le speckle est ainsi un bruit de type \textit{multiplicatif} qui confère aux observations une très grande variance, laquelle peut être réduite, pour une scène donnée, par moyennage de plusieurs observations, ou vues. -Si $L$ est le nombre de vues, le speckle est traditionnellement modélisé par la PDF suivante : +Si $L$ est le nombre de vues, le speckle est traditionnellement modélisé par la PDF Gamma suivante : \[p(v \mid u)=\frac{L^2v^{(L-1)}\mathrm{e}^{-L\frac{v}{u}}}{\Gamma (L)u^L} \] L'espérance vaut $\mathrm{E}\left[v\right]=u$ et la variance $\sigma^2=\frac{u^2}{L}$ est effectivement inversement proportionnelle à $L$, mais pour le cas mono vue où $L=1$, la variance vaut $u^2$, soit un écart type du signal $v$ égal à sa moyenne. @@ -46,7 +46,7 @@ Le bruit impulsionnel se caractérise par la probabilité $P$ d'un pixel d'être \] \subsection{Le bruit de Poisson} -Aussi appelé \textit{bruit de grenaille} (shot noise), ce type de bruit est inhérent aux dispositifs de détection des photons. Il devient prépondérant dans des conditions de faible éclairement, lorsque la variabilité naturelle du nombre de photons reçus par un photosite par intervalle d'intégration influe sur les propriétés statistiques du signal. +Aussi appelé \textit{bruit de grenaille} (shot noise), ce type de bruit est inhérent aux dispositifs de détection des photons. Dans des conditions de faible éclairement, toute variation du petit nombre de photons reçus par un photosite dans l'intervalle d'intégration peut induire de grandes variations de la valeur moyenne. Le bruit de grenaille est de type multiplicatif et suit une loi de Poisson. La PDF peut s'écrire comme suit : \[ p(v \mid u)=\mathrm{e}\frac{u^v}{v!}\] diff --git a/THESE/Chapters/chapter2/chapter2c.tex b/THESE/Chapters/chapter2/chapter2c.tex index a41ecee..8d9e79d 100644 --- a/THESE/Chapters/chapter2/chapter2c.tex +++ b/THESE/Chapters/chapter2/chapter2c.tex @@ -1,27 +1,27 @@ \section{Les techniques de réduction de bruit} -La très grande majorité des algorithmes de réduction de bruit fait l'hypothèse que la perturbation est de type gaussien, même si le développement des systèmes d'imagerie radar et médicale a favorisé l'étude des bruits multiplicatifs du type \textit{speckle} ou \textit{Poisson}. +La très grande majorité des algorithmes de réduction de bruit fait l'hypothèse que la perturbation est de type additif gaussien, même si le développement des systèmes d'imagerie radar et médicale a favorisé l'étude des bruits multiplicatifs du type \textit{speckle} ou \textit{Poisson}. Un très grand nombre de travaux proposant des méthodes de réduction de ces bruits ont été menés, ainsi que beaucoup d'états de l'art et d'études comparatives de ces diverses techniques. Aussi nous focaliserons nous sur les techniques en lien avec les travaux que nous avons menés et qui ont donné lieu à des implémentations efficaces susceptibles de fournir des éléments opérationnels rapides pour le pré-traitement des images. La figure \ref{fig-ny-noises} montre une image de synthèse issue de la base de test COIL \cite{coil}, supposée sans bruit et qui sera considérée comme référence, ainsi que deux versions bruitées, respectivement avec un bruit gaussien d'écart type 25 et un bruit impulsionnel affectant 25\% des pixels. -L'indice de qualité le plus employé pour mesurer la similarité entre deux images est le PSNR (pour Peak Signal to Noise Ratio). Il est exprimé en décibels (dB) et se calcule en appliquant la formule +L'indice de qualité le plus employé pour mesurer la similarité entre deux images est le PSNR (pour Peak Signal to Noise Ratio). Il est exprimé en décibels (dB) et est défini par \[ PSNR = 10log_{10}\left(\frac{D^2}{\displaystyle\frac{1}{N}\sum_{k < N}\left(v_k - u_k\right)^2}\right)\] si l'on cherche à évaluer le PSNR de l'image observée $\bar{v}$ par rapport à l'image de référence $\bar{u}$. Le nombre $D$ représente la dynamique maximale des images, e.g 255 pour des images en niveaux de gris codés sur 8 bits. -Cet indicateur seul est cependant insuffisant pour caractériser convenablement la qualité de débruitage d'un filtre, mesure hautement subjective. Un indice global de similarité structurelle (MSSIM pour Mean Structural Similarity Index) a été proposé par Wang \textit{et al.} \cite{Wang04imagequality} et permet, en conjonction avec le PSNR, de garantir une mesure de qualité plus en rapport avec la perception visuelle. Le MSSIM prend ses valeurs dans l'intervalle $[0;1]$ avec une similarité d'autant plus grande que la valeur est proche de 1. +Cet indicateur seul est cependant insuffisant pour caractériser convenablement la qualité de débruitage d'un filtre, mesure hautement subjective. Un indice global de similarité structurelle (MSSIM pour Mean Structural Similarity Index) a été proposé par Wang \textit{et al.} \cite{Wang04imagequality} et permet, en conjonction avec le PSNR, de fournir une mesure de qualité plus en rapport avec la perception visuelle. Le MSSIM prend ses valeurs dans l'intervalle $[0;1]$ avec une similarité d'autant plus grande que la valeur est proche de 1. \begin{figure} \centering \subfigure[Sans bruit]{\includegraphics[width=4cm]{/home/zulu/Documents/these_gilles/THESE/codes/ny256.png}} \subfigure[Bruit gaussien $\sigma=25$, PSNR=22.3~dB MSSIM=0.16]{\includegraphics[width=4cm]{/home/zulu/Documents/these_gilles/THESE/codes/ny256_gauss25.png}} \subfigure[Bruit impulsionnel 25\%, PSNR=9.48~dB MSSIM=0.04]{\label{ny-sap}\includegraphics[width=4cm]{/home/zulu/Documents/these_gilles/THESE/codes/ny256_sap25.png}} - \caption{Images 256$\times$256 en niveau de gris 8 bits utilisées pour l'illustration des propriétés des filtres. a) l'image de référence non bruitée. b) l'image corrompue par un bruit gaussien d'écart type $\sigma=25$. c) l'image corrompue par un bruit impulsionnel à 25\%.} + \caption{Images 256$\times$256 en niveau de gris 8 bits utilisées pour l'illustration des propriétés des filtres. (a) l'image de référence non bruitée. (b) l'image corrompue par un bruit gaussien d'écart type $\sigma=25$. (c) l'image corrompue par un bruit impulsionnel à 25\%.} \label{fig-ny-noises} \end{figure} \subsection{Les opérateurs de base}\label{sec-op-base} \subsubsection{Le filtre de convolution} L'opération la plus employée dans les procédés de traitement d'image est sans doute la convolution. Selon les valeurs affectées aux coefficients du masque, le filtrage par convolution permet de réaliser bon nombre de traitements comme la réduction de bruit par moyennage ou noyau gaussien ou encore la détection de contours. -Si la fonction définissant le masque de convolution est notée $h$, l'expression générale de la valeur estimée de pixel de coordonnées $(i,j)$ est donnée par +Si la fonction définissant le masque de convolution est notée $h$, l'expression générale de la valeur de sortie estimée au pixel de coordonnées $(i,j)$ est donnée par \begin{equation} \widehat{u}(x, y) = \left(\bar{v} * h\right) = \sum_{(i < H)} \sum_{(j < L)}v(x-j, y-i)h(j,i) \label{convoDef} @@ -30,7 +30,7 @@ Dans les applications les plus courantes, $h$ est à support borné et de forme La figure \ref{fig-ny-convo} présente les résultats de la convolution par deux masques débruiteurs \textit{moyenneurs} $h_3$ et $h_5$ de taille différentes, appliqués à l'image corrompue par un bruit gaussien : on voit la diminution des fluctuations mais aussi le flou apporté et qui rend les contours d'autant moins définis que la taille du masque est grande. La troisième image montre l'effet d'un masque gaussien $h_{g3}$. Les matrices définissant les masques sont les suivantes : -\[h_3=\frac{1}{9}\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}, h_{5}=\frac{1}{25}\begin{bmatrix}1&1&1&1&1\\1&1&1&1&1\\1&1&1&1&1\\1&1&1&1&1\\1&1&1&1&1\end{bmatrix}, h_{g3}= \begin{bmatrix}1&2&1\\2&4&2\\1&2&1\end{bmatrix}\] +\[h_3=\frac{1}{9}\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}, h_{5}=\frac{1}{25}\begin{bmatrix}1&1&1&1&1\\1&1&1&1&1\\1&1&1&1&1\\1&1&1&1&1\\1&1&1&1&1\end{bmatrix}, h_{g3}= \frac{1}{16}\begin{bmatrix}1&2&1\\2&4&2\\1&2&1\end{bmatrix}\] \begin{figure} \centering @@ -45,9 +45,10 @@ Lorsque la matrice $h$ définissant le masque peut s'écrire comme le produit de \subsubsection{Le filtre médian} -Le filtrage médian \cite{tukey77} est également une opération très employée en pré-traitement pour sa simplicité et ses propriétés de préservation des contours alliées à une capacité de réduction du bruit gaussien importante. -La valeur du niveau de gris de chaque pixel est remplacée par la médiane des niveaux de gris des pixels voisins. Un des intérêts de ce filtre réside dans le fait que la valeur filtrée est une des valeurs du voisinage, contrairement à ce qui se produit lors d'une convolution. Un autre est de bien filtrer les valeurs extrêmes et par conséquent de trouver naturellement son application dans la réduction du bruit impulsionnel. -Toutefois, la non-linéraité de cette technique et sa complexité n'en ont pas fait un filtre très utilisé jusqu'à ce que des implémentation efficaces soient proposées, en particulier le filtre à temps de calcul \og constant \fg{} décrit par Perreault et Hebert \cite{4287006}. Il est à noter que le filtrage médian est souvent appliqué en plusieurs passes de voisinage restreint. +Le filtrage médian \cite{tukey77} est également une opération très employée en pré-traitement pour sa simplicité coneptuelle et ses propriétés de préservation des contours alliées à une capacité de réduction du bruit gaussien importante. +La valeur du niveau de gris de chaque pixel est remplacée par la médiane des niveaux de gris des pixels dans un voisinage donné. Un des intérêts de ce filtre réside dans le fait que la valeur filtrée est une des valeurs du voisinage, contrairement à ce qui se produit lors d'une convolution. +Le filtre médian est aussi un estimateur robuste de la valeur moyenne permettant de bien s'affranchir des perturbations présentant, dans le voisinage, des valeurs très éloignées de la moyenne. Par conséquent, il trouve aussi son application dans la réduction du bruit impulsionnel. +Toutefois, la non-régularité et l'importance du temps de calcul de cette technique n'en ont pas fait un filtre très utilisé jusqu'à ce que des implémentation efficaces soient proposées, en particulier le filtre à temps de calcul \og constant \fg{} décrit par Perreault et Hebert \cite{4287006}. Il est à noter que le filtrage médian est souvent appliqué en plusieurs passes de voisinage restreint, car cela permet d'obtenir des niveaux de débruitage semblables à ceux permis par des voisinages plus grands, mais avec des temps de calcul réduits. La figure \ref{fig-ny-median} montre la réduction de bruit impulsionnel obtenu sur l'image \ref{ny-sap} grâce au filtre médian, dans trois conditions distinctes : médian 3$\times$3 en une ou deux passes, puis médian 5$\times$5. \begin{figure} \centering @@ -60,7 +61,7 @@ La figure \ref{fig-ny-median} montre la réduction de bruit impulsionnel obtenu \subsubsection{Le filtre bilatéral} -Le filtre bilatéral \cite{710815} est une composition d'opérations que l'on peut voir comme un filtre de convolution dont les coefficients ne dépendraient pas uniquement de la position du pixel courant par rapport au pixel central, mais également de la différence de leurs intensités (cas des images en niveaux de gris). +Le filtre bilatéral \cite{710815} est une composition d'opérations que l'on peut voir comme un filtre de convolution dont les coefficients dépendent de la position du pixel considéré par rapport au pixel central, mais dépendent également de la différence entre leurs deux niveaux de gris (cas des images en niveaux de gris). Si l'on note $\Omega_k$ le voisinage du pixel d'indice $k$, l'expression générale du niveau de gris estimé est donnée par \[\widehat{u_k}=\displaystyle\frac{\sum_{p\in \Omega_k}\left(F_S(x_p, x_k)F_I(v_p, v_k)v_p\right)}{\sum_{p\in\Omega_k }\left(F_S(x_p, x_k)F_I(v_p, v_k)\right)} \] où $F_S$ et $F_I$ sont les fonctions de pondération spatiale et d'intensité. Classiquement, $F_S$ et $F_I$ sont des gaussiennes de moyennes nulles et d'écarts type $\sigma_S$ et $\sigma_I$. @@ -88,7 +89,9 @@ L'un de ces algorithmes cherche dans l'image bruitée, une portion de la ligne d \subsubsection{Les algorithmes de filtrage par dictionnaire} -Ces algorithmes font l'hypothèse qu'il est possible de décrire l'image à débruiter en utilisant une base de fonctions permettant de décomposer l'image en une combinaison linéaire des éléments de cette base. Les bases les plus employées sont les ondelettes \cite{Mallat:2008:WTS:1525499, Daubechies:1992:TLW:130655} ainsi que les fonctions sinusoïdales (DCT \cite{1093941,strang1999discrete}). Les éléments de la base peuvent être prédéterminés ou bien calculés à partir des données de l'image, par exemple en s'appuyant sur une analyse en composantes principales ou après apprentissage \cite{elad2006image}. Le principe du débruitage est de considérer que le bruit est décorellé des fonctions de la base et donc représenté par les petits coefficients de la décomposition, que l'on peut annuler. Diverses politiques de seuillage peuvent alors être appliquées selon le type d'image et le modèle de bruit ayant chacune ses propres avantages et inconvénients. L'intérêt principal de ces méthodes est de bien restituer les transitions rapides (grande énergie), mais elles génèrent en revanche des artefacts dus aux possibles grands coefficients de bruit. +Ces algorithmes font l'hypothèse qu'il est possible de décrire l'image à débruiter en utilisant une base de fonctions permettant de décomposer l'image en une combinaison linéaire des éléments de cette base. Les bases les plus employées sont les ondelettes \cite{Mallat:2008:WTS:1525499, Daubechies:1992:TLW:130655} ainsi que les fonctions sinusoïdales (DCT \cite{1093941,strang1999discrete}). Les éléments de la base peuvent être prédéterminés ou bien calculés à partir des données de l'image, par exemple en s'appuyant sur une analyse en composantes principales ou après apprentissage \cite{elad2006image}. On considère que le bruit, blanc, est décorellé des fonctions de la base, son énergie est ainsi répartie uniformément sur tout l'espace de décomposition, contrairement au signal informatif. Le principe du filtrage est alors de supprimer les composantes à faible énergie, représentées par les petits coefficients de la décomposition. + + Diverses politiques de seuillage peuvent alors être appliquées selon le type d'image et le modèle de bruit ayant chacune ses propres avantages et inconvénients. L'intérêt principal de ces méthodes est de bien restituer les transitions rapides (grande énergie), mais elles peuvent en revanche générer des artefacts, par exemple lorsque la PDF du bruit partage avec le signal une composante d'énergie élevée. La figure \ref{fig-ny-dwt} illustre cela en montrant le résultat du débruitage obtenu par décomposition en ondelettes et seuillage \og dur \fg{} : lorsque la valeur du seuil croît, des aplats apparaissent et sont visuellement génants bien que les valeurs des indices de qualité n'aient pas diminué significativement. Certains algorithmes récents, en particulier ceux utilisant une base d'ondelettes adaptative, comme dans \cite{elad2006image} sont proches, en terme de qualité, de l'état de l'art du domaine, avec souvent un avantage lié à des vitesses d'exécution assez rapides. @@ -135,7 +138,7 @@ L'opération de convolution a fait l'objet d'une étude et d'une optimisation po Les résultats montrent que l'emploi de texture comme mémoire principale pour le stockage des images à traiter apporte un gain d'environ 50\% par rapport à l'utilisation de la mémoire globale. Par ailleurs, les transactions par paquets de 128 bits apportent également une amélioration sensible, ainsi que l'emploi de la mémoire partagée comme zone de travail pour le calcul des valeurs de sortie. Le traitement de référence effectué pour les mesures est la convolution générique (non séparable) d'une image 8 bits de 2048$\times$2048 pixels par un masque de convolution de 5$\times$5 pixels, expression que l'on raccourcira dorénavant en \textit{convolution 5$\times$5}. Le meilleur résultat obtenu dans les conditions détaillées précédemment, sur architecture GT200 (carte GTX280) est de 1,4~ms pour le calcul, ce qui représente un débit global de 945~MP/s lorsque l'on prend en compte les temps de transfert aller et retour des images (1,5~ms d'après nos mesures). -Nous continuerons d'utiliser cette mesure de débit en \textit{pixels par seconde} pour toutes les évaluations à venir ; elle permet en particulier de fournir des valeurs de performance indépendantes de la taille des images soumises au traitement. +Nous continuerons d'utiliser cette mesure de débit en \textit{pixels par seconde} pour toutes les évaluations à venir ; elle permet en particulier de fournir des valeurs de performance indépendamment de la taille des images soumises au traitement\footnote{Dans la pratique, le débit dépend peu de la taille de l'image, pour les images suffisamment grandes que nous traitons. Le débit croit légèrement avec la taille de l'image en raison des transferts plus efficaces.}. \subsection{Le filtre médian}\label{sec-median} On connaît peu de versions GPU du filtre médian, peut-être en raison des implémentations CPU performantes et génériques que l'on a déjà évoquées (voir par exemple \cite{4287006}) et dont le portage sur GPU ne laisse pas entrevoir de potentiel, ou bien reste à inventer. Néanmoins, une bibliothèque commerciale (LibJacket et ArrayFire) en propose une implémentation GPU dont nous avons pu mesurer les performances pour un masque de 3$\times$3 et qui est également prise comme référence par Sanchez \textit{et al.} pour évaluer les performances de leur propre implémentation appelée PCMF \cite{6288187}. @@ -175,12 +178,12 @@ Le principe est de pré-charger les valeurs utiles au bloc de threads dans la m \begin{figure} \centering - \includegraphics[width=10cm]{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter2/img/shmem_prefetch_zheng2011.png} + \includegraphics[width=12cm]{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter2/img/shmem_prefetch_zheng2011.png} \caption{Illustration du pré-chargement en mémoire partagée mis en \oe uvre dans \cite{zheng2011performance} pour l'implémentation, entre autres, du filtre bilatéral. a) en vert le bloc de threads associé aux pixels centraux. b-e) les blocs de pixels successivement pré-chargés en mémoire partagée. f) la configuration finale de la ROI en mémoire partagée.