From 9f26a74684e7eb33d10029d02e3ea2759be5f183 Mon Sep 17 00:00:00 2001 From: Gilles Perrot Date: Tue, 15 Mar 2011 15:28:43 +0100 Subject: [PATCH] Added paper source --- doc/biblio.bib | 134 +++ doc/img/GPU_block.png | Bin 0 -> 164737 bytes doc/img/GPUaddsoms2cumuls.fig | 322 ++++++ doc/img/GPUaddsoms2cumuls.pdf | Bin 0 -> 7081 bytes doc/img/GPUaddsoms2cumuls.pdf_t | 62 + doc/img/GPUcumuls.fig | 331 ++++++ doc/img/GPUcumuls.pdf | Bin 0 -> 6894 bytes doc/img/GPUcumuls.pdf_t | 59 + doc/img/GPUscansomblocs.fig | 202 ++++ doc/img/GPUscansomblocs.pdf | Bin 0 -> 5470 bytes doc/img/GPUscansomblocs.pdf_t | 30 + doc/img/SAVE.fig | 244 ++++ doc/img/cochon_b_entier.jpg | Bin 0 -> 815518 bytes doc/img/cochon_init.png | Bin 0 -> 192748 bytes doc/img/cochon_it1.png | Bin 0 -> 208186 bytes doc/img/cochon_it2_1.png | Bin 0 -> 209796 bytes doc/img/cochon_it2_2.png | Bin 0 -> 210489 bytes doc/img/cochon_it4.png | Bin 0 -> 213499 bytes doc/img/cochon_petit_detail_16segments.jpg | Bin 0 -> 2737 bytes 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doc/img/contribs_segments.pdf_t create mode 100644 doc/img/data_profile_cpu.png create mode 100644 doc/img/data_profile_cpu.txt create mode 100644 doc/img/detail_segments.fig create mode 100644 doc/img/detail_segments.pdf create mode 100644 doc/img/detail_segments.pdf_t create mode 100644 doc/img/topologie.fig create mode 100644 doc/img/topologie.pdf create mode 100644 doc/img/topologie.pdf_t create mode 100644 doc/img/tripix.fig create mode 100644 doc/img/tripix.pdf create mode 100644 doc/img/tripix.pdf_t create mode 100644 doc/snake_gpu.aux create mode 100644 doc/snake_gpu.bbl create mode 100644 doc/snake_gpu.blg create mode 100644 doc/snake_gpu.log create mode 100644 doc/snake_gpu.pdf create mode 100644 doc/snake_gpu.tex diff --git a/doc/biblio.bib b/doc/biblio.bib new file mode 100644 index 0000000..1d370d2 --- /dev/null +++ b/doc/biblio.bib @@ -0,0 +1,134 @@ +@InProceedings{ AllainBG08, + author = "Marc Allain and Nicolas Bertaux and Fr{\'e}d{\'e}ric Galland", + title = "Nonparametric Level-Set Segmentation Based on the Minimization of the Stochastic Complexity", + booktitle = "ACIVS", + year = "2008", + pages = "506--517", + ee = "http://dx.doi.org/10.1007/978-3-540-88458-3_46", + crossref = "DBLP:conf/acivs/2008", + bibsource = "DBLP, http://dblp.uni-trier.de" +} + +@Article{ KassWT88, + author = "Michael Kass and Andrew P. Witkin and Demetri Terzopoulos", + title = "Snakes: Active contour models", + journal = "International Journal of Computer Vision", + volume = "1", + number = "4", + year = "1988", + pages = "321--331", + ee = "http://dx.doi.org/10.1007/BF00133570", + bibsource = "DBLP, http://dblp.uni-trier.de" +} + +@Article{ XuP98, + author = "Chenyang Xu and Jerry L. Prince", + title = "Snakes, shapes, and gradient vector flow", + journal = "IEEE Transactions on Image Processing", + volume = "7", + number = "3", + year = "1998", + pages = "359--369", + bibsource = "DBLP, http://dblp.uni-trier.de", + ee = "http://dx.doi.org/10.1109/83.661186" +} + +@Article{ GallandBR03, + author = "Fr{\'e}d{\'e}ric Galland and Nicolas Bertaux and Philippe R{\'e}fr{\'e}gier", + title = "Minimum description length synthetic aperture radar image segmentation", + journal = "IEEE Transactions on Image Processing", + volume = "12", + number = "9", + year = "2003", + pages = "995--1006", + ee = "http://dx.doi.org/10.1109/TIP.2003.816005", + bibsource = "DBLP, http://dblp.uni-trier.de" +} + +@Article{ Brunett, + location = "http://www.scientificcommons.org/41680702", + title = "GPU-Accelerated Contour Extraction on Large Images Using Snakes", + author = "Enrico {Dipl.-Inf. Kienel} and Guido {Prof. Dr. Brunnett}", + year = "2009", + keywords = "Active Contours, GPGPU, Gradient Vector Flow, Image Segmentation, Snakes, Tiling, 004", + abstract = "Abstract. Active contours have been proven to be a powerful semiautomatic image segmentation approach, that seems to cope with many applications and different image modalities. However, they exhibit inherent drawbacks, including the sensibility to contour initialization due to the limited capture range of image edges and problems with concave boundary regions. The Gradient Vector Flow replaces the traditional image force and provides an enlarged capture range as well as enhanced concavity extraction capabilities, but it involves an expensive computational effort and considerably increased memory requirements at the time of computation. In this paper, we present an enhancement of the active contour model to facilitate semiautomatic contour detection in huge images. We propose a tile-based image decomposition accompanying an image force computation scheme on demand in order to minimize both