} \label{fig-prefetch-zheng} \end{figure} -Cette recette est ensuite appliquée dans l'implémentation d'un filtre bilatéral et d'un filtre à moyennes non locales (NL-means). Concernant le filtre bilatéral, les auteurs pré-calculent aussi les coefficients de la pondération spatiale, alors que ceux de la pondération d'intensité restent calculés à la volée. +Cette méthode empirique de pré-chargement est ensuite appliquée dans l'implémentation d'un filtre bilatéral et d'un filtre à moyennes non locales (NL-means). Concernant le filtre bilatéral, les auteurs pré-calculent aussi les coefficients de la pondération spatiale, alors que ceux de la pondération d'intensité restent calculés à la volée. Ces deux optimisations permettent un gain de 20\% sur le temps de calcul du filtre bilatéral pour arriver à 0.326~ms dans les mêmes conditions que ci-dessus (bilatéral 7$\times$7 sur image 1~MP). Toutefois, le débit global ne progresse pas (132~MP/s) en raison de la prépondérance des temps de transfert annoncés à 7,5~ms pour l'image de 1~MP, alors qu'ils n'étaient que de 7,1~ms dans les conditions décrites par Nvidia. Ce travail d'optimisation ne perd toutefois pas son intérêt dans la mesure où, si le filtre fait partie d'une chaîne de traitement entièrement exécutée par le GPU, le transfert des données n'a besoin d'être effectué qu'une seule fois en tout début et en toute fin de traitement. diff --git a/THESE/Chapters/chapter2/chapter2d.tex b/THESE/Chapters/chapter2/chapter2d.tex index 96a530b..a9c8e1e 100644 --- a/THESE/Chapters/chapter2/chapter2d.tex +++ b/THESE/Chapters/chapter2/chapter2d.tex @@ -1,4 +1,4 @@ -\section{Les techniques de segmentation} +\section{Introduction} La segmentation représente un enjeu particulièrement important dans le domaine du traitement d'image et a ainsi fait l'objet d'abondants travaux et publications touchant les nombreux cas d'analyse dans lesquels une segmentation est utilisée. On peut citer la reconnaissance de formes, la détections et/ou la poursuite de cibles, la cartographie, le diagnostic médical, l'interaction Homme-machine, la discrimination d'arrière plan, etc. On pourrait donner de la segmentation une définition spécifique par type d'usage, mais dans un souci d'unification, nous proposons la formulation générique suivante :\\ @@ -7,9 +7,10 @@ Le caractère \textit{homogène} s'entend au sens d'un critère pré-établi, ad Devant la diversité des cas à traiter et des objectifs à atteindre, on sait aujourd'hui qu'à l'instar du filtre unique, la méthode universelle de segmentation n'existe pas et qu'une bonne segmentation est celle qui conduit effectivement à l'extraction des structures pertinentes d'une image selon l'interprétation qui doit en être faite. -Les éléments constitutifs de la segmentation sont soit des régions (les segments), soit des contours. Les deux notions sont complémentaires étant donné que les contours délimitent des régions, mais les techniques de calcul basées sur l'un ou l'autre de ces éléments relèvent d'analyses différentes. +Les éléments constitutifs de la segmentation sont soit des régions (les segments), soit des contours. Les deux notions sont complémentaires étant donné que les contours délimitent des régions\footnote{Nous excluons ici les contours non-fermés qui peuvent être obtenus à l'aide d'un simple détecteur de bords.}, mais les techniques de calcul basées sur l'un ou l'autre de ces éléments relèvent d'analyses différentes. -Les algorithmes de segmentation orientés régions s'appuient pour beaucoup sur des techniques de regroupement, ou \textit{clustering}, pour l'identification et le peuplement des régions. Ce lien trouve son origine dans la théorie du \textit{gestalt} \cite{humphrey1924psychology} où l'on considère que la perception conceptuelle s'élabore au travers de regroupements visuels d'éléments. +\section{Les techniques de segmentation orientées régions} +Les algorithmes de cette classe s'appuient pour beaucoup sur des techniques de regroupement, ou \textit{clustering}, pour l'identification et le peuplement des régions. Ce lien trouve son origine dans la théorie du \textit{gestalt} \cite{humphrey1924psychology} où l'on considère que la perception conceptuelle s'élabore au travers de regroupements visuels d'éléments. La plupart des approches proposées jusqu'à très récemment consistent à minimiser une fonction d'énergie qui n'a pas de solution formelle et que l'on résout donc à l'aide de techniques numériques souvent itératives. @@ -20,14 +21,14 @@ Différents critères peuvent être appliqués pour cette analyse, visant par ex Malgré la multitude de variantes proposées, ces méthodes demeurent peu robustes et présentent l'inconvénient majeur de ne pas garantir la connexité des régions déterminées. On les réserve à des applications très spécifiques où, par exemple, on dispose d'une image de référence dont l'histogramme peut être comparé à celui des images à traiter. C'est le cas de certaines applications de contrôle industriel où la simplicité algorithmique permet de surcroît des implémentations très rapides, voire câblées. Ces techniques peuvent aujourd'hui être considérées comme rudimentaires mais les calculs d'histogrammes et les analyses associées interviennent dans beaucoup d'algorithmes récents parmi les plus évolués et performants. -La figure \ref{fig-histo-cochon} illustre le traitement typique de l'histogramme de l'image d'entrée \ref{fig-histo-cochon-a} dans le but de distinguer les deux régions du fond et du cochon (la cible). La première étape consiste à dresser l'histogramme des niveaux de gris sur tout le domaine de l'image \ref{fig-histo-cochon-b}. Il faut ensuite identifier le seuil de séparation des deux régions supposées, ici, homogènes au sens des valeurs de niveau de gris. Une estimation visuelle peut-être faite, mais on voit immédiatement que même dans une situation aussi claire, le choix du seuil n'est pas évident. Pour un traitement automatique, on peut par exemple proposer la technique itérative présentée par l'Algorithme \ref{algo-histo-cochon} qui conduit à la segmentation de la figure \ref{fig-histo-cochon-c}. +La figure \ref{fig-histo-cochon} illustre le traitement typique de l'histogramme de l'image d'entrée \ref{fig-histo-cochon-a} dans le but de distinguer les deux régions du fond et de la peluche (la cible). La première étape consiste à dresser l'histogramme des niveaux de gris sur tout le domaine de l'image \ref{fig-histo-cochon-b}. Il faut ensuite identifier le seuil de séparation des deux régions supposées, ici, homogènes au sens des valeurs de niveau de gris. Une estimation visuelle peut-être faite, mais on voit immédiatement que même dans une situation aussi claire, le choix du seuil n'est pas évident. Pour un traitement automatique, on peut par exemple proposer la technique itérative présentée par l'Algorithme \ref{algo-histo-cochon} qui conduit à la segmentation de la figure \ref{fig-histo-cochon-c}. Le principe mis en \oe uvre est de fixer arbitrairement une valeur initiale au seuil (ici 128), puis de calculer les \og poids \fg{} respectifs des valeurs situées au-dessus et en-dessous de ce seuil (ligne 6). Cette évaluation de la répartition énergétique permet d'ajuster la valeur du seuil (ligne 8), puis de recommencer jusqu'à convergence, lorsque l'écart entre deux valeurs successives du seuil devient inférieur à une limite fixée à l'avance ($\epsilon$, ligne 9). L'image \ref{fig-histo-cochon-d} est l'image initiale, corrompue par un bruit gaussien de moyenne nulle et d'écart type 25. Les résultats de la segmentation (\ref{fig-histo-cochon-c} et \ref{fig-histo-cochon-f}) de cette image sont clairement insuffisants : les régions identifiées présentent des discontinuités et dans le cas de l'image bruitée, quantité de pixels orphelins subsistent en quantité. Cette technique nécessiterait une étape supplémentaire pour obtenir une segmentation pertinente. \begin{figure} \centering - \subfigure[Image initiale comportant deux zones : le fond et le cochon (la cible)]{\label{fig-histo-cochon-a} \includegraphics[height=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/cochon256.png}}\quad + \subfigure[Image initiale comportant deux zones : le fond et la peluche (la cible)]{\label{fig-histo-cochon-a} \includegraphics[height=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/cochon256.png}}\quad \subfigure[Histogramme des niveaux de gris]{\label{fig-histo-cochon-b} \includegraphics[height=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/seg_histogramme/histo-cochon256.png}}\quad \subfigure[Image binaire représentant la segmentation. Seuil estimé à 101 après 4 itérations.]{\label{fig-histo-cochon-c} \includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/seg_histogramme/cochon256-seghisto-101-255.png}}\\ \subfigure[Image initiale bruitée]{\label{fig-histo-cochon-d} \includegraphics[height=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/cochon256-sig25.png}}\quad @@ -54,7 +55,7 @@ $\epsilon \leftarrow 1$ \; \end{algorithm} \subsection{Partitionnement de graphe} -Un autre formalisme qui a généré une vaste classe d'algorithmes de segmentation est celui des graphes. Il repose sur l'idée que les régions de l'image sont représentées par les n\oe uds du graphe, alors que les liens traduisent les relations de voisinage existant entre les régions, l'idée de base étant d'initialiser le graphe avec un n\oe ud pour chaque pixel. La segmentation est obtenue par partitionnement itératif du graphe, en évaluant les liens et en déterminant ceux à supprimer, et ce jusqu'à convergence. +Un autre formalisme qui a généré une vaste classe d'algorithmes de segmentation est celui des graphes. Il repose sur l'idée que les régions de l'image sont représentées par les n\oe uds d'un graphe, alors que les liens traduisent les relations de voisinage existant entre les régions, l'idée de base étant d'initialiser le graphe avec un n\oe ud pour chaque pixel. La segmentation est obtenue par partitionnement itératif du graphe, en évaluant les liens et en déterminant ceux à supprimer, et ce jusqu'à convergence. L'essentiel de la problématique réside donc dans la métrique retenue pour évaluer les liens ainsi que dans le critère de sélection et, là encore, la littérature regorge d'une grande variété de propositions. Les premières d'entre elles, qui n'étaient pas spécifiquement dédiées à la segmentation d'images numériques mais au regroupement d'éléments répartis sur un domaine (1D ou 2D), ont été élaborées autour d'une mesure locale des liens basée sur la distance entre les éléments. La réduction du graphe est ensuite effectuée en utilisant un algorithme spécifique, comme le \textit{minimum spanning tree}, dont l'application a été décrite dès 1970 dans \cite{Zahn:1971:GMD:1309266.1309359} et où il s'agit simplement de supprimer les liens \textit{inconsistants}, c'est à dire ceux dont le poids est significativement plus élevé que la moyenne des voisins se trouvant de chaque coté du lien en question. @@ -74,7 +75,7 @@ On construit également la matrice de connectivité $D$, diagonale et dont les \[d_{i} = \displaystyle\sum_jw_{ij}\] Une famille de méthodes, inspirée par le \textit{graphe optimal} de Wu et Leahy \cite{wu1993optimal}, réalise le partitionnement sur la base des valeurs propres $\lambda_k$ et vecteurs propres $Y_k$ du système -\[\left(D-W)\right)Y=\lambda DY \] +\[\left(D-W\right)Y=\lambda DY \] Certains algorithmes proposés plus récemment s'inscrivent dans cette veine \cite{wang2001image,wang2003image,felzenszwalb2004efficient,shi2000normalized}, avec comme principal point faible, une difficulté à trouver un compromis acceptable entre identification de structures globales et préservation des éléments de détails. Cela se traduit dans la pratique par un ensemble de paramètres à régler pour chaque type de segmentation à effectuer. La figure \ref{fig-graph-cochon} montre un exemple de l'application de l'algorithme \textit{normalized cuts} décrit dans \cite{shi2000normalized} et implémenté par Cour, Yu et Shi en 2004. Cette implémentation utilise des valeurs pré-établies des paramètres de calcul de la matrice de similarité produisant de bonnes segmentations de sujets dans les images naturelles, mais requiert de prédéterminer le nombre de segments. Les images de la figure représentent les résultats obtenus avec un nombre de segments variant de 2 à 5 et montrent qu'il est difficile de trouver un compromis acceptable. De plus, les temps d'exécution peuvent devenir très rapidement prohibitifs, même avec des implémentations plus optimisées. Les résultats de la figure \ref{fig-graph-cochon} ont été obtenus en 1,5~s environ (Matlab R2010 sur CPU intel core i5-2520M \@ 2.50GHz - linux 3.2.0) @@ -93,9 +94,9 @@ Ce procédé est mis en \oe uvre avec de bons résultats dans plusieurs algorith \subsection{kernel-means, mean-shift et apparentés} Parallèlement à la réduction de graphes, d'autres approches ont donné naissance à une multitude de variantes tournées vers la recherche des moindres carrés. -Il s'agit simplement de minimiser l'erreur quadratique totale, ce qui peut se résumer, pour une image de $N$ pixels, en la détermination du nombre $C$ de segments $\Omega_i$ et leur contenu, de sorte à minimiser l'expression -\[\sum_{i\in[1..C]}\sum_{x_k\in\Omega_i} \left(v_k-\mu_i\right)^2\] -où $\mu_i$ représente la valeur affectée au segment $\Omega_i$, i.e la valeur moyenne des observations $v_k$ sur $\Omega_i$, et $\displaystyle{\bigcup_{i\in[1..C]}\Omega_i=\Omega}$ +Il s'agit simplement de minimiser l'erreur quadratique totale, ce qui peut se résumer, pour une image de $N$ pixels, en la détermination du nombre $K$ de segments $\Omega_i$ et leur contenu, de sorte à minimiser l'expression +\[\sum_{i\in[1..K]}\sum_{x_k\in\Omega_i} \left(v_k-\mu_i\right)^2\] +où $\mu_i$ représente la valeur affectée au segment $\Omega_i$, i.e la valeur moyenne des observations $v_k$ sur $\Omega_i$, et $\displaystyle{\bigcup_{i\in[1..K]}\Omega_i=\Omega}$. Cette idée est très intuitive et simple, mais n'a pas souvent de solution explicite, d'autant que le nombre des segments est \textit{a priori} inconnu. Dès 1965, Mac Queen a proposé l'appellation k-means pour cette procédure itérative de regroupement \cite{macqueen1967some} qui débute avec $k$ groupes d'un seul pixel\footnote{Dans son article, MacQueen ne parle pas de pixel mais de point. En effet, la méthode décrite ne visait pas à segmenter des images, mais des données de natures diverses.} @@ -105,15 +106,15 @@ Un autre est d'être très dépendant du choix des $k$ éléments initiaux, en n Toutefois, vraisemblablement du fait de sa simplicité d'implémentation et de son temps d'exécution rapide, la communauté scientifique s'est beaucoup penchée sur cette méthode pour en compenser les défauts, jusqu'à en faire une des plus employées, en particulier par les statisticiens. On compte aussi beaucoup de variantes telles les \textit{k-centers} \cite{agarwal2002exact} et les \textit{k-médians} \cite{arora1998approximation} qui n'employent pas la moyenne arithmétique comme expression du \og centre \fg{} d'un segment. -Des solutions ont aussi été apportées pour l'estimation de $k$ en employant, par exemple, un critère de vraisemblance pour choisir la meilleure valeur de $k$ dans un intervalle donné \cite{pelleg2000x}. -À titre d'illustration et de comparaison, l'image du cochon a été traitée par une implémentation naïve de l'algorithme original des \textit{k-means} en donnant successivement au nombre de segments les valeurs $s=2$ à $s=5$. Les résultats sont reproduits à la figure \ref{fig-kmeans-cochon} et montrent encore une fois l'influence de $s$ sur la segmentation. +Des solutions ont aussi été apportées pour l'estimation de $K$ en employant, par exemple, un critère BIC (Bayesian Information Criterion) pour choisir la meilleure valeur de $K$ dans un intervalle donné \cite{pelleg2000x}. +À titre d'illustration et de comparaison, l'image de la peluche a été traitée par une implémentation naïve de l'algorithme original des \textit{k-means} en donnant successivement au nombre de segments les valeurs $K=2$ à $K=5$. Les résultats sont reproduits à la figure \ref{fig-kmeans-cochon} et montrent encore une fois l'influence de $s$ sur la segmentation. \begin{figure} \centering - \subfigure[$s = 2$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/kmeans/cochon128_kmeans_2seg.png}} - \subfigure[$s = 3$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/kmeans/cochon128_kmeans_3seg.png}} - \subfigure[$s = 4$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/kmeans/cochon128_kmeans_4seg.png}} - \subfigure[$s = 5$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/kmeans/cochon128_kmeans_5seg.png}} - \caption{Segmentation d'une image en niveaux de gris de 128 $\times$ 128 pixels par algorithme \textit{k-means} pour un nombre $s$ de segments variant de 2 à 5. Chaque couleur est associée à un segment. Les couleurs sont choisies pour une meilleure visualisation des différents segments.} + \subfigure[$K = 2$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/kmeans/cochon128_kmeans_2seg.png}} + \subfigure[$K = 3$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/kmeans/cochon128_kmeans_3seg.png}} + \subfigure[$K = 4$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/kmeans/cochon128_kmeans_4seg.png}} + \subfigure[$K = 5$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/kmeans/cochon128_kmeans_5seg.png}} + \caption{Segmentation d'une image en niveaux de gris de 128 $\times$ 128 pixels par algorithme \textit{k-means} pour un nombre $K$ de segments variant de 2 à 5. Chaque couleur est associée à un segment. Les couleurs sont choisies pour une meilleure visualisation des différents segments.} \label{fig-kmeans-cochon} \end{figure} @@ -125,22 +126,22 @@ Comaniciu et Peer en ont alors étendu l'étude et proposé une application à l Une implémentation de la variante proposée par Keselman et Micheli-Tzanakou dans \cite{keselman1998extraction} appliquée à notre image de test, fournit les résultats reproduits à la figure \ref{fig-meanshift-cochon}. Pour se rapprocher des traitements précédents, nous avons identifié, par essais successifs, les tailles de voisinage conduisant à des nombres de segments identiques à ceux des figures précédentes (de 2 à 5), le volume minimal admis pour un segment étant arbitrairement fixé à 100 pixels. \begin{figure} \centering - \subfigure[$r=100 \Rightarrow s = 2$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/meanshift/cochon128_meanshift_r100m100.png}} - \subfigure[$r=50 \Rightarrow s = 3$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/meanshift/cochon128_meanshift_r50m100.png}} -\subfigure[$r=35 \Rightarrow s = 4$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/meanshift/cochon128_meanshift_r35m100.png}} - \subfigure[$r=25 \Rightarrow s = 5$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/meanshift/cochon128_meanshift_r25m100.png}} - \caption{Segmentation d'une image en niveaux de gris de 128 $\times$ 128 pixels par algorithme \textit{mean-shift} pour un rayon de voisinage $r$ de 100, 50, 35 et 25 pixels permettant d'obtenir un nombre $s$ de segments variant respectivement de 2 à 5. Le volume minimal admis pour un segment est fixé à 100 pixels. Chaque couleur est associée à un segment. Les couleurs sont choisies pour une meilleure visualisation des différents segments.} + \subfigure[$r=100 \Rightarrow K = 2$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/meanshift/cochon128_meanshift_r100m100.png}} + \subfigure[$r=50 \Rightarrow K = 3$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/meanshift/cochon128_meanshift_r50m100.png}} +\subfigure[$r=35 \Rightarrow K = 4$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/meanshift/cochon128_meanshift_r35m100.png}} + \subfigure[$r=25 \Rightarrow K = 5$]{\includegraphics[width=3cm]{/home/zulu/Documents/these_gilles/THESE/codes/meanshift/cochon128_meanshift_r25m100.png}} + \caption{Segmentation d'une image en niveaux de gris de 128 $\times$ 128 pixels par algorithme \textit{mean-shift} pour un rayon de voisinage $r$ de 100, 50, 35 et 25 pixels permettant d'obtenir un nombre $K$ de segments variant respectivement de 2 à 5. Le volume minimal admis pour un segment est fixé à 100 pixels. Chaque couleur est associée à un segment. Les couleurs sont choisies pour une meilleure visualisation des différents segments.