computational and memory requirements. We show an efficient implementation of this approach on the basis of general purpose GPU processing providing for continuous active contour deformation without a considerable delay.", + publisher = {TU Chemnitz, Fakult{\"a}t f{\"u}r Informatik}, + url = "http://archiv.tu-chemnitz.de/pub/2009/0035", + institution = "MONARCH - Dokumenten- und Publikationsservice [http://archiv.tu-chemnitz.de/cgi-bin/interfaces/oai/oai2.pl] (Germany)" +} + +@Article{ ChesnaudRB99, + author = "Christophe Chesnaud and Philippe R{\'e}fr{\'e}gier and Vlady Boulet", + title = "Statistical Region Snake-Based Segmentation Adapted to Different Physical Noise Models", + journal = "IEEE Trans. Pattern Anal. Mach. Intell.", + volume = "21", + number = "11", + year = "1999", + pages = "1145--1157", + ee = "http://www.computer.org/tpami/tp1999/i1145abs.htm", + bibsource = "DBLP, http://dblp.uni-trier.de" +} + +@Article{ GermainR01, + author = "Olivier Germain and Philippe R{\'e}fr{\'e}gier", + title = "Statistical active grid for segmentation refinement", + journal = "Pattern Recognition Letters", + volume = "22", + number = "10", + year = "2001", + pages = "1125--1132", + bibsource = "DBLP, http://dblp.uni-trier.de" +} + +@Article{ Ruch01, + author = "Olivier Ruch and Philippe R{\'e}fr{\'e}gier", + title = "Minimal-complexity segmentation with a polygonal snake adapted to different optical noise models", + journal = "Optics Letters", + volume = "26", + number = "13", + month = "july", + year = "2001", + ee = "http://www.computer.org/tpami/tp1999/i1145abs.htm", + bibsource = "DBLP, http://dblp.uni-trier.de" +} + +@TechReport{ BlellochTR90, + author = "Guy~E. Blelloch", + title = "Prefix Sums and Their Applications", + institution = "School of Computer Science, Carnegie Mellon University", + number = "CMU-CS-90-190", + month = nov, + year = 1990 +} + +@InBook{ Harris07, + author = "Mark Harris and Shubhabrata Sengupta and John D. Owens", + title = "Gpu gems 3", + year = "2007", + isbn = "9780321545428", + edition = "first", + publisher = "Addison-Wesley Professional", + chapter = "39 - Parallel Prefix Sum with CUDA" +} + +@Manual{ CUDAPG, + title = "NVIDIA CUDA C Programming Guide v3.1.1", + organization = "NVIDIA Corporation", + month = "7", + year = "2010" +} + +@Manual{ CUDAFC, + title = "NVIDIA Fermi Compatibility Guide", + organization = "NVIDIA Corporation", + month = "7", + year = "2010" +} + +@Manual{ CUDAFT, + title = "NVIDIA Fermi Tuning Guide", + organization = "NVIDIA Corporation", + month = "7", + year = "2010" +} + diff --git a/doc/img/GPU_block.png b/doc/img/GPU_block.png new file mode 100644 index 0000000000000000000000000000000000000000..fd3233eebdec967f706fdc5ffe9bf99f71bfaea5 GIT binary patch literal 164737 zcmeFZhg*|b*EfozBV&VSbQI~MfJh&D2gim1AxiJ4lt>LN1PBQ_j*Y6JNw*M?8l*#j zs7No78ahaa0Fe>`2}!;k-{<+hIp1}?f53arxxMz4aOci0tNhk)t-a&(TV_TljtU*+ 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GPU kernel parallel process.}}{8}} +\@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces GPU (C2050, sm20) vs CPU timings.}}{8}} +\newlabel{tabresults}{{I}{8}} +\newlabel{secConclusion}{{VII}{8}} +\@writefile{toc}{\contentsline {section}{\numberline {VII}Conclusion}{8}} +\@writefile{toc}{\contentsline {section}{References}{8}} diff --git a/doc/snake_gpu.bbl b/doc/snake_gpu.bbl new file mode 100644 index 0000000..92a7ea5 --- /dev/null +++ b/doc/snake_gpu.bbl @@ -0,0 +1,71 @@ +% Generated by IEEEtran.bst, version: 1.13 (2008/09/30) +\begin{thebibliography}{10} +\providecommand{\url}[1]{#1} +\csname url@samestyle\endcsname +\providecommand{\newblock}{\relax} +\providecommand{\bibinfo}[2]{#2} +\providecommand{\BIBentrySTDinterwordspacing}{\spaceskip=0pt\relax} +\providecommand{\BIBentryALTinterwordstretchfactor}{4} +\providecommand{\BIBentryALTinterwordspacing}{\spaceskip=\fontdimen2\font plus +\BIBentryALTinterwordstretchfactor\fontdimen3\font minus + \fontdimen4\font\relax} +\providecommand{\BIBforeignlanguage}[2]{{% +\expandafter\ifx\csname l@#1\endcsname\relax +\typeout{** WARNING: IEEEtran.bst: No hyphenation pattern has been}% +\typeout{** loaded for the language `#1'. Using the pattern for}% +\typeout{** the default language instead.}% +\else +\language=\csname l@#1\endcsname +\fi +#2}} +\providecommand{\BIBdecl}{\relax} +\BIBdecl + +\bibitem{KassWT88} +M.~Kass, A.~P. Witkin, and D.~Terzopoulos, ``Snakes: Active contour models,'' + \emph{International Journal of Computer Vision}, vol.~1, no.~4, pp. 321--331, + 1988. + +\bibitem{Ruch01} +O.~Ruch and P.~R{\'e}fr{\'e}gier, ``Minimal-complexity segmentation with a + polygonal snake adapted to different optical noise models,'' \emph{Optics + Letters}, vol.~26, no.~13, july 2001. + +\bibitem{XuP98} +C.~Xu and J.~L. Prince, ``Snakes, shapes, and gradient vector flow,'' + \emph{IEEE Transactions on Image Processing}, vol.~7, no.~3, pp. 359--369, + 1998. + +\bibitem{ChesnaudRB99} +C.~Chesnaud, P.~R{\'e}fr{\'e}gier, and V.~Boulet, ``Statistical region + snake-based segmentation adapted to different physical noise models,'' + \emph{IEEE Trans. Pattern Anal. Mach. Intell.}, vol.~21, no.~11, pp. + 1145--1157, 1999. + +\bibitem{AllainBG08} +M.~Allain, N.~Bertaux, and F.~Galland, ``Nonparametric level-set segmentation + based on the minimization of the stochastic complexity,'' in \emph{ACIVS}, + 2008, pp. 506--517. + +\bibitem{Brunett} +\BIBentryALTinterwordspacing +E.~{Dipl.-Inf. Kienel} and G.~{Prof. Dr. Brunnett}, ``Gpu-accelerated contour + extraction on large images using snakes,'' 2009. [Online]. Available: + \url{http://archiv.tu-chemnitz.de/pub/2009/0035} +\BIBentrySTDinterwordspacing + +\bibitem{CUDAPG} +\emph{NVIDIA CUDA C Programming Guide v3.1.1}, NVIDIA Corporation, 7 2010. + +\bibitem{CUDAFT} +\emph{NVIDIA Fermi Tuning Guide}, NVIDIA Corporation, 7 2010. + +\bibitem{CUDAFC} +\emph{NVIDIA Fermi Compatibility Guide}, NVIDIA Corporation, 7 2010. + +\bibitem{Harris07} +M.~Harris, S.~Sengupta, and J.~D. Owens, \emph{Gpu gems 3}, 1st~ed.\hskip 1em + plus 0.5em minus 0.4em\relax Addison-Wesley Professional, 2007, ch. 39 - + Parallel Prefix Sum with CUDA. + +\end{thebibliography} diff --git a/doc/snake_gpu.blg b/doc/snake_gpu.blg new file mode 100644 index 0000000..69feba7 --- /dev/null +++ b/doc/snake_gpu.blg @@ -0,0 +1,57 @@ +This is BibTeX, Version 0.99c (TeX Live 2009/Debian) +The top-level auxiliary file: snake_gpu.aux +The style file: IEEEtran.bst +Reallocated wiz_functions (elt_size=4) to 6000 items from 3000. +Database file #1: IEEEabrv.bib +Database file #2: biblio.bib +A bad cross reference---entry "AllainBG08" +refers to entry "DBLP:conf/acivs/2008", which doesn't exist +Warning--I didn't find a database entry for "DBLP:conf/acivs/2008" +-- IEEEtran.bst version 1.13 (2008/09/30) by Michael Shell. +-- http://www.michaelshell.org/tex/ieeetran/bibtex/ +-- See the "IEEEtran_bst_HOWTO.pdf" manual for usage information. +Warning--empty journal in Brunett + +Done. +You've used 10 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./img/cochon_petit_it4.jpg Graphic file (type jpg) + + +Underfull \vbox (badness 4621) has occurred while \output is active [] + + [2 <./img/cochon_petit_init.jpg> <./img/cochon_petit_it1.jpg> <./img/cochon_pe +tit_it2.jpg> <./img/cochon_petit_it4.jpg>] +Underfull \hbox (badness 10000) in paragraph at lines 539--540 +[]\OT1/pcr/m/n/10 compute_pixels_coordinate() \OT1/ptm/m/n/10 which is + [] + +<./img/data_profile_cpu.png, id=25, 695.59875pt x 420.97275pt> +File: ./img/data_profile_cpu.png Graphic file (type png) + + + +LaTeX Warning: `h' float specifier changed to `ht'. + + +Underfull \hbox (badness 2334) in paragraph at lines 548--553 +\OT1/ptm/m/n/10 that func-tion \OT1/pcr/m/n/10 compute_segment_contribution() + [] + + +Underfull \hbox (badness 1824) in paragraph at lines 548--553 +\OT1/ptm/m/n/10 the func-tion \OT1/pcr/m/n/10 compute_cumulated_images() \OT1/p +tm/m/n/10 costs + [] + +<./img/GPU_block.png, id=27, 2719.15875pt x 1077.02374pt> +File: ./img/GPU_block.png Graphic file (type png) + + [3 <./img/data_profile_cpu.png>] +(./img/GPUcumuls.pdf_t +File: img/GPUcumuls.pdf Graphic file (type pdf) + + +LaTeX Font Info: Try loading font information for OT1+phv on input line 14. + (/usr/share/texmf-texlive/tex/latex/psnfss/ot1phv.fd +File: ot1phv.fd 2001/06/04 scalable font definitions for OT1/phv. +) +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <12> on input line 14. +) +[4 <./img/GPU_block.png>] (./img/GPUscansomblocs.pdf_t + +File: img/GPUscansomblocs.pdf Graphic file (type pdf) + +) (./img/GPUaddsoms2cumuls.pdf_t + +File: img/GPUaddsoms2cumuls.pdf Graphic file (type pdf) + +) (./img/topologie.pdf_t + +File: img/topologie.pdf Graphic file (type pdf) + +LaTeX Font Info: Calculating math sizes for size <14> on input line 14. +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <14> on input line 14. +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <9.79996> on input line 14. +) + +LaTeX Warning: `h' float specifier changed to `ht'. + +[5 <./img/GPUcumuls.pdf>] +Underfull \vbox (badness 10000) has occurred while \output is active [] + + +(./img/contribs_segments.pdf_t + +File: img/contribs_segments.pdf Graphic file (type pdf) + +) [6 <./img/GPUscansomblocs.pdf> <./img/GPUaddso +ms2cumuls.pdf> <./img/topologie.pdf>] (./img/tripix.pdf_t + +File: img/tripix.pdf Graphic file (type pdf) + ) + +LaTeX Warning: `h' float specifier changed to `ht'. + + +Underfull \hbox (badness 2799) in paragraph