} \label{fig-meanshift-cochon} \end{figure} Il est à noter que les segmentations basées sur des algorithmes de \textit{clustering} comme ceux que l'on vient de présenter nécessitent le plus souvent une phase supplémentaire de génération des frontières inter-segments et d'affectation de la valeur de chaque segment aux éléments qui le composent. Par ailleurs, dans les deux cas du \textit{k-means} et du \textit{mean-shift}, chaque itération génère une réduction de la variance (due au moyennage) et on peut donc rapprocher ces techniques de celles de réduction de bruit par minimisation de variance. -\subsection{Les contours actifs, ou snakes} +\section{Les techniques de segmentation par contours actifs, ou snakes} Contrairement aux précédentes techniques et comme leur nom le laisse deviner, les éléments constitutifs de ces méthodes sont cette fois des \textit{contours} et non plus des \textit{régions}. De fait, ils définissent nativement une segmentation de l'image. Le principe général est de superposer une courbe paramétrique $S$ à l'image, le \textit{snake}, puis de lui appliquer des déformations successives destinées à rapprocher le \textit{snake} des contours de l'objet. Les déformations à appliquer sont guidées par l'évaluation d'une fonction d'énergie $E_{snake}$ prenant en compte : \begin{itemize} -\item l'énergie interne $E_{int}$ de la courbe, fonction de son allongement de sa courbure. +\item l'énergie interne $E_{int}$ de la courbe, fonction de son allongement de sa courbure et qui vise à régulariser les courbes obtenues. \item l'énergie externe $E_{ext}$ liée à l'image, fonction de la proximité de la courbe avec les zones de fort gradient et éventuellement une contrainte fixée par l'utilisateur comme des points imposés par exemple. \end{itemize} L'expression générique peut alors s'écrire @@ -179,7 +180,7 @@ Parmi les variantes élaborées qui tentent de pallier ces défauts, les plus in \item les \textit{level-sets}, dont la particularité est de ne pas employer directement une courbe paramétrique plane mais de définir l'évolution des frontières comme l'évolution temporelle de l'ensemble des points d'élévation nulle d'une surface 3D soumise à un champ de force. Les propriétés des contours actifs par \textit{level-sets} se sont révélées intéressantes, en particulier la faculté de se disjoindre ou de fusionner, mais les temps de calcul se sont avérés très pénalisants. Après la formulation initiale de Osher et Sethian en 1988 \cite{osher1988fronts}, plusieurs façons de réduire le coût du calcul ont été formulées, dont les plus importantes restent la technique dite \textit{narrow band} \cite{adalsteinsson1994fast} (bande étroite) qui ne calcule à chaque itération que les points dans une bande étroite autour du plan $z=0$ de l'itération courante et celle du \textit{fast marching} \cite{sethian1996fast} qui s'applique dans le cas particulier d'une évolution monotone des fronts. -\item les \textit{snake} orientés régions, qui visent essentiellement à mieux caractériser les zones à segmenter et améliorer la robustesse vis-à-vis du bruit en employant une formulation de l'énergie calculée sur le domaine complet de l'image \cite{cohen1993surface, ronfard1994region}. Les premiers résultats confirment la qualité de cette méthode, mais la nécessité d'effectuer les calculs sur l'image entière générait des temps de traitement prohibitifs jusqu'à ce que Bertaux \textit{et al.} proposent une amélioration algorithmique exacte permettant à nouveau un calcul en 1D, le long de la courbe, moyennant une simple étape initiale générant un certain nombre d'images intégrales \cite{ChesnaudRB99,GallandBR03,GermainR01}. La section \ref{snake-formulation} en donnera une description détaillée. +\item les \textit{snake} orientés régions, qui visent essentiellement à mieux caractériser les zones à segmenter et améliorer la robustesse vis-à-vis du bruit en employant une formulation de l'énergie calculée sur le domaine complet de l'image \cite{cohen1993surface, ronfard1994region}. Les premiers résultats confirment la qualité de cette méthode, mais la nécessité d'effectuer les calculs sur l'image entière générait des temps de traitement prohibitifs jusqu'à ce que les auteurs de \cite{ChesnaudRB99} proposent une amélioration algorithmique exacte permettant à nouveau un calcul en 1D, le long de la courbe, moyennant une simple étape initiale générant un certain nombre d'images intégrales. Des travaux ultérieurs leur ont permis d'étendre la portée de leur algorithme à la segmentation multirégions \cite{GallandBR03,GermainR01}, puis de proposer des variantes non paramétriques ne nécessitant aucune connaissance \textit{a priori} sur le bruit. La plus récente de ces versions présente des temps de traitement très courts, inférieurs à 10~ms pour l'image de la peluche en 256$\times$256 pixels \cite{galland2005minimal,5767240}. La section \ref{snake-formulation} donnera une description détaillée de la variante de \cite{ChesnaudRB99} qui a servi de base à nos travaux. \end{itemize} \subsection{Méthodes hybrides} Aujourd'hui, les algorithmes de segmentation les plus performants en termes de qualité emploient des techniques qui tentent de tirer le meilleur parti de plusieurs des méthodes \og historiques \fg{} décrites précédemment. @@ -275,16 +276,16 @@ Si l'on considère que malgré les stratégies adoptées, tenir à jour cette li \label{fig-l7-narrow} \end{figure} -Les algorithmes de type \textit{snake}, très coûteux en temps de calcul, pouvaient prétendre à bénéficier largement de la technologie des GPU pour améliorer leurs performances, mais seule la variante paramétrique GVF à été véritablement implémentée de manière spécifique et efficace \cite{snakegvf06, bauer2009segmentation, li2011robust, snakegvfopencl12}. Les variantes de type géométrique restent à ce jour sans implémentation GPU, principalement en raison de l'irrégularité des motifs d'accès à la mémoire. +Les algorithmes de type \textit{snake}, très coûteux en temps de calcul, pouvaient prétendre à bénéficier largement de la technologie des GPU pour améliorer leurs performances, mais seule la variante paramétrique GVF à été véritablement implémentée de manière spécifique et efficace \cite{snakegvf06, bauer2009segmentation, li2011robust, snakegvfopencl12}. Les variantes de type polygonal restent à ce jour sans implémentation GPU, principalement en raison de l'irrégularité des motifs d'accès à la mémoire. -Parmi les premières solutions décrites, \cite{snakegvf06} propose une implémentation réalisée en openGL, où les données de gradient sont compactées en texture RVBA de manière à s'affranchir du format 16 bits de la représentation : les deux premiers canaux R et V contiennent les valeurs représentant respectivement les gradients selon $dx$ et $dy$ sous une forme codée par la valeur des 2 autres canaux. +Parmi les premières solutions décrites, \cite{snakegvf06} propose une implémentation réalisée en openGL, où les données de gradient sont compactées en texture à quatre canaux (R,V,B,A) de manière à s'affranchir du format 16 bits de la représentation : les deux premiers canaux R et V contiennent les valeurs représentant respectivement les gradients selon $dx$ et $dy$ sous une forme codée selon les valeur des 2 autres canaux B et A. Par ailleurs, une approximation du système linéaire à résoudre est proposée afin de donner une structure bande symétrique à la matrice à inverser, ce qui améliore considérablement l'efficacité des accès aux données au travers du cache. \begin{figure} \centering \subfigure[Contour initial]{\label{fig-epaule-init}\includegraphics[height=4cm]{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter2/img/snake-epaule-init-t.png}}\quad \subfigure[Contour final]{\label{fig-epaule-fin}\includegraphics[height=4cm]{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter2/img/snake-epaule-fin-t.png}} -\caption{Segmentation d'une image d'épaule en 1024$^2$ pixels issue d'un examen IRM par l'implémentation du snake GVF de \cite{snakegvf06}. Le contour est représenté en rouge et le contour final est obtenu en 11~s. Le tracé initial du contour a été artificiellement épaissi pour le rendre visible à l'échelle de l'impression.} +\caption{Segmentation d'une image d'épaule en 1024$\times$1024 pixels issue d'un examen IRM par l'implémentation du snake GVF de \cite{snakegvf06}. Le contour est représenté en rouge et son état final est obtenu en 11~s. Le tracé initial du contour a été artificiellement épaissi pour le rendre visible à l'échelle de l'impression.} \label{fig-snakegvf} \end{figure} diff --git a/THESE/Chapters/chapter3/chapter3.tex b/THESE/Chapters/chapter3/chapter3.tex index bae9ff9..52b00b7 100644 --- a/THESE/Chapters/chapter3/chapter3.tex +++ b/THESE/Chapters/chapter3/chapter3.tex @@ -1,10 +1,10 @@ \section{Introduction} La principale difficulté soulevée par l'emploi d'algorithmes de type \textit{snake} orientés contour est le choix de la fonction d'énergie externe et la détermination de la nature des images auxquelles elle convient. Dans l'approche orientée régions, les deux régions que sont l'extérieur et l'intérieur du contour (cas mono cible) sont prises en compte dans l'estimation de la forme du contour ; cela permet d'extraire des formes dans des images où les contours de la cible sont mal définis, en raison d'un fort niveau de bruit par exemple. -Les algorithmes découlant de cette approche n'ont fait l'objet, à notre connaissance, d'aucune parallèlisation sur GPU, malgré le grand intérêt qu'elles revêtent dans l'interprétation d'images fortement bruitées ( RADAR, médicales,\dots ) et le besoin de réduire suffisamment les temps de traiement pour permettre l'interactivité. +Les algorithmes découlant de cette approche n'ont fait l'objet, à notre connaissance, d'aucune parallèlisation sur GPU, malgré le grand intérêt qu'elles revêtent dans l'interprétation d'images fortement bruitées ( imagerie ultrasonore, RADAR ) et le besoin de réduire suffisamment les temps de traitement pour permettre l'interactivité. Nous proposons dans la suite de ce chapitre de commencer par détailler l'algorithme séquentiel que nous avons pris comme référence, puis d'en présenter la version parallèle pour GPU que nous avons conçue. -L'algorithme a été décrit et proposé initialement en 1999 par Chesnaud \textit{et al.} dans \cite{ChesnaudRB99}. L'implémentation que les auteurs ont développée a continué d'être améliorée jusqu'à aujourd'hui et est employée comme brique élémentaire dans des algorithmes plus complexes. La version qui sert de référence ici est une implémentation séquentielle optimisée qui met à profit les capacités de parallélisme des CPU actuels en employant le jeu d'instruction SSE2 des microprocesseurs. La description que nous en faisons dans les lignes qui suivent est très largement inspirée de \cite{ChesnaudRB99} à la différence que nous n'implémentons pas les critères de régularisation du contour ni de minimisation de la longueur de description pour nous focaliser sur la déformation du contour et sa convergence. +L'algorithme a été décrit et proposé initialement en 1999 par Chesnaud \textit{et al.} dans \cite{ChesnaudRB99}. L'implémentation que les auteurs ont développée a continué d'être améliorée jusqu'à aujourd'hui et est employée comme brique élémentaire dans des algorithmes plus complexes. La version qui sert de référence ici est une implémentation séquentielle optimisée et dont nous faisons ici une description très largement inspirée de \cite{ChesnaudRB99} à la différence que nous n'implémentons pas les critères de régularisation du contour ni de minimisation de la longueur de description pour nous focaliser sur la déformation du contour et sa convergence. \section{Présentation de l'algorithme} \subsection{Formulation} @@ -96,7 +96,7 @@ où $C(i,j)$ est un coefficient lié à la direction du contour au point $(i,j)$ \end{equation} La valeur de $C(i,j)$ est déterminée pour chaque pixel d'indice $l$ du contour en considérant les pixels d'indices $l-1$ et $l+1$ qui définissent les deux vecteurs $f_{in}$ et $f_{out}$ et leur code selon le codage de Freeman, comme l'illustre la figure \ref{fig-freeman}. La table \ref{tab-freeman} donne les valeurs de $C(i,j)$ selon les valeurs des codes de Freeman des vecteurs $f_{in}$ et $f_{out}$. -Il faut noter que les valeurs dans la table \ref{tab-freeman} diffèrent de celles proposées initialement dans \cite{ChesnaudRB99}. Cette modification a été proposée pour permettre de s'adapter à la segmentation multi-cibles. +Il faut noter que les valeurs dans la table \ref{tab-freeman} diffèrent de celles proposées initialement dans \cite{ChesnaudRB99}. Cette modification a été proposée pour permettre de s'adapter à la segmentation multi-cibles \cite{GallandBR03}. \begin{figure}[htb] \centering \includegraphics[height=3cm]{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter3/img/codage-freeman.png} @@ -122,17 +122,17 @@ Il faut noter que les valeurs dans la table \ref{tab-freeman} diffèrent de cell 7 &0&0&0&0&0&-1&-1&-1\\ \bottomrule \end{tabular} - \caption{Valeur du coefficient $C(i,j)$ en fonction des valeurs des codes de Freeman des vecteurs $f_{in}$ et $f_{out}$.} + \caption{Valeur du coefficient $C(i,j)$ en fonction des valeurs des codes de Freeman des vecteurs $f_{in}$ et $f_{out}$ \cite{GallandBR03}.} \label{tab-freeman} \end{table} L'intérêt de cette transformation est majeur : \begin{itemize} \item La sommation en deux dimensions sur la région $\Omega_t$ est ainsi réduite à une sommation à une dimension sur le contour $\Gamma$. -\item Les valeurs $T_g(i,j)$ peuvent être calculées préalablement à la phase de segmentation proprement dite. Pour le cas gaussien qui nous intéresse, cela revient à pré-calculer les trois images \textit{cumulées} $S_1$, $S_x$ et $S_{x^2}$ définies par +\item Les valeurs $T_g(i,j)$ peuvent être calculées préalablement à la phase de segmentation proprement dite. Pour le cas gaussien qui nous intéresse, cela revient à pré-calculer les trois images \textit{cumulées} $S_1$, $S_I$ et $S_{I^2}$ définies par \begin{alignat}{4} \label{eq-img-cumul} - S_1(i,j) &= \sum_{x=0}^jx & \quad \text{,}\quad S_x(i,j) &= \sum_{x=0}^jv(i,x) & \quad \text{et}&\quad & S_{x^2}(i,j) &= \sum_{x=0}^jv(i,x)^2 + S_1(i,j) &= \sum_{x=0}^jx & \quad \text{,}\quad S_I(i,j) &= \sum_{x=0}^jv(i,x) & \quad \text{et}&\quad & S_{I^2}(i,j) &= \sum_{x=0}^jv(i,x)^2 \end{alignat} \item Les valeurs du coefficient $C(i,j)$ se calculent très facilement durant la génération du contour $\Gamma$. \end{itemize} @@ -167,24 +167,24 @@ Un des inconvénients des algorithmes de type \textit{snake} est l'influence du \small \label{algo-snake-cpu2} Lire l'image $\bar{v}$\; - Calculer les images cumulées $S_1$, $S_x$ $S_{x^2}$ \nllabel{li-img-cumul}\tcc*[r]{en parallèle via SSE2} + Calculer les images cumulées $S_1$, $S_I$ $S_{I^2}$ \nllabel{li-img-cumul}\tcc*[r]{en parallèle via SSE2} $n \leftarrow 0$ \tcc*[r]{indice de boucle niveau contour} $N_n \leftarrow 4$ \tcc*[r]{nombre de n\oe uds} $\Gamma \leftarrow \{\Gamma_0,\Gamma_1,\Gamma_2,\Gamma_3\} $\; $d \leftarrow d_{max}$ \tcc*[r]{pas de déplacement des n\oe uds} $l_{min} = 32$ \tcc*[r]{longueur mini des segments sécables} $\Gamma_i \leftarrow \Gamma_0$ \tcc*[r]{sommet courant} - $GL_{ref} \leftarrow GL(\Gamma, N_n, \bar{v}, S_y, S_{y^2})$ \tcc*[r]{voir à partir de ligne 18 pour le détail} + $GL_{ref} \leftarrow GL(\Gamma, N_n, \bar{v}, S_I, S_{I^2})$ \tcc*[r]{voir à partir de ligne 18 pour le détail} \Repeter(\tcc*[f]{niveau contour}){$N_{add}=0$}{ $N_{add}\leftarrow 0$\; \Repeter(\tcc*[f]{niveau n\oe ud}){$N_{move}=0$}{ $N_{move}\leftarrow 0$\; \Pour{$i=0$ à $i=N_n-1$}{ - Calculer les positions $\{\Gamma_i^0, \dots, \Gamma_i^7\}$ \tcc*[r]{les 8 voisins de $\Gamma_i$ } + Calculer les positions $\{\Gamma_i^0, \dots, \Gamma_i^7\}$ \tcc*[r]{les 8 voisins de $\Gamma_i$ à distance $d$ } $GL_w \leftarrow GL_{ref} - $ la contribution des segments $\Gamma_{i-1}\Gamma_i$ et $\Gamma_{i}\Gamma_{i+1}$\; \Pour{$w=0$ à $w=7$}{ Discrétiser les segments $\Gamma_{i-1}\Gamma_i^w$ et $\Gamma_{i}^w\Gamma_{i+1}$\nllabel{li-bresen}\; - Lire dans $S_1$, $S_x$ et $S_{x^2}$ les contributions des pixels de $\Gamma_{i-1}\Gamma_i^w$ et $\Gamma_{i}^w\Gamma_{i+1}$\nllabel{li-contrib-seg-deb}\; + Lire dans $S_1$, $S_I$ et $S_{I^2}$ les contributions des pixels de $\Gamma_{i-1}\Gamma_i^w$ et $\Gamma_{i}^w\Gamma_{i+1}$\nllabel{li-contrib-seg-deb}\; Calculer les directions et lire les codes de Freeman \; Calculer $GL_w$ incluant les contributions de $\Gamma_{i-1}\Gamma_i^w$ et $\Gamma_{i}^w\Gamma_{i+1}$ \nllabel{li-contrib-seg-fin}\; \Si{$GL_w > GL_{ref}$}{ @@ -204,31 +204,30 @@ Un des inconvénients des algorithmes de type \textit{snake} est l'influence du } $N_n \leftarrow N_n + N_{add}$\; \lSi{$d > 1$}{ $d \leftarrow d/2$ } \lSinon{ $d \leftarrow 1$ }\; - $GL_{ref} \leftarrow GL(\Gamma, N_n, \bar{v}, S_y, S_{y^2})$ \; + $GL_{ref} \leftarrow GL(\Gamma, N_n, \bar{v}, S_I, S_{I^2})$ \; } \end{algorithm} -\pagebreak -Les différentes sommations nécessaires au calcul de la valeur du critère $GL$ sont effectuées en parallèle à l'aide du jeu d'instructions SSE2, qui permet de travailler avec des registres de grande capacité (128 bits) et d'envisager d'y ranger côte à côte les opérandes des trois sommes pour les effectuer simultanément. -Si l'on cherche à traiter des images en niveaux de gris sont codés sur 16 bits, les sommes $S_1$, $S_X$ et $S_{X^2}$ vont utiliser : -\begin{itemize} -\item $N_c$ bits par opérande de chaque somme pour représenter les coordonnées des pixels. -\item $N_p$ bits pour traduire le nombre d'opérandes dans chaque somme. -\item 16 bits par valeur de niveau de gris dans $S_X$. -\item 32 bits par valeur de niveau de gris au carré dans $S_{X^2}$. -\end{itemize} -Les trois sommes utilisent donc, par opérande, un total de $\left(3\left(N_c+N_p\right)+16+32\right)$ bits devant être contenu dans un registre de 128 bits, ce qui nous donne un maximum de 26 bits pour $N_c+N_p$. -La longueur des segments pouvant être au maximum $\sqrt{2}$ fois supérieure au coté de l'image, on peut donc considérer qu'il est nécessaire d'avoir $N_p = N_c+1$ pour ne pas générer de restriction sur la longueur des segments. Cela nous conduit donc à $N_c = 12$ et $N_p=13$ ($12+13 = 25 < 26$). -La répartition retenue pour les données dans les registres SSE2 de 128 bits est alors la suivante : -\begin{itemize} -\item $N_c+N_p=25$ bits pour les opérandes des sommes de $S_1$. -\item $N_c+N_p+16=41$ bits pour les opérandes des sommes de $S_X$. -\item $N_c+N_p+32=57$ bits pour les opérandes des sommes de $S_{X^2}$. -\end{itemize} +% Les différentes sommations nécessaires au calcul de la valeur du critère $GL$ sont effectuées en parallèle à l'aide du jeu d'instructions SSE2, qui permet de travailler avec des registres de grande capacité (128 bits) et d'envisager d'y ranger côte à côte les opérandes des trois sommes pour les effectuer simultanément. +% Si l'on cherche à traiter des images en niveaux de gris sont codés sur 16 bits, les sommes $S_1$, $S_X$ et $S_{X^2}$ vont utiliser : +% \begin{itemize} +% \item $N_c$ bits par opérande de chaque somme pour représenter les coordonnées des pixels. +% \item $N_p$ bits pour traduire le nombre d'opérandes dans chaque somme. +% \item 16 bits par valeur de niveau de gris dans $S_X$. +% \item 32 bits par valeur de niveau de gris au carré dans $S_{X^2}$. +% \end{itemize} +% Les trois sommes utilisent donc, par opérande, un total de $\left(3\left(N_c+N_p\right)+16+32\right)$ bits devant être contenu dans un registre de 128 bits, ce qui nous donne un maximum de 26 bits pour $N_c+N_p$. +% La longueur des segments pouvant être au maximum $\sqrt{2}$ fois supérieure au coté de l'image, on peut donc considérer qu'il est nécessaire d'avoir $N_p = N_c+1$ pour ne pas générer de restriction sur la longueur des segments. Cela nous conduit donc à $N_c = 12$ et $N_p=13$ ($12+13 = 25 < 26$). +% La répartition retenue pour les données dans les registres SSE2 de 128 bits est alors la suivante : +% \begin{itemize} +% \item $N_c+N_p=25$ bits pour les opérandes des sommes de $S_1$. +% \item $N_c+N_p+16=41$ bits pour les opérandes des sommes de $S_X$. +% \item $N_c+N_p+32=57$ bits pour les opérandes des sommes de $S_{X^2}$. +% \end{itemize} \subsection{Performances} Les images de 1024$\times$1024 pixels de la figure \ref{fig-snakecpu-cochon512} montrent l'évolution du contour lors de la segmentation d'une image photographique prise en faible éclairement et bruitée artificiellement par un bruit gaussien d'écart type 25. Les paramètres de la séquence sont fixés empiriquement aux valeurs $d_{max}=16, l_{min}=8$. -Les temps d'exécution indiqués sont mesurés sur Intel Xeon E5530-2.4GHz with 12Go RAM et sont les valeurs moyennes obtenues pour 10 exécutions. +Les temps d'exécution indiqués sont mesurés sur Intel Xeon E5530-2.4GHz avec 12Go RAM. \begin{figure} \centering \subfigure[Initialisation : 4 n\oe uds]{\includegraphics[height=3.5cm]{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter3/img/im000.png}} @@ -239,11 +238,11 @@ Les temps d'exécution indiqués sont mesurés sur Intel Xeon E5530-2.4GHz with \subfigure[Itération 10 : 244 n\oe uds 3~ms]{\includegraphics[height=3.5cm]{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter3/img/im010.png}} \subfigure[Itération 13 : 256 n\oe uds 3~ms]{\includegraphics[height=3.5cm]{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter3/img/im013.png}} \subfigure[Itération 14 : 256 n\oe uds 3~ms]{\includegraphics[height=3.5cm]{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter3/img/im014.png}} - \caption{Évolution du contour lors de la segmentation d'une image de 512$^2$ pixels. La convergence est obtenue à l'itération 14 après 44~ms pour un total de 256 n\oe uds.} + \caption{Évolution du contour lors de la segmentation d'une image de 512$\times$512 pixels. La convergence est obtenue à l'itération 14 après 44~ms pour un total de 256 n\oe uds.} \label{fig-snakecpu-cochon512} \end{figure} -La dépendance vis à vis du contour initial, qui est un des principaux soucis liés au snake est ici fortement relativisée. La figure \ref{fig-snakecpu-compinit} montre le contour final segmentant l'image de test de la figure \ref{fig-snakecpu-cochon512} à partir d'un état initial très éloigné du précédent et, \textit{a priori}, très défavorable compte tenu du fait qu'il est loin de la cible et sans intersection avec elle. Toutefois, le contour final est très proche de celui obtenu à partir d'un état initial englobant la cible, malgré un n\oe ud qui s'est \og accroché \fg{} au bord de l'image. La convergence est également plus longue à obtenir dans ce cas avec 87~ms pour de 17 itérations et 273 n\oe uds. +La dépendance vis à vis du contour initial, qui est un des principaux soucis liés au snake est ici fortement relativisée. La figure \ref{fig-snakecpu-compinit} montre le contour final segmentant l'image de test de la figure \ref{fig-snakecpu-cochon512} à partir d'un état initial très éloigné du précédent et, \textit{a priori}, très défavorable compte tenu du fait qu'il est loin de la cible et sans intersection avec elle. Toutefois, le contour final est très proche de celui obtenu à partir d'un état initial englobant la cible, avec la particularité d'avoir identifié la peluche au fond et la zone sombre à la cible avec un n\oe ud à chaque coin de l'image. Cela est du à l'initialisation des zones avec comme cible une portion de la zone sombre, relativement homogène. La convergence est également plus longue à obtenir dans ce cas avec 87~ms pour 17 itérations et 273 n\oe uds. \begin{figure} \centering @@ -254,7 +253,8 @@ La dépendance vis à vis du contour initial, qui est un des principaux soucis l \label{fig-snakecpu-compinit} \end{figure} -La dimension de l'image à traiter a également un effet sur le résultat et naturellement sur le temps de calcul. Si l'on conserve les mêmes paramètres d'optimisation que pour la segmentation de l'image 512$\times$512 pixels et un contour initial dont les cotés sont à une distance des bords équivalente à 10\% des cotés de l'image, le résultat sur une image identique de 4000$^2$4000 pixels est obtenu en 1,3~s avec 1246 n\oe uds ; il est reproduit à la figure \ref{fig-snakecpu-cochon4ka}. Le nombre de pixels appartenant à la région cible est tel que l'amplitude des déplacements autorisés pour chaque n\oe ud ($d$) peut se révéler trop faible vis-à-vis du seuil d'acceptation des mouvements. On observe que les zones à gradient élevé ne posent pas de problème et sont détourées de la même manière, alors que dans le bas de l'image où figure une zone de gradient faible (ombre), la cible se trouve maintenant quelque peu surévaluée en surface là ou elle était plutôt sous évaluée dans l'image en 512$\times$512 pixels. +La dimension de l'image à traiter a également un effet sur le résultat et naturellement sur le temps de calcul. Si l'on conserve la même stratégie d'optimisation que pour la segmentation de l'image 512$\times$512 pixels et un contour initial dont les cotés sont à une distance des bords équivalente à 10\% des cotés de l'image, le résultat sur une image identique de 4000$^2$4000 pixels est obtenu en 1,3~s avec 1246 n\oe uds ; il est reproduit à la figure \ref{fig-snakecpu-cochon4ka}. Le nombre de pixels appartenant à la région cible est tel que l'amplitude des déplacements autorisés pour chaque n\oe ud ($d$) peut se révéler trop faible vis-à-vis du seuil d'acceptation des mouvements. On observe que les zones à fort contraste ne posent pas de problème et sont détourées de la même manière, alors que dans le bas de l'image où figure une zone de faible contraste (ombre), la cible se trouve maintenant quelque peu surévaluée en surface là ou elle était plutôt sous évaluée dans l'image en 512$\times$512 pixels. +Ces deux contours correspondent chacun à un minimum local vers lequel l'algorithme du snake a convergé, mais les variances associées demeurent extrêmement proches. On parvient à un résultat très proche beaucoup plus rapidement en adaptant les paramètres à la taille de l'image, comme le montre par exemple la segmentation de la figure \ref{fig-snakecpu-cochon4kb}, effectuée avec $d_{max}=128$ et $l_{min}=32$ et qui converge vers un contour de 447 n\oe uds en moins de 0,7~s. Au delà des 16 millions de pixels (4000$\times$4000 pixels), l'implémentation séquentielle est toujours possible mais doit se priver des instructions SSE. Nous avons, avec l'accord des auteurs, adapté leur code en ce sens et réalisé les mesures pour des tailles allant jusqu'à 150~MP. La table \ref{tab-snakecpu-speed-size} en synthétise les résultats en distinguant chaque fois le temps pris par les pré-calculs et celui nécessaire à la convergence de la segmentation. On constate que les deux étapes et donc le temps total varient linéairement avec la taille de l'image. @@ -294,7 +294,7 @@ Au delà des 16 millions de pixels (4000$\times$4000 pixels), l'implémentation \end{table} -Enfin, il faut aussi considérer les tailles relatives de la cible et de l'image. Ainsi, si on fait l'hypothèse d'une cible de petite taille \og noyée \fg{} dans une image de grandes dimensions, les résultats de la segmentation seront impactés en raison, cette fois, d'une moindre adaptation à la cible lors des toutes premières itérations, les plus grossières, où le nombre de n\oe uds est réduit et le pas de déplacement potentiellement grand vis à vis de la cible. Ce cas de figure est illustré par la segmentation reproduite à la figure \ref{fig-snakecpu-cochon4kc3} et qui met en évidence une qualité moindre par la confusion des zones les plus sombres de la cible avec le fond. +Enfin, il faut aussi considérer les tailles relatives de la cible et de l'image. Ainsi, si on fait l'hypothèse d'une cible de petite taille \og noyée \fg{} dans une image de grandes dimensions, les résultats de la segmentation seront impactés en raison, cette fois, d'une moindre adaptation à la cible lors des toutes premières itérations, les plus grossières, où le nombre de n\oe uds est réduit et le pas de déplacement potentiellement grand vis à vis de la cible. Ce cas de figure est illustré par la segmentation reproduite à la figure \ref{fig-snakecpu-cochon4kc3} et qui met en évidence une qualité moindre par la confusion des zones les plus sombres de la cible avec le fond et confirme ainsi la nécessité d'adapter la stratégie d'optimisation au problème posé. @@ -319,7 +319,7 @@ Si l'effort de parallélisation porte essentiellement sur ces fonctions coûteus Les traitements étant totalement indépendants, nous traitons séparément la parallélisation des pré-calculs et celle de la segmentation. \subsection{Pré-calculs des images cumulées} -Pour réduire la quantité de mémoire requise, nous avons choisi de ne pas générer l'image $S_1$ mais plutôt d'en calculer les valeurs à la volée. L'expression en est simple et le temps pris par les opérations élémentaires qu'elle met en jeu est largement compensé par le gain obtenu en économisant les accès mémoire qui auraient été nécessaires, ce qui n'est pas le cas des deux autres images $S_x$ et $S_x^2$ dont le calcul est quant à lui réalisé en appliquant une variante de la méthode des sommes préfixées (\textit{prefixsums}) décrite dans \cite{BlellochTR90} et qui permet d'évaluer les expressions de l'équation \eqref{eq-img-cumul}. +Pour réduire la quantité de mémoire requise, nous avons choisi de ne pas générer l'image $S_1$ mais plutôt d'en calculer les valeurs à la volée. L'expression en est simple et le temps pris par les opérations élémentaires qu'elle met en jeu est largement compensé par le gain obtenu en économisant les accès mémoire qui auraient été nécessaires, ce qui n'est pas le cas des deux autres images $S_I$ et $S_I^2$ dont le calcul est quant à lui réalisé en appliquant une variante de la méthode des sommes préfixées (\textit{prefixsums}) décrite dans \cite{BlellochTR90} et qui permet d'évaluer les expressions de l'équation \eqref{eq-img-cumul}. Les sommations se font au niveau de chaque ligne de l'image, que l'on décompose en $n$ blocs de $bs$ pixels où $bs$ correspond aussi au nombre de threads exécutés par chaque bloc de la grille de calcul. La valeur $bs$ étant obligatoirement une puissance de 2 supérieure à 32, le bloc de pixels d'indice $n-1$ doit éventuellement être complété par des valeurs nulles. Chaque bloc de thread réalise son traitement indépendemment des autres, mais l'ensemble des sommes de bloc étant requise pour le calcul des sommes globales, une synchronisation est nécessaire à deux endroits du calcul. Nous avons choisi d'assurer ces synchronisations en découpant le traitement en trois \textit{kernels} distincts, rendant par la même occasion le code plus concis : \begin{itemize} @@ -328,14 +328,14 @@ Les sommations se font au niveau de chaque ligne de l'image, que l'on décompose \item \texttt{add\_sums2prefixes()} est le \textit{kernel} effectuant les additions de chaque élément d'indice $i$ des vecteurs $V_x$ (respectivement $V_x^2$) avec tous les éléments du prefixsum du bloc de même indice $i$. \end{itemize} -Les diagrammes de la figure \ref{fig-calcul-cumuls} donnent le détail des opérations effectuées par ces trois \textit{kernels} pour l'image cumulée $S_x$. La seconde image cumulée $S_x^2$ est obtenues exactement de la même manière en sommant non plus les valeurs $v_k$ mais $v^2_k$. +Les diagrammes de la figure \ref{fig-calcul-cumuls} donnent le détail des opérations effectuées par ces trois \textit{kernels} pour l'image cumulée $S_I$. La seconde image cumulée $S_{I^2}$ est obtenues exactement de la même manière en sommant non plus les valeurs $v_k$ mais $v^2_k$. \begin{figure} \centering \subfigure[Détail des opérations effectuées par le \textit{kernel} \texttt{compute\_block\_prefixes()}. La valeur $bs$ correspond au nombre de pixels de chaque bloc, qui est aussi le nombre de threads exécuté par chaque bloc de la grille de calcul.]{\resizebox{0.9\linewidth}{!}{ \input{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter3/img/GPUcumuls.pdf_t}}}\vspace{1cm} \subfigure[Détail des opérations effectuées par le \textit{kernel} \texttt{scan\_blocksums()}.]{\resizebox{0.9\linewidth}{!}{ \input{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter3/img/GPUscansomblocs.pdf_t}}}\vspace{1cm} \subfigure[Détail des opérations effectuées par le \textit{kernel} \texttt{add\_sums2prefixes()}.]{\resizebox{0.9\linewidth}{!}{ \input{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter3/img/GPUaddsoms2cumuls.pdf_t}}} - \caption{Calcul des images cumulées $S_x$ et $S_x^2$ en trois étapes successives. a) cumul partiel bloc par bloc et mémorisation de la somme de chaque bloc. b) cumul sur le vecteur des sommes partielles. c) ajout des sommes partielles à chaque élément des blocs cumulés.} + \caption{Calcul des images cumulées $S_I$ et $S_{I^2}$ en trois étapes successives. a) cumul partiel bloc par bloc et mémorisation de la somme de chaque bloc. b) cumul sur le vecteur des sommes partielles. c) ajout des sommes partielles à chaque élément des blocs cumulés.} \label{fig-calcul-cumuls} \end{figure} @@ -470,8 +470,8 @@ Les accès en mémoire aux contributions des pixels de coefficient $C(i,j)=0$, d Dans l'hypothèse la plus contraignante d'images en niveaux de gris codés sur 16 bits, l'implémentation parallèle que nous venons de décrire utilise de manière permanente 20 octets par pixel de l'image d'entrée, qui se détaillent en \begin{itemize} \item l'image d'entrée pour 4 octets par pixel (1 entier). -\item l'image cumulée $S_x$ pour 8 octets par pixel (1 entier long) -\item l'image cumulée $S_x^2$ pour 8 octets par pixel (1 entier long) +\item l'image cumulée $S_I$ pour 8 octets par pixel (1 entier long) +\item l'image cumulée $S_{I^2}$ pour 8 octets par pixel (1 entier long) \end{itemize} auxquels il faut ajouter un maximum d'environ 50~Mo d'espace nécessaire à la mémorisation des variables temporaires des calculs et données diverses comme le contour lui-même (n\oe uds, milieux, Freemans, etc.). @@ -539,7 +539,7 @@ Le gain de performance apporté par cette initialisation \og intelligente \fg{} \subfigure[Détermination de $j_L$ et $j_H$.]{\resizebox{6cm}{!}{\input{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter3/img/smart_init1.pdf_t}}}\quad \subfigure[Détermination de $i_L$ et $i_H$.]{\resizebox{6cm}{!}{\input{/home/zulu/Documents/these_gilles/THESE/Chapters/chapter3/img/smart_init2.pdf_t}}} \label{fig-smart-init} - \caption{Détermination intelligente du contour initial en deux phases successives. a) La première étape repose sur un échantillonnage horizontal. b) La seconde étape repose sur un échantillonnage vertical.} + \caption{Détermination intelligente du contour initial en deux phases successives. (a) La première étape repose sur un échantillonnage horizontal. (b) La seconde étape repose sur un échantillonnage vertical.} \end{figure} \subsection{Conclusion} diff --git a/THESE/Chapters/chapter3/img/GPUscansomblocs.pdf_t b/THESE/Chapters/chapter3/img/GPUscansomblocs.pdf_t index 5fcf436..d35a71e 100644 --- a/THESE/Chapters/chapter3/img/GPUscansomblocs.pdf_t +++ b/THESE/Chapters/chapter3/img/GPUscansomblocs.pdf_t @@ -29,7 +29,7 @@ }}}} \put(2971,-3931){\makebox(0,0)[rb]{\smash{{\SetFigFont{12}{14.4}{\sfdefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}en mémoire globale du GPU}% }}}} -\put(2971,-5686){\makebox(0,0)[rb]{\smash{{\SetFigFont{12}{14.4}{\sfdefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}vecteurr $V$}% +\put(2971,-5686){\makebox(0,0)[rb]{\smash{{\SetFigFont{12}{14.4}{\sfdefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}vecteur $V$}% }}}} \put(2971,-5866){\makebox(0,0)[rb]{\smash{{\SetFigFont{12}{14.4}{\sfdefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}en mémoire globale}% }}}} diff --git a/THESE/Chapters/chapter4/chapter4.tex b/THESE/Chapters/chapter4/chapter4.tex index e9c28e6..89e5fd7 100644 --- a/THESE/Chapters/chapter4/chapter4.tex +++ b/THESE/Chapters/chapter4/chapter4.tex @@ -401,7 +401,7 @@ La figure \ref{fig-lniv-classification} présente le résultat de la classificat \centering \subfigure[Image bruitée]{\includegraphics{Chapters/chapter4/img/airplane_noisy_small.jpg}}\qquad \subfigure[Classification des pixels. ]{\includegraphics{Chapters/chapter4/img/img_bords_T2_small.jpg}} -\caption{Classification des pixels d'une image bruitée, pour une valeur de seuil $T2=2$ du détecteur. b) Les pixels en noir sont ceux à qui le PI-PD sera appliqué. Les pixels en blancs se verront appliquer une moyenne sur tout ou partie du voisinage.} +\caption{Classification des pixels d'une image bruitée, pour une valeur de seuil $T2=2$ du détecteur. (b) Les pixels en noir sont ceux à qui le PI-PD sera appliqué. Les pixels en blancs se verront appliquer une moyenne sur tout ou partie du voisinage.} \label{fig-lniv-classification} \end{figure} diff --git a/THESE/Chapters/chapter6/chapter6.tex b/THESE/Chapters/chapter6/chapter6.tex index 7699db5..1225802 100644 --- a/THESE/Chapters/chapter6/chapter6.tex +++ b/THESE/Chapters/chapter6/chapter6.tex @@ -300,9 +300,9 @@ Les expérimentations conduites sur les kernels de convolution tendent égalemen Conscients du manque de souplesse découlant de l'optimisation de ces kernels et pour que cela ne soit pas un frein à l'utilisation de ces solutions, nous avons enfin proposé une application en ligne qui génère, à la demande, les codes des kernels médians et de convolution d'après les critères indiqués par l'utilisateur. Ce dernier peut alors télécharger un ensemble suffisant et immédiatement fonctionnel comprenant un fichier kernel GPU, un fichier main.c, un Makefile et une image de test. Il est accessible à l'adresse http://info.iut-bm.univ-fcomte.fr/staff/perrot/convomed et ses pages d'accueil et de téléchargement sont reproduites à la figure \ref{fig-convomed-copie}. \begin{figure}[h] - \hfill - \subfigure[Sélection des paramètres.]{\includegraphics[height=4cm]{Chapters/chapter6/img/convomed1.png}}\hfill - \subfigure[Téléchargement des fichiers.]{\includegraphics[height=4cm]{Chapters/chapter6/img/convomed2.png}}\hfill +\centering + \subfigure[Sélection des paramètres.]{\includegraphics[width=10cm]{Chapters/chapter6/img/convomed1.png}}\\ + \subfigure[Téléchargement des fichiers.]{\includegraphics[width=10cm]{Chapters/chapter6/img/convomed2.png}} \caption{Générateur de codes sources pour les filtres GPU rapides.