at lines 786--786 +[]\OT1/ptm/b/n/10 Algorithm 3: \OT1/ptm/m/n/10 Par-ralel GPU al-go-rithm : out- +lines. + [] + + +LaTeX Warning: `h' float specifier changed to `ht'. + +[7 <./img/contribs_segments.pdf> <./img/tripix.pdf>] (./snake_gpu.bbl) + +** Conference Paper ** +Before submitting the final camera ready copy, remember to: + + 1. Manually equalize the lengths of two columns on the last page + of your paper; + + 2. Ensure that any PostScript and/or PDF output post-processing + uses only Type 1 fonts and that every step in the generation + process uses the appropriate paper size. + +[8] (./snake_gpu.aux) ) +Here is how much of TeX's memory you used: + 4161 strings out of 493848 + 62117 string characters out of 1152824 + 150152 words of memory out of 3000000 + 7379 multiletter control sequences out of 15000+50000 + 52358 words of font info for 94 fonts, out of 3000000 for 9000 + 714 hyphenation exceptions out of 8191 + 39i,21n,45p,287b,512s stack positions out of 5000i,500n,10000p,200000b,50000s +{/usr/share/texmf-texlive/fonts/enc/dvips/base/8r.enc} +Output written on snake_gpu.pdf (8 pages, 928099 bytes). +PDF statistics: + 161 PDF objects out of 1000 (max. 8388607) + 0 named destinations out of 1000 (max. 500000) + 61 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/doc/snake_gpu.pdf b/doc/snake_gpu.pdf new file mode 100644 index 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display the relative costs of the most time-consumming functions. +It appears that more than 80\% of the total execution time is always spent by only three functions~: +\begin{itemize} + \item \texttt{compute\_segment\_contribution()} which is responsible for point \ref{CPUcontrib_segments} above, + \item \texttt{compute\_cumulated\_images()} which computes the 3 lookup tables at the very beginning, + \item \texttt{compute\_pixels\_coordinate()} which is called by \texttt{compute\_segment\_contribution()}. +\end{itemize} + +\begin{figure}[h] + \centering + \includegraphics[width=0.9\linewidth, height=0.5\linewidth]{./img/data_profile_cpu.png} + \caption{\label{CPUprofile}the three most-consumming functions for various image sizes} +\end{figure} + +Measurements have been performed for several image sizes from 15~MPixels (about 3900 x 3900) +to 144 MPixels (about 12000 x 12000). On the one hand, we can notice that function \texttt{compute\_segment\_contribution()} always lasts more than 45\% of the total running time, and even +more when the image gets larger. +On the other hand, the function \texttt{compute\_cumulated\_images()} costs more than 23\%, decreasing with image size, while function \texttt{compute\_pixels\_coordinate()} always takes around 6\%. +It confirms that the need for parallelization resides in line \ref{kernelPLH} and line \ref{cumuls} of Algorithm \ref{cpualgo} as they contain every call to those three functions. + +The following sections detail how we managed to implement these time-consumming functions in parallel, but +a brief reminder on GPU's recent architecture is presented first. + + + +\section{\label{GPUgeneralites}NVidia's GPU architecture} +GPUs are multi-core, multi-threaded processors, optimized for highly parallel computation. Their design focuses on SIMT model by devoting +more transistors to data processing rather than data-caching and flow control \cite{CUDAPG}. + +For example, Figure \ref{GPUC1060} shows a Tesla C1060 with its 4GB of global memory and 30 SM processors, each including : +\begin{itemize} + \item 8 Scalar Processors (SP) + \item a Floating Point Unit (FPU) + \item a parallel execution unit (SIMT) that runs threads by warps of 32. + \item 16KB of shared memory, organized in 16 banks of 32 bits words +\end{itemize} +Nvidia uses a parameter called the \emph{compute capability} of each GPU model. Its value is composed of a major number and a minor number ; for example the C1060 is a sm13 GPU (major=1 minor=3) +and C2050 is a sm20 GPU. + +\begin{figure*}[htbp] + \centering + \includegraphics[width=0.7\linewidth]{./img/GPU_block.png} + \caption{\label{GPUC1060}schematic diagram of GPU's internal architecture} +\end{figure*} + +The recent Fermi cards (eg. C2050,) have improved performances by supplying more shared memory in a 32 banks array, a second execution +unit and several managing +capabilities on both the shared memory and level 1 cache memory ( \cite{CUDAPG}, \cite{CUDAFT}, \cite{CUDAFC}. +However, writing efficient code for such architectures is not obvious, as re-serialization must be avoided as much as possible. Thus, when designing, one must +keep a few key points in mind : +\begin{itemize} + \item CUDA model organizes threads by a) threads blocks in which synchronization is possible, b) a grid of blocks with