} \label{fig-convomed-copie} \end{figure} diff --git a/THESE/biblio.bib b/THESE/biblio.bib index 9b9b9fb..7174359 100755 --- a/THESE/biblio.bib +++ b/THESE/biblio.bib @@ -1395,4 +1395,25 @@ keywords={GPU; Denoising; Filter; Isoline; Level line}, author={Perrot, Gilles and Domas, Stéphane and Couturier, Raphaël and Bertaux, Nicolas}, pages={1-12}, language={English} -} \ No newline at end of file +} +@article{galland2005minimal, + title={Minimal stochastic complexity snake-based technique adapted to an unknown noise model}, + author={Galland, Fr{\'e}d{\'e}ric and R{\'e}fr{\'e}gier, Philippe}, + journal={Optics letters}, + volume={30}, + number={17}, + pages={2239--2241}, + year={2005}, + publisher={Optical Society of America} +} +@ARTICLE{5767240, +author={Bertaux, Nicolas and Galland, F{\'e}d{\'e}ric and R{\'e}fr{\'e}gier, Philippe}, +journal={Electronics Letters}, +title={Multi-initialisation segmentation with non-parametric minimum description length snake}, +year={2011}, +volume={47}, +number={10}, +pages={594-595}, +keywords={image segmentation;minimum description length principle;multiinitialisation segmentation;nonparametric minimum description length snake;nonparametric polygonal snakes;probability density functions}, +doi={10.1049/el.2011.0316}, +ISSN={0013-5194},} \ No newline at end of file diff --git a/THESE/these.aux b/THESE/these.aux index 71660ff..5f3f6bd 100644 --- a/THESE/these.aux +++ b/THESE/these.aux @@ -33,73 +33,74 @@ \newlabel{fig-gpucpu1}{{2.1}{13}{Comparaison des structures d'un c\oe ur de GPU et d'un c\oe ur de CPU (d'après \cite {CUDAPG}). 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On doit recalculer le crit\IeC {\`e}re apr\IeC {\`e}s les d\IeC {\'e}placements pour savoir s'il a \IeC {\'e}t\IeC {\'e} am\IeC {\'e}lior\IeC {\'e}.}}}{74}{figure.6.9}} +\@writefile{lof}{\contentsline {subfigure}{\numberline{(e)}{\ignorespaces {D\IeC {\'e}placement en parall\IeC {\`e}le des n\oe uds impairs. Le crit\IeC {\`e}re est am\IeC {\'e}lior\IeC {\'e}.}}}{74}{figure.6.9}} +\@writefile{lof}{\contentsline {subfigure}{\numberline{(f)}{\ignorespaces {D\IeC {\'e}placement en parall\IeC {\`e}le des n\oe uds pairs. 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Le contour initial conserve les proportions de celui de la figure \ref {fig-snakecpu-cochon512}. }}{76}{figure.6.11}} -\newlabel{fig-snakegpu-result}{{6.11}{76}{Segmentations d'une image de 100~MP en 0,59~s pour 5 itérations. Le contour initial conserve les proportions de celui de la figure \ref {fig-snakecpu-cochon512}. \relax }{figure.6.11}{}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.2.1}Cas particulier des segments dont la pente $k$ v\IeC {\'e}rifie $|k|\leq 1$}{75}{subsubsection.6.3.2.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {6.3.3}Performances}{76}{subsection.6.3.3}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.3.4}D\IeC {\'e}termination intelligente du contour initial}{76}{subsection.6.3.4}} +\@writefile{lot}{\contentsline {table}{\numberline {6.4}{\ignorespaces Comparaison des temps d'ex\IeC {\'e}cution de l'impl\IeC {\'e}mentation GPU (C2070) par rapport \IeC {\`a} l'impl\IeC {\'e}mentation CPU de r\IeC {\'e}f\IeC {\'e}rence, appliqu\IeC {\'e}s \IeC {\`a} une m\IeC {\^e}me image dilat\IeC {\'e}e (fig. \ref {fig-snakecpu-cochon512}) pour en adapter la taille.}}{77}{table.6.4}} +\newlabel{tab-snake-results}{{6.4}{77}{Comparaison des temps d'exécution de l'implémentation GPU (C2070) par rapport à l'implémentation CPU de référence, appliqués à une même image dilatée (fig. \ref {fig-snakecpu-cochon512}) pour en adapter la taille}{table.6.4}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {6.11}{\ignorespaces Segmentations d'une image de 100~MP en 0,59~s pour 5 it\IeC {\'e}rations. Le contour initial conserve les proportions de celui de la figure \ref {fig-snakecpu-cochon512}. }}{77}{figure.6.11}} +\newlabel{fig-snakegpu-result}{{6.11}{77}{Segmentations d'une image de 100~MP en 0,59~s pour 5 itérations. Le contour initial conserve les proportions de celui de la figure \ref {fig-snakecpu-cochon512}. \relax }{figure.6.11}{}} \citation{6036776} -\newlabel{fig-smart-init}{{6.3.4}{77}{Détermination intelligente du contour initial\relax }{subfigure.6.12.2}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {6.12}{\ignorespaces D\IeC {\'e}termination intelligente du contour initial en deux phases successives. a) La premi\IeC {\`e}re \IeC {\'e}tape repose sur un \IeC {\'e}chantillonnage horizontal. b) La seconde \IeC {\'e}tape repose sur un \IeC {\'e}chantillonnage vertical.}}{77}{figure.6.12}} -\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {D\IeC {\'e}termination de $j_L$ et $j_H$.}}}{77}{figure.6.12}} -\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {D\IeC {\'e}termination de $i_L$ et $i_H$.}}}{77}{figure.6.12}} -\@writefile{toc}{\contentsline {subsection}{\numberline {6.3.5}Conclusion}{77}{subsection.6.3.5}} +\newlabel{fig-smart-init}{{6.3.4}{78}{Détermination intelligente du contour initial\relax }{subfigure.6.12.2}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {6.12}{\ignorespaces D\IeC {\'e}termination intelligente du contour initial en deux phases successives. (a) La premi\IeC {\`e}re \IeC {\'e}tape repose sur un \IeC {\'e}chantillonnage horizontal. (b) La seconde \IeC {\'e}tape repose sur un \IeC {\'e}chantillonnage vertical.}}{78}{figure.6.12}} +\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {D\IeC {\'e}termination de $j_L$ et $j_H$.}}}{78}{figure.6.12}} +\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {D\IeC {\'e}termination de $i_L$ et $i_H$.}}}{78}{figure.6.12}} +\@writefile{toc}{\contentsline {subsection}{\numberline {6.3.5}Conclusion}{78}{subsection.6.3.5}} \citation{matheron75} \citation{caselles97} \citation{bertaux2004speckle} @@ -600,8 +608,8 @@ \@writefile{lof}{\contentsline {subfigure}{\numberline{(e)}{\ignorespaces {Directions d\IeC {\'e}termin\IeC {\'e}e par le PI-PD pour le tirage $n^{\circ }2$}}}{93}{figure.7.10}} \@writefile{lof}{\contentsline {figure}{\numberline {7.11}{\ignorespaces Motif de d\IeC {\'e}tection des zones \IeC {\`a} faible pente, pour le cas $\Theta =\Theta _4=45^{\circ }$. L'\IeC {\'e}l\IeC {\'e}vation des pixels permet juste de les distinguer selon 3 classes : l'\IeC {\'e}l\IeC {\'e}vation 1 est associ\IeC {\'e}e aux pixels de la r\IeC {\'e}gion $T$, l'\IeC {\'e}l\IeC {\'e}vation 0.5 est associ\IeC {\'e}e \IeC {\`a} ceux de la r\IeC {\'e}gion $B$ et l'\IeC {\'e}l\IeC {\'e}vation 0 d\IeC {\'e}signe les pixels n'intervenant pas dans la d\IeC {\'e}tection.}}{94}{figure.7.11}} \newlabel{fig-lniv-detecteur}{{7.11}{94}{Motif de détection des zones à faible pente, pour le cas $\Theta =\Theta _4=45^{\circ }$. L'élévation des pixels permet juste de les distinguer selon 3 classes : l'élévation 1 est associée aux pixels de la région $T$, l'élévation 0.5 est associée à ceux de la région $B$ et l'élévation 0 désigne les pixels n'intervenant pas dans la détection}{figure.7.11}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {7.12}{\ignorespaces Classification des pixels d'une image bruit\IeC {\'e}e, pour une valeur de seuil $T2=2$ du d\IeC {\'e}tecteur. b) Les pixels en noir sont ceux \IeC {\`a} qui le PI-PD sera appliqu\IeC {\'e}. Les pixels en blancs se verront appliquer une moyenne sur tout ou partie du voisinage.}}{94}{figure.7.12}} -\newlabel{fig-lniv-classification}{{7.12}{94}{Classification des pixels d'une image bruitée, pour une valeur de seuil $T2=2$ du détecteur. b) Les pixels en noir sont ceux à qui le PI-PD sera appliqué. Les pixels en blancs se verront appliquer une moyenne sur tout ou partie du voisinage}{figure.7.12}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {7.12}{\ignorespaces Classification des pixels d'une image bruit\IeC {\'e}e, pour une valeur de seuil $T2=2$ du d\IeC {\'e}tecteur. (b) Les pixels en noir sont ceux \IeC {\`a} qui le PI-PD sera appliqu\IeC {\'e}. Les pixels en blancs se verront appliquer une moyenne sur tout ou partie du voisinage.}}{94}{figure.7.12}} +\newlabel{fig-lniv-classification}{{7.12}{94}{Classification des pixels d'une image bruitée, pour une valeur de seuil $T2=2$ du détecteur. (b) Les pixels en noir sont ceux à qui le PI-PD sera appliqué. Les pixels en blancs se verront appliquer une moyenne sur tout ou partie du voisinage}{figure.7.12}{}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Image bruit\IeC {\'e}e}}}{94}{figure.7.12}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Classification des pixels. }}}{94}{figure.7.12}} \@writefile{toc}{\contentsline {section}{\numberline {7.4}R\IeC {\'e}sultats}{94}{section.7.4}} @@ -763,107 +771,109 @@ \bibcite{arora1998approximation}{7} \bibcite{bauer2009segmentation}{8} \bibcite{bertaux2004speckle}{9} -\bibcite{BlellochTR90}{10} -\bibcite{boykov2004experimental}{11} -\bibcite{bresenham1965algorithm}{12} -\bibcite{1467423}{13} -\bibcite{BuadesCM06}{14} -\bibcite{Caselles99topographicmaps}{15} -\bibcite{caselles97}{16} -\bibcite{5459410}{17} -\bibcite{cates2004gist}{18} -\bibcite{chandran2009computational}{19} -\bibcite{che2008performance}{20} -\bibcite{chen09}{21} -\bibcite{1093941}{22} -\bibcite{cheng1995mean}{23} -\bibcite{cherkassky1997implementing}{24} -\bibcite{ChesnaudRB99}{25} -\bibcite{cohen1993surface}{26} -\bibcite{comaniciu1999mean}{27} -\bibcite{comaniciu2002mean}{28} -\bibcite{cutrona1990synthetic}{29} -\bibcite{Dabov06imagedenoising}{30} -\bibcite{Dabov09bm3dimage}{31} -\bibcite{Daubechies:1992:TLW:130655}{32} -\bibcite{dixit2005gpu}{33} -\bibcite{elad2006image}{34} -\bibcite{felzenszwalb2004efficient}{35} -\bibcite{fluck2006gpu}{36} -\bibcite{foley1994introduction}{37} -\bibcite{ford1955simple}{38} -\bibcite{fukunaga1975estimation}{39} -\bibcite{fulkerson2012really}{40} -\bibcite{GallandBR03}{41} -\bibcite{GermainR01}{42} -\bibcite{nlmeansgpubelge}{43} -\bibcite{snakegvf06}{44} -\bibcite{healey1994radiometric}{45} -\bibcite{hochbaum2013simplifications}{46} -\bibcite{5170921}{47} -\bibcite{humphrey1924psychology}{48} -\bibcite{jeong2009scalable}{49} -\bibcite{5402362}{50} -\bibcite{KassWT88}{51} -\bibcite{keselman1998extraction}{52} -\bibcite{cmla2009Kes}{53} -\bibcite{kohli2007dynamic}{54} -\bibcite{lefohn2003inter}{55} -\bibcite{lefohn2003interactive}{56} -\bibcite{lefohn2005streaming}{57} -\bibcite{li2009mean}{58} -\bibcite{li2011robust}{59} -\bibcite{macqueen1967some}{60} -\bibcite{Mallat:2008:WTS:1525499}{61} -\bibcite{mancuso2001introduction}{62} -\bibcite{martin2001database}{63} -\bibcite{matheron75}{64} -\bibcite{coil}{65} -\bibcite{CUDAPG}{66} -\bibcite{osher1988fronts}{67} -\bibcite{4310076}{68} -\bibcite{medianggems5}{69} -\bibcite{PALHANOXAVIERDEFONTES}{70} -\bibcite{pelleg2000x}{71} -\bibcite{4287006}{72} -\bibcite{6036776}{73} -\bibcite{perrotbookgpu}{74} -\bibcite{perrot2013fine}{75} -\bibcite{perrotlniv}{76} -\bibcite{1521458}{77} -\bibcite{tid2008a}{78} -\bibcite{psnrhvsm}{79} -\bibcite{4587843}{80} -\bibcite{Roberts:2010:WGA:1921479.1921499}{81} -\bibcite{ronfard1994region}{82} -\bibcite{rumpf2001level}{83} -\bibcite{sanchezICASSP12}{84} -\bibcite{6288187}{85} -\bibcite{sethian1996fast}{86} -\bibcite{kmeansgpuopengl}{87} -\bibcite{shi2000normalized}{88} -\bibcite{snakegvfopencl12}{89} -\bibcite{convolutionsoup}{90} -\bibcite{graphcutscuda}{91} -\bibcite{strang1999discrete}{92} -\bibcite{sanchez2013highly}{93} -\bibcite{theuwissen2001ccd}{94} -\bibcite{710815}{95} -\bibcite{tukey77}{96} -\bibcite{vedaldi2008quick}{97} -\bibcite{4563095}{98} -\bibcite{Vineet:2009:FMS:1572769.1572796}{99} -\bibcite{volkov2010better}{100} -\bibcite{wang2001image}{101} -\bibcite{wang2003image}{102} -\bibcite{Wang04imagequality}{103} -\bibcite{wong2010demystifying}{104} -\bibcite{wu1993optimal}{105} -\bibcite{xiao2010efficient}{106} -\bibcite{5206542}{107} -\bibcite{Zahn:1971:GMD:1309266.1309359}{108} -\bibcite{zheng2011performance}{109} -\bibcite{zheng2012fast}{110} +\bibcite{5767240}{10} +\bibcite{BlellochTR90}{11} +\bibcite{boykov2004experimental}{12} +\bibcite{bresenham1965algorithm}{13} +\bibcite{1467423}{14} +\bibcite{BuadesCM06}{15} +\bibcite{Caselles99topographicmaps}{16} +\bibcite{caselles97}{17} +\bibcite{5459410}{18} +\bibcite{cates2004gist}{19} +\bibcite{chandran2009computational}{20} +\bibcite{che2008performance}{21} +\bibcite{chen09}{22} +\bibcite{1093941}{23} +\bibcite{cheng1995mean}{24} +\bibcite{cherkassky1997implementing}{25} +\bibcite{ChesnaudRB99}{26} +\bibcite{cohen1993surface}{27} +\bibcite{comaniciu1999mean}{28} +\bibcite{comaniciu2002mean}{29} +\bibcite{cutrona1990synthetic}{30} +\bibcite{Dabov06imagedenoising}{31} +\bibcite{Dabov09bm3dimage}{32} +\bibcite{Daubechies:1992:TLW:130655}{33} +\bibcite{dixit2005gpu}{34} +\bibcite{elad2006image}{35} +\bibcite{felzenszwalb2004efficient}{36} +\bibcite{fluck2006gpu}{37} +\bibcite{foley1994introduction}{38} +\bibcite{ford1955simple}{39} +\bibcite{fukunaga1975estimation}{40} +\bibcite{fulkerson2012really}{41} +\bibcite{GallandBR03}{42} +\bibcite{galland2005minimal}{43} +\bibcite{GermainR01}{44} +\bibcite{nlmeansgpubelge}{45} +\bibcite{snakegvf06}{46} +\bibcite{healey1994radiometric}{47} +\bibcite{hochbaum2013simplifications}{48} +\bibcite{5170921}{49} +\bibcite{humphrey1924psychology}{50} +\bibcite{jeong2009scalable}{51} +\bibcite{5402362}{52} +\bibcite{KassWT88}{53} +\bibcite{keselman1998extraction}{54} +\bibcite{cmla2009Kes}{55} +\bibcite{kohli2007dynamic}{56} +\bibcite{lefohn2003inter}{57} +\bibcite{lefohn2003interactive}{58} +\bibcite{lefohn2005streaming}{59} +\bibcite{li2009mean}{60} +\bibcite{li2011robust}{61} +\bibcite{macqueen1967some}{62} +\bibcite{Mallat:2008:WTS:1525499}{63} +\bibcite{mancuso2001introduction}{64} +\bibcite{martin2001database}{65} +\bibcite{matheron75}{66} +\bibcite{coil}{67} +\bibcite{CUDAPG}{68} +\bibcite{osher1988fronts}{69} +\bibcite{4310076}{70} +\bibcite{medianggems5}{71} +\bibcite{PALHANOXAVIERDEFONTES}{72} +\bibcite{pelleg2000x}{73} +\bibcite{4287006}{74} +\bibcite{6036776}{75} +\bibcite{perrotbookgpu}{76} +\bibcite{perrot2013fine}{77} +\bibcite{perrotlniv}{78} +\bibcite{1521458}{79} +\bibcite{tid2008a}{80} +\bibcite{psnrhvsm}{81} +\bibcite{4587843}{82} +\bibcite{Roberts:2010:WGA:1921479.1921499}{83} +\bibcite{ronfard1994region}{84} +\bibcite{rumpf2001level}{85} +\bibcite{sanchezICASSP12}{86} +\bibcite{6288187}{87} +\bibcite{sethian1996fast}{88} +\bibcite{kmeansgpuopengl}{89} +\bibcite{shi2000normalized}{90} +\bibcite{snakegvfopencl12}{91} +\bibcite{convolutionsoup}{92} +\bibcite{graphcutscuda}{93} +\bibcite{strang1999discrete}{94} +\bibcite{sanchez2013highly}{95} +\bibcite{theuwissen2001ccd}{96} +\bibcite{710815}{97} +\bibcite{tukey77}{98} +\bibcite{vedaldi2008quick}{99} +\bibcite{4563095}{100} +\bibcite{Vineet:2009:FMS:1572769.1572796}{101} +\bibcite{volkov2010better}{102} +\bibcite{wang2001image}{103} +\bibcite{wang2003image}{104} +\bibcite{Wang04imagequality}{105} +\bibcite{wong2010demystifying}{106} +\bibcite{wu1993optimal}{107} +\bibcite{xiao2010efficient}{108} +\bibcite{5206542}{109} +\bibcite{Zahn:1971:GMD:1309266.1309359}{110} +\bibcite{zheng2011performance}{111} +\bibcite{zheng2012fast}{112} \citation{CUDAPG} \citation{CUDAPG} \citation{zheng2011performance} @@ -873,3 +883,4 @@ \citation{snakegvf06} \citation{martin2001database} \citation{wong2010demystifying} +\citation{GallandBR03} diff --git a/THESE/these.bbl b/THESE/these.bbl index e18f237..1810dfd 100644 --- a/THESE/these.bbl +++ b/THESE/these.bbl @@ -13,7 +13,7 @@ David Adalsteinsson and James Sethian. \newblock PhD thesis, University of California, 1994. \bibitem{agarwal2002exact} -Pankaj~K Agarwal and Cecilia~Magdalena Procopiuc. +Pankaj~K. Agarwal and Cecilia~Magdalena Procopiuc. \newblock Exact and approximation algorithms for clustering. \newblock {\em Algorithmica}, 33(2):201--226, 2002. @@ -47,6 +47,12 @@ Nicolas Bertaux, Yann Frauel, Philippe R{\'e}fr{\'e}gier, and Bahram Javidi. gray-level regularization. \newblock {\em JOSA A}, 21(12):2283--2291, 2004. +\bibitem{5767240} +Nicolas Bertaux, F{\'e}d{\'e}ric Galland, and Philippe R{\'e}fr{\'e}gier. +\newblock Multi-initialisation segmentation with non-parametric minimum + description length snake. +\newblock {\em Electronics Letters}, 47(10):594--595, 2011. + \bibitem{BlellochTR90} Guy~E. Blelloch. \newblock Prefix sums and their applications. @@ -94,13 +100,13 @@ Bryan Catanzaro, Bor-Yiing Su, N.~Sundaram, Yunsup Lee, Mark Murphy, and pages 2381--2388, 2009. \bibitem{cates2004gist} -Joshua~E Cates, Aaron~E Lefohn, and Ross~T Whitaker. +Joshua~E. Cates, Aaron~E. Lefohn, and Ross~T. Whitaker. \newblock Gist: an interactive, gpu-based level set segmentation tool for 3d medical images. \newblock {\em Medical Image Analysis}, 8(3):217--231, 2004. \bibitem{chandran2009computational} -Bala~G Chandran and Dorit~S Hochbaum. +Bala~G. Chandran and Dorit~S. Hochbaum. \newblock A computational study of the pseudoflow and push-relabel algorithms for the maximum flow problem. \newblock {\em Operations research}, 57(2):358--376, 2009. @@ -131,7 +137,7 @@ Yizong Cheng. on}, 17(8):790--799, 1995. \bibitem{cherkassky1997implementing} -Boris~V Cherkassky and Andrew~V Goldberg. +Boris~V. Cherkassky and Andrew~V. Goldberg. \newblock On implementing the push—relabel method for the maximum flow problem. \newblock {\em Algorithmica}, 19(4):390--410, 1997. @@ -144,7 +150,7 @@ Christophe Chesnaud, Philippe R{\'e}fr{\'e}gier, and Vlady Boulet. 1999. \bibitem{cohen1993surface} -Laurent~D Cohen, Eric Bardinet, Nicholas Ayache, et~al. +Laurent~D. Cohen, Eric Bardinet, Nicholas Ayache, et~al. \newblock Surface reconstruction using active contour models. \newblock 1993. @@ -161,7 +167,7 @@ Dorin Comaniciu and Peter Meer. on}, 24(5):603--619, 2002. \bibitem{cutrona1990synthetic} -LJ~Cutrona. +L.J. Cutrona. \newblock Synthetic aperture radar. \newblock {\em Radar Handbook, second edition, ed. M. Skolnik, McGraw-Hill, New York}, 1990. @@ -199,7 +205,7 @@ Michael Elad and Michal Aharon. 2006. \bibitem{felzenszwalb2004efficient} -Pedro~F Felzenszwalb and Daniel~P Huttenlocher. +Pedro~F. Felzenszwalb and Daniel~P. Huttenlocher. \newblock Efficient graph-based image segmentation. \newblock {\em International Journal of Computer Vision}, 59(2):167--181, 2004. @@ -209,13 +215,13 @@ Oliver Fluck, Shmuel Aharon, Daniel Cremers, and Mikael Rousson. \newblock In {\em ACM SIGGRAPH 2006 Research posters}, page~53. ACM, 2006. \bibitem{foley1994introduction} -James~D Foley, Andries Van~Dam, Steven~K Feiner, John~F Hughes, and Richard~L - Phillips. +James~D. Foley, Andries Van~Dam, Steven~K. Feiner, John~F. Hughes, and + Richard~L. Phillips. \newblock {\em Introduction to computer graphics}, volume~55. \newblock Addison-Wesley Reading, 1994. \bibitem{ford1955simple} -Lester~Randolph Ford and Delbert~R Fulkerson. +Lester~Randolph Ford and Delbert~R. Fulkerson. \newblock {\em A simple algorithm for finding maximal network flows and an application to the Hitchcock problem}. \newblock Rand Corporation, 1955. @@ -238,6 +244,12 @@ Fr{\'e}d{\'e}ric Galland, Nicolas Bertaux, and Philippe R{\'e}fr{\'e}gier. segmentation. \newblock {\em IEEE Transactions on Image Processing}, 12(9):995--1006, 2003. +\bibitem{galland2005minimal} +Fr{\'e}d{\'e}ric Galland and Philippe R{\'e}fr{\'e}gier. +\newblock Minimal stochastic complexity snake-based technique adapted to an + unknown noise model. +\newblock {\em Optics letters}, 30(17):2239--2241, 2005. + \bibitem{GermainR01} Olivier Germain and Philippe R{\'e}fr{\'e}gier. \newblock Statistical active grid for segmentation refinement. @@ -263,13 +275,13 @@ Zhiyu He and Falko Kuester. pages 191--201. Springer Berlin Heidelberg, 2006. \bibitem{healey1994radiometric} -Glenn~E Healey and Raghava Kondepudy. +Glenn~E. Healey and Raghava Kondepudy. \newblock Radiometric ccd camera calibration and noise estimation. \newblock {\em Pattern Analysis and Machine Intelligence, IEEE Transactions on}, 16(3):267--276, 1994. \bibitem{hochbaum2013simplifications} -Dorit~S Hochbaum and James~B Orlin. +Dorit~S. Hochbaum and James~B. Orlin. \newblock Simplifications and speedups of the pseudoflow algorithm. \newblock {\em Networks}, 61(1):40--57, 2013. @@ -323,20 +335,20 @@ Pushmeet Kohli and Philip~HS Torr. on}, 29(12):2079--2088, 2007. \bibitem{lefohn2003inter} -Aaron~E Lefohn, Joshua~E Cates, and Ross~T Whitaker. +Aaron~E. Lefohn, Joshua~E. Cates, and Ross~T. Whitaker. \newblock Interactive, gpu-based level sets for 3d segmentation. \newblock In {\em Medical Image Computing and Computer-Assisted Intervention-MICCAI 2003}, pages 564--572. Springer, 2003. \bibitem{lefohn2003interactive} -Aaron~E Lefohn, Joe~M Kniss, Charles~D Hansen, and Ross~T Whitaker. +Aaron~E. Lefohn, Joe~M. Kniss, Charles~D. Hansen, and Ross~T. Whitaker. \newblock Interactive deformation and visualization of level set surfaces using graphics hardware. \newblock In {\em Proceedings of the 14th IEEE Visualization 2003 (VIS'03)}, page~11. IEEE Computer Society, 2003. \bibitem{lefohn2005streaming} -Aaron~E Lefohn, Joe~M Kniss, Charles~D Hansen, and Ross~T Whitaker. +Aaron~E. Lefohn, Joe~M. Kniss, Charles~D. Hansen, and Ross~T. Whitaker. \newblock A streaming narrow-band algorithm: interactive computation and visualization of level sets. \newblock In {\em ACM SIGGRAPH 2005 Courses}, page 243. ACM, 2005. @@ -394,7 +406,7 @@ NVIDIA Corporation. \newblock {\em NVIDIA CUDA C Programming Guide v4.2}, 7 2012. \bibitem{osher1988fronts} -Stanley Osher and James~A Sethian. +Stanley Osher and James~A. Sethian. \newblock Fronts propagating with curvature-dependent speed: algorithms based on hamilton-jacobi formulations. \newblock {\em Journal of computational physics}, 79(1):12--49, 1988. @@ -508,13 +520,13 @@ R.M. Sanchez and P.A. Rodriguez. International Conference on}, pages 1549 --1552, march 2012. \bibitem{sethian1996fast} -James~A Sethian. +James~A. Sethian. \newblock A fast marching level set method for monotonically advancing fronts. \newblock {\em Proceedings of the National Academy of Sciences}, 93(4):1591--1595, 1996. \bibitem{kmeansgpuopengl} -S.A.Arul Shalom, Manoranjan Dash, and Minh Tue. +S.A.~Arul Shalom, Manoranjan Dash, and Minh Tue. \newblock Efficient k-means clustering using accelerated graphics processors. \newblock In Il-Yeol Song, Johann Eder, and ThoManh Nguyen, editors, {\em Data Warehousing and Knowledge Discovery}, volume 5182 of {\em Lecture Notes in @@ -527,7 +539,7 @@ Jianbo Shi and Jitendra Malik. on}, 22(8):888--905, 2000. \bibitem{snakegvfopencl12} -Erik Smistad, AnneC. Elster, and Frank Lindseth. +Erik Smistad, Anne~C. Elster, and Frank Lindseth. \newblock Real-time gradient vector flow on gpus using opencl. \newblock {\em Journal of Real-Time Image Processing}, pages 1--8, 2012. @@ -553,7 +565,7 @@ RicardoM. Sánchez and PaulA. Rodríguez. \newblock {\em Journal of Signal Processing Systems}, 71(3):221--235, 2013. \bibitem{theuwissen2001ccd} -Albert~JP Theuwissen. +Albert~J.P. Theuwissen. \newblock Ccd or cmos image sensors for consumer digital still photography? \newblock In {\em VLSI Technology, Systems, and Applications, 2001. Proceedings of Technical Papers. 2001 International Symposium on}, pages 168--171. IEEE, diff --git a/THESE/these.blg b/THESE/these.blg index 132d9d9..c4a4bac 100644 --- a/THESE/these.blg +++ b/THESE/these.blg @@ -11,45 +11,45 @@ Warning--empty journal in cohen1993surface Warning--empty journal in dixit2005gpu Warning--can't use both volume and number fields in macqueen1967some Warning--can't use both volume and number fields in xiao2010efficient -You've used 110 entries, +You've used 112 entries, 2118 wiz_defined-function locations, - 1111 strings with 22750 characters, -and the built_in function-call counts, 41591 in all, are: -= -- 4179 -> -- 1768 + 1123 strings with 23168 characters, +and the built_in function-call counts, 42296 in all, are: += -- 4250 +> -- 1799 < -- 60 -+ -- 713 -- -- 580 -* -- 2826 -:= -- 6501 -add.period$ -- 352 -call.type$ -- 110 -change.case$ -- 602 ++ -- 725 +- -- 590 +* -- 2884 +:= -- 6618 +add.period$ -- 358 +call.type$ -- 112 +change.case$ -- 613 chr.to.int$ -- 0 -cite$ -- 119 -duplicate$ -- 1725 -empty$ -- 3357 -format.name$ -- 580 -if$ -- 9059 +cite$ -- 121 +duplicate$ -- 1747 +empty$ -- 3413 +format.name$ -- 590 +if$ -- 9204 int.to.chr$ -- 0 -int.to.str$ -- 110 -missing$ -- 109 -newline$ -- 549 -num.names$ -- 220 -pop$ -- 685 +int.to.str$ -- 112 +missing$ -- 111 +newline$ -- 559 +num.names$ -- 224 +pop$ -- 692 preamble$ -- 1 -purify$ -- 498 +purify$ -- 507 quote$ -- 0 -skip$ -- 1307 +skip$ -- 1322 stack$ -- 0 -substring$ -- 2799 -swap$ -- 545 +substring$ -- 2861 +swap$ -- 547 text.length$ -- 60 text.prefix$ -- 0 top$ -- 0 -type$ -- 428 +type$ -- 436 warning$ -- 9 -while$ -- 401 -width$ -- 113 -write$ -- 1226 +while$ -- 408 +width$ -- 115 +write$ -- 1248 (There were 9 warnings) diff --git a/THESE/these.lof b/THESE/these.lof index 424dc8c..4785d1b 100644 --- a/THESE/these.lof +++ b/THESE/these.lof @@ -5,96 +5,96 @@ \contentsline {figure}{\numberline {2.2}{\ignorespaces Comparaison des performances des GPUs Nvidia et des CPU Intel (d'apr\IeC {\`e}s \cite {CUDAPG}).}}{14}{figure.2.2} \contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Nombre maximum th\IeC {\'e}orique d'op\IeC {\'e}rations en virgule flottante par seconde en fonction de l'ann\IeC {\'e}e et de l'architecture.}}}{14}{figure.2.2} \contentsline {subfigure}{\numberline {(b)}{\ignorespaces {Bande passante th\IeC {\'e}orique maximale des diverses architectures.}}}{14}{figure.2.2} -\contentsline {figure}{\numberline {2.3}{\ignorespaces Organisation des GPUs d'architecture Fermi, comme le C2070 (d'apr\IeC {\`e}s www.hpcresearch.nl).}}{15}{figure.2.3} -\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Organisation en groupes de SMs }}}{15}{figure.2.3} -\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {Constitution d'un SM.}}}{15}{figure.2.3} -\contentsline {figure}{\numberline {2.4}{\ignorespaces Repr\IeC {\'e}sentation d'une grille de calcul en 2D et des blocs de threads, \IeC {\`a} 2 dimensions, qui la composent.}}{16}{figure.2.4} +\contentsline {figure}{\numberline {2.3}{\ignorespaces 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Ligne du bas : version parall\IeC {\`e}le. Les segments en rouge sont des segments du contour non \IeC {\'e}valu\IeC {\'e}s, alors que ceux en pointill\IeC {\'e}s sont les paires ayant re\IeC {\c c}u les meilleures \IeC {\'e}valuations parmi les 8 d\IeC {\'e}placements possibles des n\oe uds correspondant.}}{73}{figure.6.9} -\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Contour de r\IeC {\'e}f\IeC {\'e}rence.}}}{73}{figure.6.9} -\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {D\IeC {\'e}placement du n\oe ud $N_1$. Le crit\IeC {\`e}re est am\IeC {\'e}lior\IeC {\'e}.}}}{73}{figure.6.9} -\contentsline {subfigure}{\numberline {(c)}{\ignorespaces {D\IeC {\'e}placement du n\oe ud $N_2$. Le crit\IeC {\`e}re est am\IeC {\'e}lior\IeC {\'e}.}}}{73}{figure.6.9} -\contentsline {subfigure}{\numberline {(d)}{\ignorespaces {D\IeC {\'e}placement en parall\IeC {\`e}le de tous les n\oe uds. Les segments du contour n'ont pas \IeC {\'e}t\IeC {\'e} valid\IeC {\'e}s. On doit recalculer le crit\IeC {\`e}re apr\IeC {\`e}s les d\IeC {\'e}placements pour savoir s'il a \IeC {\'e}t\IeC {\'e} am\IeC {\'e}lior\IeC {\'e}.}}}{73}{figure.6.9} -\contentsline {subfigure}{\numberline {(e)}{\ignorespaces {D\IeC {\'e}placement en parall\IeC {\`e}le des n\oe uds impairs. Le crit\IeC {\`e}re est am\IeC {\'e}lior\IeC {\'e}.}}}{73}{figure.6.9} -\contentsline {subfigure}{\numberline {(f)}{\ignorespaces {D\IeC {\'e}placement en parall\IeC {\`e}le des n\oe uds pairs. Un seul segment n'a pas \IeC {\'e}t\IeC {\'e} \IeC {\'e}valu\IeC {\'e}.}}}{73}{figure.6.9} +\contentsline {figure}{\numberline {6.3}{\ignorespaces Influence du contour initial sur la segmentation. Le contour final 1 est celui de la figure \ref {fig-snakecpu-cochon512}.}}{67}{figure.6.3} +\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Initialisation 2 }}}{67}{figure.6.3} +\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {Contour final 2 : 273 n\oe uds 87~ms}}}{67}{figure.6.3} +\contentsline {subfigure}{\numberline {(c)}{\ignorespaces {Contour final 1 : 256 n\oe uds 44~ms}}}{67}{figure.6.3} +\contentsline {figure}{\numberline {6.4}{\ignorespaces Segmentation de l'image de test en 4000$\times $4000 pixels. Le trac\IeC {\'e} du contour a \IeC {\'e}t\IeC {\'e} artificiellement \IeC {\'e}paissi pour le rendre visible \IeC {\`a} l'\IeC {\'e}chelle de l'impression.}}{68}{figure.6.4} +\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {$d_{max}=16$ et $l_{min}=8$, 1246 n\oe uds en 1.3~s}}}{68}{figure.6.4} +\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {$d_{max}=128$ et $l_{min}=32$, 447 n\oe uds en 0.7~s}}}{68}{figure.6.4} +\contentsline {figure}{\numberline {6.5}{\ignorespaces Segmentation de l'image de test en 4000$\times $4000 pixels avec une cible de petite taille. Le contour initial est la transcription de celui utilis\IeC {\'e} \IeC {\`a} la figure \ref {fig-snakecpu-cochon512}. Le trac\IeC {\'e} du contour a \IeC {\'e}t\IeC {\'e} artificiellement \IeC {\'e}paissi pour le rendre visible \IeC {\`a} l'\IeC {\'e}chelle de l'impression.}}{68}{figure.6.5} +\contentsline {figure}{\numberline {6.6}{\ignorespaces \IeC {\'E}volution du co\IeC {\^u}t relatif des trois fonctions les plus consommatrices en temps de calcul en fonction de la taille de l'image \IeC {\`a} traiter.}}{69}{figure.6.6} +\contentsline {figure}{\numberline {6.7}{\ignorespaces Calcul des images cumul\IeC {\'e}es $S_I$ et $S_{I^2}$ en trois \IeC {\'e}tapes successives. a) cumul partiel bloc par bloc et m\IeC {\'e}morisation de la somme de chaque bloc. b) cumul sur le vecteur des sommes partielles. c) ajout des sommes partielles \IeC {\`a} chaque \IeC {\'e}l\IeC {\'e}ment des blocs cumul\IeC {\'e}s.}}{71}{figure.6.7} +\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {D\IeC {\'e}tail des op\IeC {\'e}rations effectu\IeC {\'e}es par le \textit {kernel} \texttt {compute\_block\_prefixes()}. La valeur $bs$ correspond au nombre de pixels de chaque bloc, qui est aussi le nombre de threads ex\IeC {\'e}cut\IeC {\'e} par chaque bloc de la grille de calcul.}}}{71}{figure.6.7} +\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {D\IeC {\'e}tail des op\IeC {\'e}rations effectu\IeC {\'e}es par le \textit {kernel} \texttt {scan\_blocksums()}.}}}{71}{figure.6.7} +\contentsline {subfigure}{\numberline {(c)}{\ignorespaces {D\IeC {\'e}tail des op\IeC {\'e}rations effectu\IeC {\'e}es par le \textit {kernel} \texttt {add\_sums2prefixes()}.}}}{71}{figure.6.7} +\contentsline {figure}{\numberline {6.8}{\ignorespaces Structuration des donn\IeC {\'e}es en m\IeC {\'e}moire du GPU pour l'\IeC {\'e}valuation en parall\IeC {\`e}le de l'ensemble des \IeC {\'e}volutions possibles du contour.}}{73}{figure.6.8} +\contentsline {figure}{\numberline {6.9}{\ignorespaces Comparaison des cycles de d\IeC {\'e}placement des n\oe uds. Ligne du haut : version s\IeC {\'e}quentielle. Ligne du bas : version parall\IeC {\`e}le. Les segments en rouge sont des segments du contour non \IeC {\'e}valu\IeC {\'e}s, alors que ceux en pointill\IeC {\'e}s sont les paires ayant re\IeC {\c c}u les meilleures \IeC {\'e}valuations parmi les 8 d\IeC {\'e}placements possibles des n\oe uds correspondant.}}{74}{figure.6.9} +\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Contour de r\IeC {\'e}f\IeC {\'e}rence.}}}{74}{figure.6.9} +\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {D\IeC {\'e}placement du n\oe ud $N_1$. Le crit\IeC {\`e}re est am\IeC {\'e}lior\IeC {\'e}.}}}{74}{figure.6.9} +\contentsline {subfigure}{\numberline {(c)}{\ignorespaces {D\IeC {\'e}placement du n\oe ud $N_2$. Le crit\IeC {\`e}re est am\IeC {\'e}lior\IeC {\'e}.}}}{74}{figure.6.9} +\contentsline {subfigure}{\numberline {(d)}{\ignorespaces {D\IeC {\'e}placement en parall\IeC {\`e}le de tous les n\oe uds. Les segments du contour n'ont pas \IeC {\'e}t\IeC {\'e} valid\IeC {\'e}s. On doit recalculer le crit\IeC {\`e}re apr\IeC {\`e}s les d\IeC {\'e}placements pour savoir s'il a \IeC {\'e}t\IeC {\'e} am\IeC {\'e}lior\IeC {\'e}.}}}{74}{figure.6.9} +\contentsline {subfigure}{\numberline {(e)}{\ignorespaces {D\IeC {\'e}placement en parall\IeC {\`e}le des n\oe uds impairs. Le crit\IeC {\`e}re est am\IeC {\'e}lior\IeC {\'e}.}}}{74}{figure.6.9} +\contentsline {subfigure}{\numberline {(f)}{\ignorespaces {D\IeC {\'e}placement en parall\IeC {\`e}le des n\oe uds pairs. Un seul segment n'a pas \IeC {\'e}t\IeC {\'e} \IeC {\'e}valu\IeC {\'e}.}}}{74}{figure.6.9} \contentsline {figure}{\numberline {6.10}{\ignorespaces D\IeC {\'e}termination des coefficients $C(i,j)$ des pixels du contour.}}{75}{figure.6.10} \contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Quadrants 1 et 4}}}{75}{figure.6.10} \contentsline {subfigure}{\numberline {(b)}{\ignorespaces {Quadrants 2 et 3}}}{75}{figure.6.10} -\contentsline {figure}{\numberline {6.11}{\ignorespaces Segmentations d'une image de 100~MP en 0,59~s pour 5 it\IeC {\'e}rations. Le contour initial conserve les proportions de celui de la figure \ref {fig-snakecpu-cochon512}. }}{76}{figure.6.11} -\contentsline {figure}{\numberline {6.12}{\ignorespaces D\IeC {\'e}termination intelligente du contour initial en deux phases successives. a) La premi\IeC {\`e}re \IeC {\'e}tape repose sur un \IeC {\'e}chantillonnage horizontal. b) La seconde \IeC {\'e}tape repose sur un \IeC {\'e}chantillonnage vertical.}}{77}{figure.6.12} -\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {D\IeC {\'e}termination de $j_L$ et $j_H$.}}}{77}{figure.6.12} -\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {D\IeC {\'e}termination de $i_L$ et $i_H$.}}}{77}{figure.6.12} +\contentsline {figure}{\numberline {6.11}{\ignorespaces Segmentations d'une image de 100~MP en 0,59~s pour 5 it\IeC {\'e}rations. Le contour initial conserve les proportions de celui de la figure \ref {fig-snakecpu-cochon512}. }}{77}{figure.6.11} +\contentsline {figure}{\numberline {6.12}{\ignorespaces D\IeC {\'e}termination intelligente du contour initial en deux phases successives. (a) La premi\IeC {\`e}re \IeC {\'e}tape repose sur un \IeC {\'e}chantillonnage horizontal. (b) La seconde \IeC {\'e}tape repose sur un \IeC {\'e}chantillonnage vertical.}}{78}{figure.6.12} +\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {D\IeC {\'e}termination de $j_L$ et $j_H$.}}}{78}{figure.6.12} +\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {D\IeC {\'e}termination de $i_L$ et $i_H$.}}}{78}{figure.6.12} \addvspace {10\p@ } \contentsline {figure}{\numberline {7.1}{\ignorespaces D\IeC {\'e}tail des motifs et de leur repr\IeC {\'e}sentation interne, pour la taille $a=5$. }}{82}{figure.7.1} \contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Les 8 premi\IeC {\`e}res lignes de la table $P_5$. Les \IeC {\'e}l\IeC {\'e}ments sont les positions relatives des pixels de chaque motif par rapport au pixel central.}}}{82}{figure.7.1} @@ -187,7 +187,7 @@ \contentsline {subfigure}{\numberline {(d)}{\ignorespaces {Directions d\IeC {\'e}termin\IeC {\'e}es par le PI-PD pour le tirage $n^{\circ }1$}}}{93}{figure.7.10} \contentsline {subfigure}{\numberline {(e)}{\ignorespaces {Directions d\IeC {\'e}termin\IeC {\'e}e par le PI-PD pour le tirage $n^{\circ }2$}}}{93}{figure.7.10} \contentsline {figure}{\numberline {7.11}{\ignorespaces Motif de d\IeC {\'e}tection des zones \IeC {\`a} faible pente, pour le cas $\Theta =\Theta _4=45^{\circ }$. L'\IeC {\'e}l\IeC {\'e}vation des pixels permet juste de les distinguer selon 3 classes : l'\IeC {\'e}l\IeC {\'e}vation 1 est associ\IeC {\'e}e aux pixels de la r\IeC {\'e}gion $T$, l'\IeC {\'e}l\IeC {\'e}vation 0.5 est associ\IeC {\'e}e \IeC {\`a} ceux de la r\IeC {\'e}gion $B$ et l'\IeC {\'e}l\IeC {\'e}vation 0 d\IeC {\'e}signe les pixels n'intervenant pas dans la d\IeC {\'e}tection.}}{94}{figure.7.11} -\contentsline {figure}{\numberline {7.12}{\ignorespaces Classification des pixels d'une image bruit\IeC {\'e}e, pour une valeur de seuil $T2=2$ du d\IeC {\'e}tecteur. b) Les pixels en noir sont ceux \IeC {\`a} qui le PI-PD sera appliqu\IeC {\'e}. Les pixels en blancs se verront appliquer une moyenne sur tout ou partie du voisinage.}}{94}{figure.7.12} +\contentsline {figure}{\numberline {7.12}{\ignorespaces Classification des pixels d'une image bruit\IeC {\'e}e, pour une valeur de seuil $T2=2$ du d\IeC {\'e}tecteur. (b) Les pixels en noir sont ceux \IeC {\`a} qui le PI-PD sera appliqu\IeC {\'e}. Les pixels en blancs se verront appliquer une moyenne sur tout ou partie du voisinage.}}{94}{figure.7.12} \contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Image bruit\IeC {\'e}e}}}{94}{figure.7.12} \contentsline {subfigure}{\numberline {(b)}{\ignorespaces {Classification des pixels. }}}{94}{figure.7.12} \contentsline {figure}{\numberline {7.13}{\ignorespaces Comparaison des rendus des traitements compar\IeC {\'e}s. Rang\IeC {\'e}e du haut : les images compl\IeC {\`e}tes. Rang\IeC {\'e}e du bas : Zooms sur une zone de l'\IeC {\'\i }mage au dessus.}}{95}{figure.7.13} diff --git a/THESE/these.log b/THESE/these.log index 29ef7a4..0abc992 100644 --- a/THESE/these.log +++ b/THESE/these.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2012.12.6) 19 DEC 2013 15:18 +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2012.12.6) 8 JAN 2014 17:29 entering extended mode %&-line parsing enabled. **these.tex @@ -1194,7 +1194,7 @@ LaTeX Info: Redefining \Ref on input line 131. pdfTeX warning: pdflatex (file /usr/share/texmf/tex/latex/upmethodology-extensi ons/phd_thesis/spimufcphdthesis/spimufcphdthesis-frontpage.pdf): PDF inclusion: found PDF version <1.5>, but at most version <1.4> allowed - + File: spimufcphdthesis-frontpage.pdf Graphic file (type pdf) [1 @@ -1205,7 +1205,7 @@ File: spimufcphdthesis-frontpage.pdf Graphic file (type pdf) e.pdf>] [2 ] - + File: spimufcphdthesis-p3-head.pdf Graphic file (type pdf) @@ -1237,66 +1237,63 @@ Package Fancyhdr Warning: \headheight is too small (12.0pt): We now make it that large for the rest of the document. This may cause the page layout to be inconsistent, however. -[5] -Underfull \vbox (badness 1946) has occurred while \output is active [] - - [6] -Overfull \hbox (1.29184pt too wide) detected at line 74 +[5] [6] +Overfull \hbox (1.29184pt too wide) detected at line 76 [][]\T1/phv/m/n/10.95 103[] [] -Overfull \hbox (1.29184pt too wide) detected at line 75 +Overfull \hbox (1.29184pt too wide) detected at line 77 [][]\T1/phv/m/n/10.95 103[] [] -Overfull \hbox (1.29184pt too wide) detected at line 76 +Overfull \hbox (1.29184pt too wide) detected at line 78 [][]\T1/phv/m/n/10.95 104[] [] -Overfull \hbox (1.29184pt too wide) detected at line 77 +Overfull \hbox (1.29184pt too wide) detected at line 79 [][]\T1/phv/m/n/10.95 105[] [] -Overfull \hbox (1.29184pt too wide) detected at line 78 +Overfull \hbox (1.29184pt too wide) detected at line 80 [][]\T1/phv/m/n/10.95 107[] [] -Overfull \hbox (1.29184pt too wide) detected at line 79 +Overfull \hbox (1.29184pt too wide) detected at line 81 [][]\T1/phv/m/n/10.95 109[] [] -Overfull \hbox (1.29184pt too wide) detected at line 80 +Overfull \hbox (1.29184pt too wide) detected at line 82 [][]\T1/phv/m/n/10.95 111[] [] -Overfull \hbox (1.29184pt too wide) detected at line 82 +Overfull \hbox (1.29184pt too wide) detected at line 84 [][]\T1/phv/m/n/10.95 113[] [] -Overfull \hbox (1.29184pt too wide) detected at line 83 +Overfull \hbox (1.29184pt too wide) detected at line 85 [][]\T1/phv/m/n/10.95 113[] [] -Overfull \hbox (1.29184pt too wide) detected at line 84 +Overfull \hbox (1.29184pt too wide) detected at line 86 [][]\T1/phv/m/n/10.95 115[] [] -Overfull \hbox (1.29184pt too wide) detected at line 85 +Overfull \hbox (1.29184pt too wide) detected at line 87 [][]\T1/phv/m/n/10.95 119[] [] -Overfull \hbox (1.29184pt too wide) detected at line 86 +Overfull \hbox (1.29184pt too wide) detected at line 88 [][]\T1/phv/m/n/10.95 124[] [] @@ -1328,67 +1325,64 @@ LaTeX Font Warning: Font shape `TS1/phv/m/sc' undefined (Font) for symbol `textregistered' on input line 141. 