no possible synchronization + between blocks. + \item there is no way to know in what order the blocks are to be scheduled during one single kernel execution. + \item data must be kept in GPU memory, to reduce the overhead due to copying between CPU and GPU memories. + \item the total amount of threads running the same computation must be maximized. + \item the number of execution branches inside a block should be reduced as much as possible. + \item global memory accesses should be coalescent, \emph{ie}. memory accesses done by physically parallel threads (16 at a time) must be consecutive and contained in a 128 Bytes range. + \item shared memory is organized by 16 x 32 bits wide banks. To avoid bank conflicts, each parallel thread (16 at a time) must access a different bank. +\end{itemize} + +All the above charasteristics make it always a quite constrained problem to solve when designing a GPU code. +%detailler +Moreover, a non suited code would probably run even slower on GPU than on CPU due to the automatic serialization which would be done at run time. +%% + +\section{\label{GPUimplementation}GPU implementation} + +In the implementation described below, pre-computations and proper segmentation are discussed separately. +To keep data in GPU memory, the whole computation is assigned to the GPU. CPU still hosts : +\begin{itemize} + \item data reading from HDD + \item data writing on HDD if needed + \item main loops control (corresponding to lines \ref{loopnewnodes} and \ref{loopmovenodes} of Algorithm \ref{cpualgo}) +\end{itemize} + +It must be noticed that controlling these loops is achieved with only a very small amount of data being transferred between host (CPU) and device (GPU), +which does not produce high overhead. \\ +Morever, the structures described below need 20 Bytes per pixel of the image to process (plus an offset of about 50~MByte). +It defines the maximum image size we can accept : approximately 150 M Pixels. + +\subsection{Pre-computations} +To replace 2D sums by 1D sums, Chesnaud \textit{et al.} \cite{ChesnaudRB99} have shown that the three matrices below should be computed : +$$C_1(i,j) = \sum_{k=0}^{k=j} (1+k)$$ +$$C_z(i,j) = \sum_{k=0}^{k=j} z(i,k)$$ and +$$C_{z^2}(i,j) = \sum_{k=0}^{k=j} z^2(i,k)$$ +Where $z(i,k)$ is the gray level of pixel of coordinate $(i,j)$, so that $C_1$, $C_z$ and $C_{z^2}$ are the same size as image $I$. + +\begin{figure*}[htbp] + \centering + \resizebox{0.8\linewidth}{0.3\linewidth}{\input{./img/GPUcumuls.pdf_t}} + \caption{\label{GPUcumuls}\texttt{compute\_blocks\_prefixes()} details.} +\end{figure*} + +\medskip +First, we chose not to generate $C_1(i,j)$, which requires that values should be computed when needed, but saves global memory and does not lead to any overhead. +The computation of $C_{z}$ and $C_{z^2}$ easily decomposes into series of \emph{inclusive prefixsums} \cite{Harris07}. +However, by keeping the \emph{1 thread per pixel} rule, as the total number of threads that can be run in a grid cannot exceed $2^{25}$ (Cf. \cite{CUDAPG}), +slicing is necessary for images exceeding a size threshold which can vary according to the GPU model (e.g. 33 MPix for sm13 GPU, eg. C1060). +It's quite easy to do, but it leads to a small overhead as the process requires multiple calls to one kernel. +Slicing can be done in two ways : +\begin{itemize} + \item all slices are of the same size (balanced) + \item slices fit the maximum size allowed by the GPU, leaving one smaller slice at the end of the process (full-sized). +\end{itemize} +The balanced slice option has proved to run faster.\\ +For example : if a given image has 9000 lines and the GPU can process up to 4000 lines at a time, it's faster to run 3 times with 3000 lines rather than twice with +4000 and once with 1000. + +As the sums in $C_z$ and $C_{z^2}$ are row-wide, it is easy to see that every block-wide sum will be needed before being able to use it in the global sum. +But as mentioned earlier, the scheduling of blocks must be considered as random. +So, in order to ensure synchronizations, each row of the original image is then treated by three different kernels : +\begin{itemize} + \item \texttt{compute\_blocks\_prefixes()}. + \item \texttt{scan\_blocksums()}. + \item \texttt{add\_sums2prefixes()}. +\end{itemize} +Figures \ref{GPUcumuls}, \ref{GPUscansomblocs} and \ref{GPUaddsoms2cumuls} show relevant data structures for a given row $i$ of $I$. +We assume that each thread block runs $bs$ threads in parallel and each row of $C_z$ needs $n$ blocks to cover its $L$ pixels. + +Figure \ref{GPUcumuls} shows the details of the process for row $i$ of the original image $I$, already stored in GPU global memory. +Operands are first copied into GPU shared