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[36 ] [37] [38 + [38 ]) [39] [40 ] Chapitre 5. -(./Chapters/chapter2/chapter2d.tex -Underfull \vbox (badness 10000) has occurred while \output is active [] - - [39] - File: /home/zulu/Documents/these_gilles/THESE/codes/cochon256.png Graphic file (type png) -Underfull \hbox (badness 10000) in paragraph at lines 30--30 +Underfull \hbox (badness 10000) in paragraph at lines 31--31 []\T1/phv/m/n/9 (a) Image ini-tiale [] -Underfull \hbox (badness 10000) in paragraph at lines 30--30 +Underfull \hbox (badness 10000) in paragraph at lines 31--31 \T1/phv/m/n/9 com-por-tant deux [] +png, id=912, 289.883pt x 242.506pt> File: /home/zulu/Documents/these_gilles/THESE/codes/seg_histogramme/histo-cocho n256.png Graphic file (type png) +to-101-255.png, id=913, 204.765pt x 204.765pt> File: /home/zulu/Documents/these_gilles/THESE/codes/seg_histogramme/cochon256-s eghisto-101-255.png Graphic file (type png) - File: /home/zulu/Documents/these_gilles/THESE/codes/cochon256-sig25.png Graphic file (type png) +sig25.png, id=915, 287.474pt x 240.097pt> File: /home/zulu/Documents/these_gilles/THESE/codes/seg_histogramme/histo-cocho n256-sig25.png Graphic file (type png) +seghisto-99-255.png, id=916, 204.765pt x 204.765pt> File: /home/zulu/Documents/these_gilles/THESE/codes/seg_histogramme/cochon256-s ig25-seghisto-99-255.png Graphic file (type png) -Underfull \hbox (badness 1067) in paragraph at lines 35--35 +Underfull \hbox (badness 1067) in paragraph at lines 36--36 []\T1/phv/m/n/9 (f) Image bi-naire re- [] Package hyperref Info: bookmark level for unknown algocf defaults to 0 on input - 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- [78] -[79] [80 +) [78 <./Chapters/chapter3/img/smart +_init1.pdf> <./Chapters/chapter3/img/smart_init2.pdf>]) [79] [80 ] Chapitre 7. @@ -2547,11 +2531,11 @@ Chapitre 7. 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File: Chapters/chapter4/img/hist_seg1_elaine_25_l3.png Graphic file (type png) - File: Chapters/chapter4/img/hist_seg1_finger_25_l3.png Graphic file (type png) - File: Chapters/chapter4/img/hist_seg1_goldhill_25_l3.png Graphic file (type png ) - + File: Chapters/chapter4/img/hist_seg1_lena_25_l3.png Graphic file (type png) - + File: Chapters/chapter4/img/hist_seg1_man_25_l3.png Graphic file (type png) - File: Chapters/chapter4/img/hist_seg1_peppers_25_l3.png Graphic file (type png) - File: Chapters/chapter4/img/hist_seg1_stream_25_l3.png Graphic file (type png) - File: Chapters/chapter4/img/hist_seg1_zelda_25_l3.png Graphic file (type png) @@ -2746,14 +2730,14 @@ g1_goldhill_25_l3.png (PNG copy)> <./Chapters/chapter4/img/hist_seg1_lena_25_l3 ./Chapters/chapter4/img/hist_seg1_peppers_25_l3.png (PNG copy)> <./Chapters/cha pter4/img/hist_seg1_stream_25_l3.png (PNG copy)> <./Chapters/chapter4/img/hist_ seg1_zelda_25_l3.png (PNG copy)>] - + File: Chapters/chapter4/img/PI-PD_detail_sub1.jpg Graphic file (type jpg) - 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+ File: Chapters/chapter4/img/zoom_edge2_bruit.jpg Graphic file (type jpg) - File: Chapters/chapter4/img/zoom_edge1_2D_superpose3.jpg Graphic file (type jpg ) @@ -2809,7 +2793,7 @@ Underfull \hbox (badness 7081) in paragraph at lines 349--349 [] - File: Chapters/chapter4/img/zoom_edge2_2D_superpose2.jpg Graphic file (type jpg ) @@ -2822,7 +2806,7 @@ Underfull \hbox (badness 7081) in paragraph at lines 350--350 LaTeX Warning: `h' float specifier changed to `ht'. 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(./Chapters/chapter5/code/median3-2pix.cu) - + File: Chapters/chapter5/img/comp512.png Graphic file (type png) - + File: Chapters/chapter5/img/comp4k.png Graphic file (type png) [109] [110 <./Chapters/chapter5/img/comp @@ -3115,11 +3099,11 @@ Chapitre 9. ] (./Chapters/chapter6/code/convoGene3Reg8.cu) [114] [115] - + File: Chapters/chapter6/img/convoOverlap1.png Graphic file (type png) - + File: Chapters/chapter6/img/convoOverlap2.png Graphic file (type png) [116 <./Chapters/chapter6/img/con @@ -3141,11 +3125,11 @@ LaTeX Warning: `h' float specifier changed to `ht'. Underfull \vbox (badness 10000) has occurred while \output is active [] [123] - + File: Chapters/chapter6/img/convomed1.png Graphic file (type png) - + File: Chapters/chapter6/img/convomed2.png Graphic file (type png) @@ -3166,7 +3150,10 @@ Underfull \vbox (badness 10000) has occurred while \output is active [] ] [130] [131] [132] [133] [134]) [135] [136 ] -(./these.lof [137] [138] +(./these.lof [137] +Underfull \vbox (badness 10000) has occurred while \output is active [] + + [138] Underfull \vbox (badness 10000) has occurred while \output is active [] [139] @@ -3295,7 +3282,7 @@ Overfull \hbox (1.29184pt too wide) detected at line 30 pdfTeX warning: pdflatex (file /usr/share/texmf/tex/latex/upmethodology-extensi ons/phd_thesis/spimufcphdthesis/spimufcphdthesis-backpage.pdf): PDF inclusion: found PDF version <1.6>, but at most version <1.4> allowed - + File: spimufcphdthesis-backpage.pdf Graphic file (type pdf) @@ -3316,10 +3303,10 @@ LaTeX Font Warning: Some font shapes were not available, defaults substituted. ) (\end occurred when \iftrue on line 185 was incomplete) Here is how much of TeX's memory you used: - 15211 strings out of 495028 - 253393 string characters out of 1181229 - 972589 words of memory out of 3000000 - 16546 multiletter control sequences out of 15000+50000 + 15224 strings out of 495028 + 253520 string characters out of 1181229 + 972741 words of memory out of 3000000 + 16549 multiletter control sequences out of 15000+50000 158788 words of font info for 231 fonts, out of 3000000 for 9000 28 hyphenation exceptions out of 8191 61i,25n,49p,1409b,1898s stack positions out of 5000i,500n,10000p,200000b,50000s @@ -3336,9 +3323,9 @@ pe1/urw/helvetic/uhvr8a.pfb> -Output written on these.pdf (146 pages, 37754507 bytes). +Output written on these.pdf (146 pages, 37765485 bytes). PDF statistics: - 3065 PDF objects out of 3580 (max. 8388607) - 1165 named destinations out of 1200 (max. 500000) - 1709 words of extra memory for PDF output out of 10000 (max. 10000000) + 3092 PDF objects out of 3580 (max. 8388607) + 1175 named destinations out of 1200 (max. 500000) + 1725 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/THESE/these.lot b/THESE/these.lot index b8f650f..feae2c1 100644 --- a/THESE/these.lot +++ b/THESE/these.lot @@ -1,15 +1,15 @@ \select@language {french} \addvspace {10\p@ } \addvspace {10\p@ } -\contentsline {table}{\numberline {2.1}{\ignorespaces Caract\IeC {\'e}ristiques des diff\IeC {\'e}rents types de m\IeC {\'e}moire disponibles sur le GPU. Pour les m\IeC {\'e}moires cach\IeC {\'e}es, les latences sont donn\IeC {\'e}es selon l'acc\IeC {\`e}s \textit {sans-cache/L1/L2}. Les mesures ont \IeC {\'e}t\IeC {\'e} obtenues \IeC {\`a} l'aide des microprogrammes de test de \cite {wong2010demystifying}.}}{16}{table.2.1} +\contentsline {table}{\numberline {2.1}{\ignorespaces Caract\IeC {\'e}ristiques des diff\IeC {\'e}rents types de m\IeC {\'e}moire disponibles sur le GPU. Pour les m\IeC {\'e}moires cach\IeC {\'e}es, les latences sont donn\IeC {\'e}es selon l'acc\IeC {\`e}s \textit {sans-cache/L1/L2} et ont \IeC {\'e}t\IeC {\'e} obtenues \IeC {\`a} l'aide des microprogrammes de test de \cite {wong2010demystifying}. Les valeurs de d\IeC {\'e}bit sont donn\IeC {\'e}es par le constructeur.}}{15}{table.2.1} \addvspace {10\p@ } \addvspace {10\p@ } \addvspace {10\p@ } \addvspace {10\p@ } -\contentsline {table}{\numberline {6.1}{\ignorespaces Valeur du coefficient $C(i,j)$ en fonction des valeurs des codes de Freeman des vecteurs $f_{in}$ et $f_{out}$.}}{62}{table.6.1} -\contentsline {table}{\numberline {6.2}{\ignorespaces Performances (en secondes) de la segmentation par snake polygonal sur CPU en fonction de la taille de l'image \IeC {\`a} traiter. Les temps sont obtenus avec la m\IeC {\^e}me image de test dilat\IeC {\'e}e et bruit\IeC {\'e}e et un contour initial carr\IeC {\'e} dont la distance aux bords est proportionnelle \IeC {\`a} la taille de l'image. Seule l'image en 15~MP a pu \IeC {\^e}tre trait\IeC {\'e}e par une impl\IeC {\'e}mentation utilisant SSE2.}}{68}{table.6.2} -\contentsline {table}{\numberline {6.3}{\ignorespaces Acc\IeC {\'e}l\IeC {\'e}ration constat\IeC {\'e}e, pour le calcul des images cumul\IeC {\'e}es, de l'impl\IeC {\'e}mentation GPU (C2070) par rapport \IeC {\`a} l'impl\IeC {\'e}mentation CPU de r\IeC {\'e}f\IeC {\'e}rence.}}{71}{table.6.3} -\contentsline {table}{\numberline {6.4}{\ignorespaces Comparaison des temps d'ex\IeC {\'e}cution de l'impl\IeC {\'e}mentation GPU (C2070) par rapport \IeC {\`a} l'impl\IeC {\'e}mentation CPU de r\IeC {\'e}f\IeC {\'e}rence, appliqu\IeC {\'e}s \IeC {\`a} une m\IeC {\^e}me image dilat\IeC {\'e}e (fig. \ref {fig-snakecpu-cochon512}) pour en adapter la taille.}}{76}{table.6.4} +\contentsline {table}{\numberline {6.1}{\ignorespaces Valeur du coefficient $C(i,j)$ en fonction des valeurs des codes de Freeman des vecteurs $f_{in}$ et $f_{out}$ \cite {GallandBR03}.}}{64}{table.6.1} +\contentsline {table}{\numberline {6.2}{\ignorespaces Performances (en secondes) de la segmentation par snake polygonal sur CPU en fonction de la taille de l'image \IeC {\`a} traiter. Les temps sont obtenus avec la m\IeC {\^e}me image de test dilat\IeC {\'e}e et bruit\IeC {\'e}e et un contour initial carr\IeC {\'e} dont la distance aux bords est proportionnelle \IeC {\`a} la taille de l'image. Seule l'image en 15~MP a pu \IeC {\^e}tre trait\IeC {\'e}e par une impl\IeC {\'e}mentation utilisant SSE2.}}{67}{table.6.2} +\contentsline {table}{\numberline {6.3}{\ignorespaces Acc\IeC {\'e}l\IeC {\'e}ration constat\IeC {\'e}e, pour le calcul des images cumul\IeC {\'e}es, de l'impl\IeC {\'e}mentation GPU (C2070) par rapport \IeC {\`a} l'impl\IeC {\'e}mentation CPU de r\IeC {\'e}f\IeC {\'e}rence.}}{70}{table.6.3} +\contentsline {table}{\numberline {6.4}{\ignorespaces Comparaison des temps d'ex\IeC {\'e}cution de l'impl\IeC {\'e}mentation GPU (C2070) par rapport \IeC {\`a} l'impl\IeC {\'e}mentation CPU de r\IeC {\'e}f\IeC {\'e}rence, appliqu\IeC {\'e}s \IeC {\`a} une m\IeC {\^e}me image dilat\IeC {\'e}e (fig. \ref {fig-snakecpu-cochon512}) pour en adapter la taille.}}{77}{table.6.4} \addvspace {10\p@ } \contentsline {table}{\numberline {7.1}{\ignorespaces Temps de calcul et de transfert des impl\IeC {\'e}mentations compar\IeC {\'e}es. }}{100}{table.7.1} \contentsline {table}{\numberline {7.2}{\ignorespaces Comparaison image par image de la qualit\IeC {\'e} de d\IeC {\'e}bruitage des filtres PI-LD et PI-PD hybride propos\IeC {\'e} par rapport \IeC {\`a} BM3D pris comme r\IeC {\'e}f\IeC {\'e}rence de qualit\IeC {\'e} et \IeC {\`a} un moyenneur GPU 5$\times $5 pris comme r\IeC {\'e}f\IeC {\'e}rence de rapidit\IeC {\'e}. Les param\IeC {\`e}tres du PI-LD/PI-PD sont $n=5$, $l=25$, $T_{max}=1$ et $T2_{max}=2$. La colonne 'Bruit\IeC {\'e}e' donne les mesures relatives \IeC {\`a} l'image d'entr\IeC {\'e}e corrompue par un bruit gaussien de moyenne nulle et d'\IeC {\'e}cart type $\sigma =25$. PI-LD s'ex\IeC {\'e}cute en 35~ms, PI-PD en 7,3~ms et BM3D en 4,3~s.}}{101}{table.7.2} diff --git a/THESE/these.out b/THESE/these.out index b735b6d..33e4ba2 100644 --- a/THESE/these.out +++ b/THESE/these.out @@ -5,6 +5,7 @@ \BOOKMARK [2][]{subsection.2.2.1}{2.2.1 Le mat\351riel}{section.2.2} \BOOKMARK [2][]{subsection.2.2.2}{2.2.2 Le logiciel}{section.2.2} \BOOKMARK [2][]{subsection.2.2.3}{2.2.3 L'occupancy}{section.2.2} +\BOOKMARK [1][]{section.2.3}{2.3 Synth\350se des contraintes d'impl\351mentation}{chapter.2} \BOOKMARK [0][]{chapter.3}{3 Mod\350les d'image et de bruits - notations}{} \BOOKMARK [1][]{section.3.1}{3.1 Mod\350le d'image bruit\351e}{chapter.3} \BOOKMARK [1][]{section.3.2}{3.2 Mod\350les de bruit}{chapter.3} @@ -26,19 +27,20 @@ \BOOKMARK [2][]{subsection.4.2.3}{4.2.3 Le filtre bilat\351ral}{section.4.2} \BOOKMARK [2][]{subsection.4.2.4}{4.2.4 Les filtres par patches}{section.4.2} \BOOKMARK [0][]{chapter.5}{5 Les techniques de segmentation des images}{} -\BOOKMARK [1][]{section.5.1}{5.1 Les techniques de segmentation}{chapter.5} -\BOOKMARK [2][]{subsection.5.1.1}{5.1.1 Analyse d'histogramme}{section.5.1} -\BOOKMARK [2][]{subsection.5.1.2}{5.1.2 Partitionnement de graphe}{section.5.1} -\BOOKMARK [2][]{subsection.5.1.3}{5.1.3 kernel-means, mean-shift et apparent\351s}{section.5.1} -\BOOKMARK [2][]{subsection.5.1.4}{5.1.4 Les contours actifs, ou snakes}{section.5.1} -\BOOKMARK [2][]{subsection.5.1.5}{5.1.5 M\351thodes hybrides}{section.5.1} -\BOOKMARK [1][]{section.5.2}{5.2 Les impl\351mentations des techniques de segmentation sur GPU}{chapter.5} -\BOOKMARK [2][]{subsection.5.2.1}{5.2.1 Calcul d'histogramme}{section.5.2} +\BOOKMARK [1][]{section.5.1}{5.1 Introduction}{chapter.5} +\BOOKMARK [1][]{section.5.2}{5.2 Les techniques de segmentation orient\351es r\351gions}{chapter.5} +\BOOKMARK [2][]{subsection.5.2.1}{5.2.1 Analyse d'histogramme}{section.5.2} \BOOKMARK [2][]{subsection.5.2.2}{5.2.2 Partitionnement de graphe}{section.5.2} -\BOOKMARK [2][]{subsection.5.2.3}{5.2.3 K-means, mean-shift et apparent\351s}{section.5.2} -\BOOKMARK [2][]{subsection.5.2.4}{5.2.4 Level set et snakes}{section.5.2} -\BOOKMARK [2][]{subsection.5.2.5}{5.2.5 Algorithmes hybrides}{section.5.2} -\BOOKMARK [1][]{section.5.3}{5.3 Conclusion}{chapter.5} +\BOOKMARK [2][]{subsection.5.2.3}{5.2.3 kernel-means, mean-shift et apparent\351s}{section.5.2} +\BOOKMARK [1][]{section.5.3}{5.3 Les techniques de segmentation par contours actifs, ou snakes}{chapter.5} +\BOOKMARK [2][]{subsection.5.3.1}{5.3.1 M\351thodes hybrides}{section.5.3} +\BOOKMARK [1][]{section.5.4}{5.4 Les impl\351mentations des techniques de segmentation sur GPU}{chapter.5} +\BOOKMARK [2][]{subsection.5.4.1}{5.4.1 Calcul d'histogramme}{section.5.4} +\BOOKMARK [2][]{subsection.5.4.2}{5.4.2 Partitionnement de graphe}{section.5.4} +\BOOKMARK [2][]{subsection.5.4.3}{5.4.3 K-means, mean-shift et apparent\351s}{section.5.4} +\BOOKMARK [2][]{subsection.5.4.4}{5.4.4 Level set et 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(subfigure.5.7.3)] >> endobj 3018 0 obj << -/Names [(subsubsection.4.1.1.4) 82 0 R (subsubsection.6.3.2.1) 206 0 R (subsubsection.7.2.1.1) 238 0 R (subsubsection.7.2.1.2) 242 0 R (subsubsection.7.3.3.1) 262 0 R (table.2.1) 604 0 R] -/Limits [(subsubsection.4.1.1.4) (table.2.1)] +/Names [(subfigure.5.7.4) 1156 0 R (subfigure.5.8.1) 1158 0 R (subfigure.5.8.2) 1159 0 R (subfigure.5.8.3) 1160 0 R (subfigure.5.9.1) 1187 0 R (subfigure.5.9.2) 1188 0 R] +/Limits [(subfigure.5.7.4) (subfigure.5.9.2)] >> endobj 3019 0 obj << -/Names [(table.6.1) 1263 0 R (table.6.2) 1391 0 R (table.6.3) 1418 0 R (table.6.4) 1510 0 R (table.7.1) 1868 0 R (table.7.2) 1652 0 R] -/Limits [(table.6.1) (table.7.2)] +/Names [(subfigure.6.10.1) 1519 0 R (subfigure.6.10.2) 1520 0 R (subfigure.6.10.3) 1521 0 R (subfigure.6.12.1) 1558 0 R (subfigure.6.12.2) 1559 0 R (subfigure.6.2.1) 1385 0 R] +/Limits [(subfigure.6.10.1) (subfigure.6.2.1)] >> endobj 3020 0 obj << -/Names [(table.7.3) 1959 0 R (table.8.1) 2044 0 R (table.8.2) 2151 0 R (table.8.3) 2152 0 R (table.8.4) 2163 0 R (table.9.1) 2235 0 R] -/Limits [(table.7.3) (table.9.1)] +/Names [(subfigure.6.2.2) 1386 0 R (subfigure.6.2.3) 1387 0 R (subfigure.6.2.4) 1388 0 R (subfigure.6.2.5) 1389 0 R (subfigure.6.2.6) 1390 0 R (subfigure.6.2.7) 1391 0 R] +/Limits [(subfigure.6.2.2) (subfigure.6.2.7)] >> endobj 3021 0 obj << -/Names [(table.9.2) 2236 0 R (table.9.3) 2266 0 R (table.9.4) 2472 0 R (table.9.5) 2560 0 R (table.9.6) 2534 0 R (table.9.7) 2562 0 R] -/Limits [(table.9.2) (table.9.7)] +/Names [(subfigure.6.2.8) 1392 0 R (subfigure.6.3.1) 1406 0 R (subfigure.6.3.2) 1407 0 R (subfigure.6.3.3) 1408 0 R (subfigure.6.4.1) 1395 0 R (subfigure.6.4.2) 1411 0 R] +/Limits [(subfigure.6.2.8) (subfigure.6.4.2)] >> endobj 3022 0 obj << -/Names [(table.9.8) 2561 0 R] -/Limits [(table.9.8) (table.9.8)] +/Names [(subfigure.6.7.1) 1452 0 R (subfigure.6.7.2) 1453 0 R (subfigure.6.7.3) 1454 0 R (subfigure.6.9.1) 1478 0 R (subfigure.6.9.2) 1479 0 R (subfigure.6.9.3) 1480 0 R] +/Limits [(subfigure.6.7.1) (subfigure.6.9.3)] >> endobj 3023 0 obj << -/Kids [2828 0 R 2829 0 R 2830 0 R 2831 0 R 2832 0 R 2833 0 R] -/Limits [(AlgoLine1.1) (AlgoLine3.25)] +/Names [(subfigure.6.9.4) 1499 0 R (subfigure.6.9.5) 1481 0 R (subfigure.6.9.6) 1500 0 R (subfigure.7.1.1) 1598 0 R (subfigure.7.1.2) 1599 0 R (subfigure.7.10.1) 1779 0 R] +/Limits [(subfigure.6.9.4) (subfigure.7.10.1)] >> endobj 3024 0 obj << -/Kids [2834 0 R 2835 0 R 2836 0 R 2837 0 R 2838 0 R 2839 0 R] -/Limits [(AlgoLine3.26) (AlgoLine5.14)] +/Names [(subfigure.7.10.2) 1780 0 R (subfigure.7.10.3) 1781 0 R (subfigure.7.10.4) 1813 0 R (subfigure.7.10.5) 1814 0 R (subfigure.7.12.1) 1864 0 R (subfigure.7.12.2) 1865 0 R] +/Limits [(subfigure.7.10.2) (subfigure.7.12.2)] >> endobj 3025 0 obj << -/Kids [2840 0 R 2841 0 R 2842 0 R 2843 0 R 2844 0 R 2845 0 R] -/Limits [(AlgoLine5.15) (AlgoLine7.10)] +/Names [(subfigure.7.13.1) 1884 0 R (subfigure.7.13.2) 1885 0 R (subfigure.7.13.3) 1886 0 R (subfigure.7.13.4) 1887 0 R (subfigure.7.13.5) 1888 0 R (subfigure.7.13.6) 1889 0 R] +/Limits [(subfigure.7.13.1) (subfigure.7.13.6)] >> endobj 3026 0 obj << -/Kids [2846 0 R 2847 0 R 2848 0 R 2849 0 R 2850 0 R 2851 0 R] -/Limits [(AlgoLine7.11) (AlgoLine8.3)] +/Names [(subfigure.7.13.7) 1890 0 R (subfigure.7.13.8) 1891 0 R (subfigure.7.14.1) 1959 0 R (subfigure.7.14.10) 1968 0 R (subfigure.7.14.11) 1969 0 R (subfigure.7.14.12) 1970 0 R] +/Limits [(subfigure.7.13.7) (subfigure.7.14.12)] >> endobj 3027 0 obj << -/Kids [2852 0 R 2853 0 R 2854 0 R 2855 0 R 2856 0 R 2857 0 R] -/Limits [(AlgoLine8.4) (Item.31)] +/Names [(subfigure.7.14.13) 1971 0 R (subfigure.7.14.14) 1972 0 R (subfigure.7.14.15) 1973 0 R (subfigure.7.14.16) 1974 0 R (subfigure.7.14.17) 1975 0 R (subfigure.7.14.18) 1976 0 R] +/Limits [(subfigure.7.14.13) (subfigure.7.14.18)] >> endobj 3028 0 obj << -/Kids [2858 0 R 2859 0 R 2860 0 R 2861 0 R 2862 0 R 2863 0 R] -/Limits [(Item.4) (cite.4587843)] +/Names [(subfigure.7.14.19) 1977 0 R (subfigure.7.14.2) 1960 0 R (subfigure.7.14.20) 1978 0 R (subfigure.7.14.21) 1979 0 R (subfigure.7.14.22) 1980 0 R (subfigure.7.14.23) 1981 0 R] +/Limits [(subfigure.7.14.19) (subfigure.7.14.23)] >> endobj 3029 0 obj << -/Kids [2864 0 R 2865 0 R 2866 0 R 2867 0 R 2868 0 R 2869 0 R] -/Limits [(cite.5170921) (cite.chandran2009computational)] +/Names [(subfigure.7.14.24) 1982 0 R (subfigure.7.14.25) 1945 0 R (subfigure.7.14.3) 1961 0 R (subfigure.7.14.4) 1962 0 R (subfigure.7.14.5) 1963 0 R (subfigure.7.14.6) 1964 0 R] +/Limits [(subfigure.7.14.24) (subfigure.7.14.6)] >> endobj 3030 0 obj << -/Kids [2870 0 R 2871 0 R 2872 0 R 2873 0 R 2874 0 R 2875 0 R] -/Limits [(cite.che2008performance) (cite.mancuso2001introduction)] +/Names [(subfigure.7.14.7) 1965 0 R (subfigure.7.14.8) 1966 0 R (subfigure.7.14.9) 1967 0 R (subfigure.7.15.1) 1990 0 R (subfigure.7.15.2) 1991 0 R (subfigure.7.15.3) 1992 0 R] +/Limits [(subfigure.7.14.7) (subfigure.7.15.3)] >> endobj 3031 0 obj << -/Kids [2876 0 R 2877 0 R 2878 0 R 2879 0 R 2880 0 R 2881 0 R] -/Limits [(cite.martin2001database) (equation.6.2.12)] +/Names [(subfigure.7.15.4) 1993 0 R (subfigure.7.15.5) 1994 0 R (subfigure.7.15.6) 1995 0 R (subfigure.7.4.1) 1670 0 R (subfigure.7.4.2) 1671 0 R (subfigure.7.4.3) 1672 0 R] +/Limits [(subfigure.7.15.4) (subfigure.7.4.3)] >> endobj 3032 0 obj << -/Kids [2882 0 R 2883 0 R 2884 0 R 2885 0 R 2886 0 R 2887 0 R] -/Limits [(equation.6.2.13) (figure.4.4)] +/Names [(subfigure.7.4.4) 1673 0 R (subfigure.7.4.5) 1674 0 R (subfigure.7.4.6) 1675 0 R (subfigure.7.5.1) 1698 0 R (subfigure.7.5.10) 1707 0 R (subfigure.7.5.11) 1708 0 R] +/Limits [(subfigure.7.4.4) (subfigure.7.5.11)] >> endobj 3033 0 obj << -/Kids [2888 0 R 2889 0 R 2890 0 R 2891 0 R 2892 0 R 2893 0 R] -/Limits [(figure.4.5) (figure.7.2)] +/Names [(subfigure.7.5.12) 1709 0 R (subfigure.7.5.13) 1678 0 R (subfigure.7.5.2) 1699 0 R (subfigure.7.5.3) 1700 0 R (subfigure.7.5.4) 1701 0 R (subfigure.7.5.5) 1702 0 R] +/Limits [(subfigure.7.5.12) (subfigure.7.5.5)] >> endobj 3034 0 obj << -/Kids [2894 0 R 2895 0 R 2896 0 R 2897 0 R 2898 0 R 2899 0 R] -/Limits [(figure.7.3) (lstnumber.8.1.24)] +/Names [(subfigure.7.5.6) 1703 0 R (subfigure.7.5.7) 1704 0 R (subfigure.7.5.8) 1705 0 R (subfigure.7.5.9) 1706 0 R (subfigure.7.7.1) 1720 0 R (subfigure.7.7.10) 1729 0 R] +/Limits [(subfigure.7.5.6) (subfigure.7.7.10)] >> endobj 3035 0 obj << -/Kids [2900 0 R 2901 0 R 2902 0 R 2903 0 R 2904 0 R 2905 0 R] -/Limits [(lstnumber.8.1.25) (lstnumber.8.1.7)] +/Names [(subfigure.7.7.11) 1730 0 R (subfigure.7.7.12) 1731 0 R (subfigure.7.7.2) 1721 0 R (subfigure.7.7.3) 1722 0 R (subfigure.7.7.4) 1723 0 R (subfigure.7.7.5) 1724 0 R] +/Limits [(subfigure.7.7.11) (subfigure.7.7.5)] >> endobj 3036 0 obj << -/Kids [2906 0 R 2907 0 R 2908 0 R 2909 0 R 2910 0 R 2911 0 R] -/Limits [(lstnumber.8.1.8) (lstnumber.9.2.11)] +/Names [(subfigure.7.7.6) 1725 0 R (subfigure.7.7.7) 1726 0 R (subfigure.7.7.8) 1727 0 R (subfigure.7.7.9) 1728 0 R (subfigure.7.8.1) 1746 0 R (subfigure.7.8.2) 1747 0 R] +/Limits [(subfigure.7.7.6) (subfigure.7.8.2)] >> endobj 3037 0 obj << -/Kids [2912 0 R 2913 0 R 2914 0 R 2915 0 R 2916 0 R 2917 0 R] -/Limits [(lstnumber.9.2.12) (lstnumber.9.2.44)] +/Names [(subfigure.7.8.3) 1748 0 R (subfigure.7.8.4) 1749 0 R (subfigure.7.9.1) 1775 0 R (subfigure.7.9.2) 1776 0 R (subfigure.8.4.1) 2186 0 R (subfigure.8.4.2) 2187 0 R] +/Limits [(subfigure.7.8.3) (subfigure.8.4.2)] >> endobj 3038 0 obj << -/Kids [2918 0 R 2919 0 R 2920 0 R 2921 0 R 2922 0 R 2923 0 R] -/Limits [(lstnumber.9.2.45) (lstnumber.9.3.20)] +/Names [(subfigure.9.1.1) 2278 0 R (subfigure.9.1.2) 2279 0 R (subfigure.9.2.1) 2600 0 R (subfigure.9.2.2) 2601 0 R (subsection.2.2.1) 18 0 R (subsection.2.2.2) 22 0 R] +/Limits [(subfigure.9.1.1) (subsection.2.2.2)] >> endobj 3039 0 obj << -/Kids [2924 0 R 2925 0 R 2926 0 R 2927 0 R 2928 0 R 2929 0 R] -/Limits [(lstnumber.9.3.21) (lstnumber.9.3.53)] +/Names [(subsection.2.2.3) 26 0 R (subsection.3.2.1) 46 0 R (subsection.3.2.2) 50 0 R (subsection.3.2.3) 54 0 R (subsection.3.2.4) 58 0 R (subsection.4.1.1) 70 0 R] +/Limits [(subsection.2.2.3) (subsection.4.1.1)] >> endobj 3040 0 obj << -/Kids [2930 0 R 2931 0 R 2932 0 R 2933 0 R 2934 0 R 2935 0 R] -/Limits [(lstnumber.9.3.54) (lstnumber.9.4.34)] +/Names [(subsection.4.1.2) 90 0 R (subsection.4.2.1) 98 0 R (subsection.4.2.2) 102 0 R (subsection.4.2.3) 106 0 R (subsection.4.2.4) 110 0 R (subsection.5.2.1) 126 0 R] +/Limits [(subsection.4.1.2) (subsection.5.2.1)] >> endobj 3041 0 obj << -/Kids [2936 0 R 2937 0 R 2938 0 R 2939 0 R 2940 0 R 2941 0 R] -/Limits [(lstnumber.9.4.35) (lstnumber.9.5.12)] +/Names [(subsection.5.2.2) 130 0 R (subsection.5.2.3) 134 0 R (subsection.5.3.1) 142 0 R (subsection.5.4.1) 150 0 R (subsection.5.4.2) 154 0 R (subsection.5.4.3) 158 0 R] +/Limits [(subsection.5.2.2) (subsection.5.4.3)] >> endobj 3042 0 obj << -/Kids [2942 0 R 2943 0 R 2944 0 R 2945 0 R 2946 0 R 2947 0 R] -/Limits [(lstnumber.9.5.13) (lstnumber.9.5.45)] +/Names [(subsection.5.4.4) 162 0 R (subsection.5.4.5) 166 0 R (subsection.6.2.1) 186 0 R (subsection.6.2.2) 190 0 R (subsection.6.2.3) 194 0 R (subsection.6.2.4) 198 0 R] +/Limits [(subsection.5.4.4) (subsection.6.2.4)] >> endobj 3043 0 obj << -/Kids [2948 0 R 2949 0 R 2950 0 R 2951 0 R 2952 0 R 2953 0 R] -/Limits [(lstnumber.9.5.46) (page.114)] +/Names [(subsection.6.3.1) 206 0 R (subsection.6.3.2) 210 0 R (subsection.6.3.3) 218 0 R (subsection.6.3.4) 222 0 R (subsection.6.3.5) 226 0 R (subsection.7.2.1) 242 0 R] +/Limits [(subsection.6.3.1) (subsection.7.2.1)] >> endobj 3044 0 obj << -/Kids [2954 0 R 2955 0 R 2956 0 R 2957 0 R 2958 0 R 2959 0 R] -/Limits [(page.115) (page.15)] +/Names [(subsection.7.3.1) 258 0 R (subsection.7.3.2) 262 0 R (subsection.7.3.3) 266 0 R (subsection.7.5.1) 282 0 R (subsection.7.5.2) 286 0 R (subsection.8.3.1) 310 0 R] +/Limits [(subsection.7.3.1) (subsection.8.3.1)] >> endobj 3045 0 obj << -/Kids [2960 0 R 2961 0 R 2962 0 R 2963 0 R 2964 0 R 2965 0 R] -/Limits [(page.16) (page.48)] +/Names [(subsection.8.3.2) 314 0 R (subsubsection.4.1.1.1) 74 0 R (subsubsection.4.1.1.2) 78 0 R (subsubsection.4.1.1.3) 82 0 R (subsubsection.4.1.1.4) 86 0 R (subsubsection.6.3.2.1) 214 0 R] +/Limits [(subsection.8.3.2) (subsubsection.6.3.2.1)] >> endobj 3046 0 obj << -/Kids [2966 0 R 2967 0 R 2968 0 R 2969 0 R 2970 0 R 2971 0 R] -/Limits [(page.49) (page.80)] +/Names [(subsubsection.7.2.1.1) 246 0 R (subsubsection.7.2.1.2) 250 0 R (subsubsection.7.3.3.1) 270 0 R (table.2.1) 611 0 R (table.6.1) 1296 0 R (table.6.2) 1409 0 R] +/Limits [(subsubsection.7.2.1.1) (table.6.2)] >> endobj 3047 0 obj << -/Kids [2972 0 R 2973 0 R 2974 0 R 2975 0 R 2976 0 R 2977 0 R] -/Limits [(page.81) (section.7.1)] +/Names [(table.6.3) 1446 0 R (table.6.4) 1541 0 R (table.7.1) 1893 0 R (table.7.2) 1677 0 R (table.7.3) 1984 0 R (table.8.1) 2069 0 R] +/Limits [(table.6.3) (table.8.1)] >> endobj 3048 0 obj << -/Kids [2978 0 R 2979 0 R 2980 0 R 2981 0 R 2982 0 R 2983 0 R] -/Limits [(section.7.2) (subfigure.4.4.8)] +/Names [(table.8.2) 2176 0 R (table.8.3) 2177 0 R (table.8.4) 2188 0 R (table.9.1) 2260 0 R (table.9.2) 2261 0 R (table.9.3) 2291 0 R] +/Limits [(table.8.2) (table.9.3)] >> endobj 3049 0 obj << -/Kids [2984 0 R 2985 0 R 2986 0 R 2987 0 R 2988 0 R 2989 0 R] -/Limits [(subfigure.4.4.9) (subfigure.5.7.2)] +/Names [(table.9.4) 2497 0 R (table.9.5) 2585 0 R (table.9.6) 2559 0 R (table.9.7) 2587 0 R (table.9.8) 2586 0 R] +/Limits [(table.9.4) (table.9.8)] >> endobj 3050 0 obj << -/Kids [2990 0 R 2991 0 R 2992 0 R 2993 0 R 2994 0 R 2995 0 R] -/Limits [(subfigure.5.7.3) (subfigure.7.1.2)] +/Kids [2854 0 R 2855 0 R 2856 0 R 2857 0 R 2858 0 R 2859 0 R] +/Limits [(AlgoLine1.1) (AlgoLine3.25)] >> endobj 3051 0 obj << -/Kids [2996 0 R 2997 0 R 2998 0 R 2999 0 R 3000 0 R 3001 0 R] -/Limits [(subfigure.7.10.1) (subfigure.7.14.5)] +/Kids [2860 0 R 2861 0 R 2862 0 R 2863 0 R 2864 0 R 2865 0 R] +/Limits [(AlgoLine3.26) (AlgoLine5.14)] >> endobj 3052 0 obj << -/Kids [3002 0 R 3003 0 R 3004 0 R 3005 0 R 3006 0 R 3007 0 R] -/Limits [(subfigure.7.14.6) (subfigure.7.7.4)] +/Kids [2866 0 R 2867 0 R 2868 0 R 2869 0 R 2870 0 R 2871 0 R] +/Limits [(AlgoLine5.15) (AlgoLine7.10)] >> endobj 3053 0 obj << -/Kids [3008 0 R 3009 0 R 3010 0 R 3011 0 R 3012 0 R 3013 0 R] -/Limits [(subfigure.7.7.5) (subsection.5.2.1)] +/Kids [2872 0 R 2873 0 R 2874 0 R 2875 0 R 2876 0 R 2877 0 R] +/Limits [(AlgoLine7.11) (AlgoLine8.3)] >> endobj 3054 0 obj << -/Kids [3014 0 R 3015 0 R 3016 0 R 3017 0 R 3018 0 R 3019 0 R] -/Limits [(subsection.5.2.2) (table.7.2)] +/Kids [2878 0 R 2879 0 R 2880 0 R 2881 0 R 2882 0 R 2883 0 R] +/Limits [(AlgoLine8.4) (Item.31)] >> endobj 3055 0 obj << -/Kids [3020 0 R 3021 0 R 3022 0 R] -/Limits [(table.7.3) (table.9.8)] +/Kids [2884 0 R 2885 0 R 2886 0 R 2887 0 R 2888 0 R 2889 0 R] +/Limits [(Item.32) (cite.1093941)] >> endobj 3056 0 obj << -/Kids [3023 0 R 3024 0 R 3025 0 R 3026 0 R 3027 0 R 3028 0 R] -/Limits [(AlgoLine1.1) 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b/THESE/these.toc @@ -2,58 +2,60 @@ \contentsline {chapter}{\numberline {1}Introduction}{9}{chapter.1} \contentsline {chapter}{\numberline {2}Les processeurs graphiques (GPU) NVidia\textregistered }{13}{chapter.2} \contentsline {section}{\numberline {2.1}Pourquoi ?}{13}{section.2.1} -\contentsline {section}{\numberline {2.2}Comment ?}{14}{section.2.2} -\contentsline {subsection}{\numberline {2.2.1}Le mat\IeC {\'e}riel}{14}{subsection.2.2.1} +\contentsline {section}{\numberline {2.2}Comment ?}{15}{section.2.2} +\contentsline {subsection}{\numberline {2.2.1}Le mat\IeC {\'e}riel}{15}{subsection.2.2.1} \contentsline {subsection}{\numberline {2.2.2}Le logiciel}{16}{subsection.2.2.2} \contentsline {subsection}{\numberline {2.2.3}L'occupancy}{17}{subsection.2.2.3} -\contentsline {chapter}{\numberline {3}Mod\IeC {\`e}les d'image et de bruits - notations}{23}{chapter.3} -\contentsline {section}{\numberline {3.1}Mod\IeC {\`e}le d'image bruit\IeC {\'e}e}{23}{section.3.1} -\contentsline {section}{\numberline {3.2}Mod\IeC {\`e}les de bruit}{23}{section.3.2} -\contentsline {subsection}{\numberline {3.2.1}Le bruit gaussien}{23}{subsection.3.2.1} -\contentsline {subsection}{\numberline {3.2.2}Le speckle}{24}{subsection.3.2.2} -\contentsline {subsection}{\numberline {3.2.3}Le bruit \FB@og sel et poivre \FB@fg {}}{24}{subsection.3.2.3} -\contentsline {subsection}{\numberline {3.2.4}Le bruit de Poisson}{25}{subsection.3.2.4} -\contentsline {chapter}{\numberline {4}Les techniques de r\IeC {\'e}duction de bruit}{27}{chapter.4} -\contentsline {section}{\numberline {4.1}Les techniques de r\IeC {\'e}duction de bruit}{27}{section.4.1} -\contentsline {subsection}{\numberline {4.1.1}Les op\IeC {\'e}rateurs de base}{28}{subsection.4.1.1} -\contentsline {subsubsection}{\numberline {4.1.1.1}Le filtre de convolution}{28}{subsubsection.4.1.1.1} -\contentsline {subsubsection}{\numberline {4.1.1.2}Le filtre m\IeC {\'e}dian}{29}{subsubsection.4.1.1.2} -\contentsline {subsubsection}{\numberline {4.1.1.3}Le filtre bilat\IeC {\'e}ral}{30}{subsubsection.4.1.1.3} -\contentsline {subsubsection}{\numberline {4.1.1.4}Les algorithmes de filtrage par dictionnaire}{30}{subsubsection.4.1.1.4} -\contentsline {subsection}{\numberline {4.1.2}Les algorithmes de filtrage par patches}{32}{subsection.4.1.2} -\contentsline {section}{\numberline {4.2}Les impl\IeC {\'e}mentations sur GPU des algorithmes de filtrage}{33}{section.4.2} -\contentsline {subsection}{\numberline {4.2.1}Le filtrage par convolution}{33}{subsection.4.2.1} -\contentsline {subsection}{\numberline {4.2.2}Le filtre m\IeC {\'e}dian}{34}{subsection.4.2.2} -\contentsline {subsection}{\numberline {4.2.3}Le filtre bilat\IeC {\'e}ral}{35}{subsection.4.2.3} -\contentsline {subsection}{\numberline {4.2.4}Les filtres par patches}{37}{subsection.4.2.4} -\contentsline {chapter}{\numberline {5}Les techniques de segmentation des images}{39}{chapter.5} -\contentsline {section}{\numberline {5.1}Les techniques de segmentation}{39}{section.5.1} -\contentsline {subsection}{\numberline {5.1.1}Analyse d'histogramme}{40}{subsection.5.1.1} -\contentsline {subsection}{\numberline {5.1.2}Partitionnement de graphe}{40}{subsection.5.1.2} -\contentsline {subsection}{\numberline {5.1.3}kernel-means, mean-shift et apparent\IeC {\'e}s}{43}{subsection.5.1.3} -\contentsline {subsection}{\numberline {5.1.4}Les contours actifs, ou snakes}{45}{subsection.5.1.4} -\contentsline {subsection}{\numberline {5.1.5}M\IeC {\'e}thodes hybrides}{47}{subsection.5.1.5} -\contentsline {section}{\numberline {5.2}Les impl\IeC {\'e}mentations des techniques de segmentation sur GPU}{47}{section.5.2} -\contentsline {subsection}{\numberline {5.2.1}Calcul d'histogramme}{48}{subsection.5.2.1} -\contentsline {subsection}{\numberline {5.2.2}Partitionnement de graphe}{48}{subsection.5.2.2} -\contentsline {subsection}{\numberline {5.2.3}K-means, mean-shift et apparent\IeC {\'e}s}{49}{subsection.5.2.3} -\contentsline {subsection}{\numberline {5.2.4}Level set et snakes}{52}{subsection.5.2.4} -\contentsline {subsection}{\numberline {5.2.5}Algorithmes hybrides}{54}{subsection.5.2.5} -\contentsline {section}{\numberline {5.3}Conclusion}{55}{section.5.3} -\contentsline {chapter}{\numberline {6}La segmentation par snake polygonal orient\IeC {\'e} r\IeC {\'e}gions}{59}{chapter.6} -\contentsline {section}{\numberline {6.1}Introduction}{59}{section.6.1} -\contentsline {section}{\numberline {6.2}Pr\IeC {\'e}sentation de l'algorithme}{59}{section.6.2} -\contentsline {subsection}{\numberline {6.2.1}Formulation}{59}{subsection.6.2.1} -\contentsline {subsection}{\numberline {6.2.2}Optimisation des calculs}{60}{subsection.6.2.2} -\contentsline {subsection}{\numberline {6.2.3}Impl\IeC {\'e}mentation s\IeC {\'e}quentielle}{62}{subsection.6.2.3} -\contentsline {subsection}{\numberline {6.2.4}Performances}{65}{subsection.6.2.4} +\contentsline {section}{\numberline {2.3}Synth\IeC {\`e}se des contraintes d'impl\IeC {\'e}mentation}{18}{section.2.3} +\contentsline {chapter}{\numberline {3}Mod\IeC {\`e}les d'image et de bruits - notations}{25}{chapter.3} +\contentsline {section}{\numberline {3.1}Mod\IeC {\`e}le d'image bruit\IeC {\'e}e}{25}{section.3.1} +\contentsline {section}{\numberline {3.2}Mod\IeC {\`e}les de bruit}{25}{section.3.2} +\contentsline {subsection}{\numberline {3.2.1}Le bruit gaussien}{25}{subsection.3.2.1} +\contentsline {subsection}{\numberline {3.2.2}Le speckle}{26}{subsection.3.2.2} +\contentsline {subsection}{\numberline {3.2.3}Le bruit \FB@og sel et poivre \FB@fg {}}{26}{subsection.3.2.3} +\contentsline {subsection}{\numberline {3.2.4}Le bruit de Poisson}{27}{subsection.3.2.4} +\contentsline {chapter}{\numberline {4}Les techniques de r\IeC {\'e}duction de bruit}{29}{chapter.4} +\contentsline {section}{\numberline {4.1}Les techniques de r\IeC {\'e}duction de bruit}{29}{section.4.1} +\contentsline {subsection}{\numberline {4.1.1}Les op\IeC {\'e}rateurs de base}{30}{subsection.4.1.1} +\contentsline {subsubsection}{\numberline {4.1.1.1}Le filtre de convolution}{30}{subsubsection.4.1.1.1} +\contentsline {subsubsection}{\numberline {4.1.1.2}Le filtre m\IeC {\'e}dian}{31}{subsubsection.4.1.1.2} +\contentsline {subsubsection}{\numberline {4.1.1.3}Le filtre bilat\IeC {\'e}ral}{32}{subsubsection.4.1.1.3} +\contentsline {subsubsection}{\numberline {4.1.1.4}Les algorithmes de filtrage par dictionnaire}{32}{subsubsection.4.1.1.4} +\contentsline {subsection}{\numberline {4.1.2}Les algorithmes de filtrage par patches}{34}{subsection.4.1.2} +\contentsline {section}{\numberline {4.2}Les impl\IeC {\'e}mentations sur GPU des algorithmes de filtrage}{35}{section.4.2} +\contentsline {subsection}{\numberline {4.2.1}Le filtrage par convolution}{35}{subsection.4.2.1} +\contentsline {subsection}{\numberline {4.2.2}Le filtre m\IeC {\'e}dian}{36}{subsection.4.2.2} +\contentsline {subsection}{\numberline {4.2.3}Le filtre bilat\IeC {\'e}ral}{37}{subsection.4.2.3} +\contentsline {subsection}{\numberline {4.2.4}Les filtres par patches}{39}{subsection.4.2.4} +\contentsline {chapter}{\numberline {5}Les techniques de segmentation des images}{41}{chapter.5} +\contentsline {section}{\numberline {5.1}Introduction}{41}{section.5.1} +\contentsline {section}{\numberline {5.2}Les techniques de segmentation orient\IeC {\'e}es r\IeC {\'e}gions}{41}{section.5.2} +\contentsline {subsection}{\numberline {5.2.1}Analyse d'histogramme}{42}{subsection.5.2.1} +\contentsline {subsection}{\numberline {5.2.2}Partitionnement de graphe}{42}{subsection.5.2.2} +\contentsline {subsection}{\numberline {5.2.3}kernel-means, mean-shift et apparent\IeC {\'e}s}{45}{subsection.5.2.3} +\contentsline {section}{\numberline {5.3}Les techniques de segmentation par contours actifs, ou snakes}{47}{section.5.3} +\contentsline {subsection}{\numberline {5.3.1}M\IeC {\'e}thodes hybrides}{49}{subsection.5.3.1} +\contentsline {section}{\numberline {5.4}Les impl\IeC {\'e}mentations des techniques de segmentation sur GPU}{49}{section.5.4} +\contentsline {subsection}{\numberline {5.4.1}Calcul d'histogramme}{50}{subsection.5.4.1} +\contentsline {subsection}{\numberline {5.4.2}Partitionnement de graphe}{50}{subsection.5.4.2} +\contentsline {subsection}{\numberline {5.4.3}K-means, mean-shift et apparent\IeC {\'e}s}{51}{subsection.5.4.3} +\contentsline {subsection}{\numberline {5.4.4}Level set et snakes}{54}{subsection.5.4.4} +\contentsline {subsection}{\numberline {5.4.5}Algorithmes hybrides}{56}{subsection.5.4.5} +\contentsline {section}{\numberline {5.5}Conclusion}{57}{section.5.5} +\contentsline {chapter}{\numberline {6}La segmentation par snake polygonal orient\IeC {\'e} r\IeC {\'e}gions}{61}{chapter.6} +\contentsline {section}{\numberline {6.1}Introduction}{61}{section.6.1} +\contentsline {section}{\numberline {6.2}Pr\IeC {\'e}sentation de l'algorithme}{61}{section.6.2} +\contentsline {subsection}{\numberline {6.2.1}Formulation}{61}{subsection.6.2.1} +\contentsline {subsection}{\numberline {6.2.2}Optimisation des calculs}{62}{subsection.6.2.2} +\contentsline {subsection}{\numberline {6.2.3}Impl\IeC {\'e}mentation s\IeC {\'e}quentielle}{64}{subsection.6.2.3} +\contentsline {subsection}{\numberline {6.2.4}Performances}{66}{subsection.6.2.4} \contentsline {section}{\numberline {6.3}Impl\IeC {\'e}mentation parall\IeC {\`e}le GPU du snake polygonal}{68}{section.6.3} \contentsline {subsection}{\numberline {6.3.1}Pr\IeC {\'e}-calculs des images cumul\IeC {\'e}es}{69}{subsection.6.3.1} -\contentsline {subsection}{\numberline {6.3.2}Calcul des contributions des segments}{71}{subsection.6.3.2} -\contentsline {subsubsection}{\numberline {6.3.2.1}Cas particulier des segments dont la pente $k$ v\IeC {\'e}rifie $|k|\leq 1$}{74}{subsubsection.6.3.2.1} -\contentsline {subsection}{\numberline {6.3.3}Performances}{74}{subsection.6.3.3} +\contentsline {subsection}{\numberline {6.3.2}Calcul des contributions des segments}{70}{subsection.6.3.2} +\contentsline {subsubsection}{\numberline {6.3.2.1}Cas particulier des segments dont la pente $k$ v\IeC {\'e}rifie $|k|\leq 1$}{75}{subsubsection.6.3.2.1} +\contentsline {subsection}{\numberline {6.3.3}Performances}{76}{subsection.6.3.3} \contentsline {subsection}{\numberline {6.3.4}D\IeC {\'e}termination intelligente du contour initial}{76}{subsection.6.3.4} -\contentsline {subsection}{\numberline {6.3.5}Conclusion}{77}{subsection.6.3.5} +\contentsline {subsection}{\numberline {6.3.5}Conclusion}{78}{subsection.6.3.5} \contentsline {chapter}{\numberline {7}R\IeC {\'e}duction de bruit par recherche des lignes de niveaux}{81}{chapter.7} \contentsline {section}{\numberline {7.1}Introduction}{81}{section.7.1} \contentsline {section}{\numberline {7.2}Pr\IeC {\'e}sentation de l'algorithme}{82}{section.7.2}