memory for efficiency reasons. +An inclusive prefixsum is then performed inside each independant thread block. +At this point, only the first shared memory block contains the final values. Its last element contains the sum of all +elements in the corresponding block of $I$. +In order to obtain the right values for the row $i$ of $C_z$, every element value in the other blocks must then be summed with an offset value. +This offset value is the sum of all element values in every corresponding previous block of row $i$. + +As the scheduling of blocks is fully unpredictable, the necessary intermediate results have to be stored in GPU global memory before exiting from kernel. +Each element of the prefixsums in GPU shared memory has been stored in its corresponding position in $C_z$ (GPU global mem), +along with the vector of block sums which will be passed later to the next kernel \texttt{scan\_blocksums()}. + +The kernel \texttt{scan\_blocksums()} (Figure \ref{GPUscansomblocs}) only makes an exclusive prefixsum on the vector of block sums described above. +The result is a vector containing, at index $x$, the value to be added to every element of block $x$ in each line of $C_z$. + +This summing is done in shared memory by kernel \texttt{add\_sums2prefixes()} as described by Figure \ref{GPUaddsoms2cumuls}. + +The values of $C_{z^2}$ are obtained together with those of $C_{z}$ and in exactly the same way. +For publishing reasons, figures do not show the $C_{z^2}$ part of structures. + + + +\begin{figure*}[htbp] + \centering + \resizebox{0.6\linewidth}{0.2\linewidth}{\input{./img/GPUscansomblocs.pdf_t}} + \caption{\label{GPUscansomblocs}\texttt{scan\_blocksums()} details.} +\end{figure*} + +\begin{figure*}[htbp] + \centering + \resizebox{0.7\linewidth}{0.4\linewidth}{\input{./img/GPUaddsoms2cumuls.pdf_t}} + \caption{\label{GPUaddsoms2cumuls}\texttt{add\_sums2prefixes()} details.} +\end{figure*} + +With this implementation, speedups are quite significant (Table \ref{tabresults}). Moreover, the larger the image, +the higher the speedup is, as the step-complexity of the sequential algorithm is of $O(N^2)$ and $O(N\log(N))$ for the parallel version. +Even higher speedups are achieved by adapting the code to specific-size images, especially when the number of columns is a power of 2. This avoids +inactive threads in the grid, and thus improves efficiency. +However, on sm13 GPUs, these computations are made with a 2-way bank conflict as sums are based on 64-bit words, thus creating overhead. + + +\subsection{Segment contributions} +The choice made for this implementation has been to keep the \emph{1 thread per pixel} rule for the main kernels. +Of course, some reduction stages need to override this principle and will be pointed out. + +As each of the $N_n$ nodes of the snake $S_{n,l}$ may move to one of the eight neighbor positions as shown in \emph{Figure \ref{GPUtopo}}, +there is $16 N_n$ segments whose contribution has to be estimated. +The best combination is then chosen to obtain $S_{n,l+1}$ (Figure \ref{GPUtopo}). +Segment contributions are computed in parallel by kernel \texttt{GPU\_compute\_segments\_contrib()}. + +\begin{figure}[h] + \centering + \resizebox{0.9\linewidth}{0.81\linewidth}{\input{./img/topologie.pdf_t}} + \caption{\label{GPUtopo}topology around nodes} +\end{figure} + +The grid parameters for this kernel are determined according to the size of the longest segment $npix_{max}$. +If $bs_{max}$ is the maximum theoritical blocksize that a GPU can accept, +\begin{itemize} + \item the block size $bs$ is taken as + \begin{itemize} + \item $npix_{max}$'s next power of two if \\${npix_{max} \in [33 ; bs_{max} ] }$ + \item 32 if ${npix_{max} < 32 }$ + \item $bs_{max}$ if ${npix_{max} > 256 }$ + \end{itemize} + \item the number of threads blocks assigned to each segment, $N_{TB} = \frac{npix_{max} + bs -1 }{bs}$ +\end{itemize} +Our implementation makes intensive use of shared memory and does not allow the use of the maximum theoritical blocksizes +(512 for sm13, 1024 for sm20, see \cite{CUDAFT} and \cite{CUDAPG}). +Instead we set $bs_{max}^{sm13} = 256$ and $bs_{max}^{sm20} = 512$. +Anyway, testing has shown that most often, the best value is 256 for both \textit{sm13} and \textit{sm20} GPU's. + +\begin{figure*}[htbp] + \centering + \resizebox{0.6\linewidth}{0.35\linewidth}{\input{./img/contribs_segments.pdf_t}} + \caption{\label{contribs_segments}structure for segments contributions computation. Gray symbols help to locate inactive threads as opposed to black + ones that figure active threads.} +\end{figure*} + +Then \texttt{GPU\_compute\_segments\_contrib()} computes in parallel : +\begin{itemize} + \item every pixel coordinates for all $16 N_n$ segments. Since the snake is only read in one direction, we have been able + to use a very simple parallel algorithm instead of Bresenham's. +It is based on the slope $k$ of each segment~: one pixel per row if $|k|>1$, one pixel per column otherwise. + \item every pixel contribution by reading the corresponding values in the lookup tables. + \item every thread blocks sums of individual pixel contributions by running a \textit{reduction} stage for each block. +\end{itemize} +The top line of Figure \ref{contribs_segments} shows the base data structure in GPU shared memory which is relative to one segment. +We concatenate the single segment structure as much as necessary to create a large vector representing every pixel of every test segment. +As each segment has a different size (most often different from any power of two), there is a non-neglectable number of inactive threads scattered in the whole structure. +Two stages are processed separately : one for all even nodes and another one for odd nodes, +as shown in the two bottom lines of Figure \ref{contribs_segments}. + + +The process is entirely done in shared memory ; only a small amount of data needs to be stored in global memory for each segment~: +\begin{itemize} + \item the coordinates of its middle point, in order to be able to add nodes easily if needed. + \item the coordinates of its first and last two points, to compute the slope at each end of the segment. +\end{itemize} +The five values above are part of the weighing coefficients determination for each segment and node. + + The \texttt{GPU\_sum\_contribs()} takes the blocks sums obtained by \texttt{GPU\_compute\_segments\_contrib()} and computes a second stage parallel summing to provide +the $16 N_n$ segment contributions. + +\subsection{Segments with a slope $k$ such as $|k|\leq1$} +Such a segment is treated with 1 thread per column and consequently, it often has more than one pixel per row as shown by Figure \ref{tripix}. +In an image row, consecutive pixels which belong to the target define an interval which can only have one low and one high ends +That's why, on each row, we choose to consider only the contributions of the innermost pixels. +This selection is also done inside \texttt{GPU\_compute\_segments\_contrib()} when reading the lookup tables for each pixel contribution. +We simply set a null contribution for pixels that need to be ignored. +\begin{figure}[h] + \centering + \resizebox{0.75\linewidth}{0.35\linewidth}{\input{./img/tripix.pdf_t}} + \caption{\label{tripix}Zoom on part a of segment with $|k| < 1$, at pixel level.} +\end{figure} + + +\subsection{Parameters estimation} +A \texttt{GPU\_compute\_PLH()} kernel computes in parallel : +\begin{itemize} + \item every $8N_n$ vector of parameters values corresponding to each possible next state of the snake. Summing is done in shared memory but relevant + data for these operations are stored in global memory. + \item every associated pseudo likelihood value. + \item node substitutions when better PLH have been found and if it does not lead to segments crossing. +\end{itemize} + +\subsection{End of segmentation} +Segmentation is considered achieved out when no other node can be added to the snake (Algorithm \ref{gpualgosimple}). +A very simple GPU kernel adds every possible node and returns the number it added. + +\begin{algorithm}[h] +\label{gpualgosimple} +\caption{Parralel GPU algorithm : outlines. \texttt{<<<...>>>} indicates a GPU kernel parallel process.} +\SetNlSty{textbf}{}{:} + load images\; + transfer image from CPU to GPU\; + \texttt{<<<}compute the 2 cumulated images\texttt{>>>}\; + \texttt{<<<}initialize the snake\texttt{>>>}\; + \Repeat(\tcc*[f]{iteration level}){no more node can be added}{ + \Repeat(\tcc*[f]{step level}){no more node can be moved}{ + \texttt{<<<}find best neighbor snake\texttt{>>>}\; + \texttt{<<<}adjust node's positions\texttt{>>>}\; + transfer the number of moves achieved from GPU memory to CPU memory. + } + \texttt{<<<}Add nodes\texttt{>>>}\; + transfert the number of nodes added from GPU memory to CPU memory. + } +\end{algorithm} + +\section{\label{secSpeedups}Speedups} +The CPU (SSE) implementation by N. Bertaux from the PhyTI team, based on \cite{AllainBG08} has been our reference to ensure segmentation's quality and to estimate speedups. +Results are given in Table \ref{tabresults}. +CPU timings were measured on an Intel Xeon E5530-2.4GHz with 12Go RAM (LIFC cluster). +GPU timings were obtained on a C2050 GPU with 3GB RAM (adonis-11.grenoble.grid5000.fr).\\ +Execution times reported are means on ten executions. +%Measurements on CPU may vary more than on GPU. So CPU results given in \ref{tabresults} are near the fastest values we observed. +The image of figure \ref{fig:labelinit} (scaled down for printing reasons) is a 16-bit gray level photo from PhyTI team, +voluntarily noisy for testing reasons. The contrast has been enhanced for better viewing. + +We separately give the timings of pre-computations as they are a very general purpose piece of code. +Segmentations have been performed with strictly the same parameters (initial shape, threshold length). +The neighborhood distance for the first iteration is 32 pixels. It has a slight influence on the +time process, but it leads to similar speedups values of approximately 7 times faster than CPU. + +Though it does not appear in Table \ref{tabresults}, we observed that during segmentation stage, higher speedups are obtained in the very first iterations, when segments are made of a lot of pixels, leading to a higher parallelism ratio.\\ +Several parameters prevent from achieving higher speedups~: +\begin{itemize} + \item accesses in the lookup tables in global memory cannot be coalescent. It would imply that the pixel contributions of a segment are stored in consecutive spaces in $C_z$ and $C_{z^2}$. + This is only the case for horizontal segments. + \item the use of 64-bit words for computations in shared memory often leads to 2-way bank conflicts. + \item the level of parallelism is not so high, ie. the total number of pixel is not large enough to achieve impressive speedups. For example, on C2050 GPU, a grid can + run about 66 million of threads, but a snake in a 10000 x 10000 image would be less than 0.1 million pixel long. +\end{itemize} + + +% \begin{table} +% \begin{center} +% \begin{tabular}{|l| r|r r r|} +% \hline +% && CPU & GPU & Speedup\\\cline{3-5} +% Image 15MP & \bf total & \bf0.51 s & \bf0.06 s & \bf x8.5 \\ +% & pre-comp. & 0.21 s & 0.02 s & x10\\ +% & segment. & 0.34 s & 0.04 s & x8.5\\\hline +% Image 100MP & \bf total & \bf 4.33 s & \bf 0.59 s & \bf x7.3\\ +% & pre-comp. & 1.49 s & 0.13 s & x11\\ +% & segment. & 2.84 s & 0.46 s & x6.1\\\hline +% Image 150Mp & \bf total & \bf 26.4 s & \bf 0.79 s & \bf x33\\ +% & pre-comp. & 8.4 s & 0.20 s & x42\\ +% & segment. & 18.0 s & 0.59 s & x30\\\hline +% \end{tabular} +% \end{center} +% +% \caption{\label{tabresults} GPU (C2050, sm20) vs CPU timings.} +% \end{table} + + +\begin{table} + \begin{center} +\begin{tabular}{|l| r|r r r|} +\hline +&& CPU & GPU & Speedup\\\cline{3-5} +Image 15MP & \bf total & \bf0.51 s & \bf0.06 s & \bf x8.5 \\ + & pre-comp. & 0.13 s & 0.02 s & x6.5\\ + & segment. & 0.46 s & 0.04 s & x11.5\\\hline +Image 100MP & \bf total & \bf 4.08 s & \bf 0.59 s & \bf x6.9\\ + & pre-comp. & 0.91 s & 0.13 s & x6.9\\ + & segment. & 3.17 s & 0.46 s & x6.9\\\hline +Image 150Mp & \bf total & \bf 5.7 s & \bf 0.79 s & \bf x7.2\\ + & pre-comp. & 1.4 s & 0.20 s & x7.0\\ + & segment. & 4.3 s & 0.59 s & x7.3\\\hline + \end{tabular} + \end{center} + +\caption{\label{tabresults} GPU (C2050, sm20) vs CPU timings.} +\end{table} + +\IEEEpeerreviewmaketitle + +\vspace{1cm} + +\section{\label{secConclusion}Conclusion} +The algorithm we have focused on is not easy to adapt for high speedups on GPGPU, though we managed to make it work faster than on CPU. +The main drawback is clearly its relative low level of parallelism. Nevertheless, we proposed different kernels that allowed us to take advantage of the computation power of GPUs. + In future works, we plan to try and manage to benefit from larger computing grids of thread blocks. Among the possible solutions, we plan to work on: +\begin{itemize} + \item slicing the image and proceeding the parts in parallel. This is made possible since sm20 GPU provide multi kernel capabilities. + \item slicing the image and proceeding the parts on two different GPUs, hosted by the same CPU. + \item translating the parallelism from pixel level (\emph{1 thread per pixel}) to snake level (\emph{1 thread per snake}), at least during the first iteration, which +is often the longest lasting one. + \item designing an algorithm, in a GPU way of thinking, instead of adapting the existing CPU-designed algorithm to GPU constraints as we did. +\end{itemize} + + +%%RAPH +%%Est ce qu'on parle du fait qu'on va également réfléchir à repenser l'algo en gpu? + + +% trigger a \newpage just before the given reference +% number - used to balance the columns on the last page +% adjust value as needed - may need to be readjusted if +% the document is modified later +%\IEEEtriggeratref{8} +% The "triggered" command can be changed if desired: +%\IEEEtriggercmd{\enlargethispage{-5in}} + +% references section + + +\bibliographystyle{IEEEtran} + +\bibliography{IEEEabrv,biblio} + + +% that's all folks +\end{document} + + -- 2.39.5

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