From bf273ca48657e1dd9e23cb0e5afe4b41838e3f2a Mon Sep 17 00:00:00 2001 From: =?utf8?q?Jean-Fran=C3=A7ois=20Couchot?= Date: Fri, 19 Sep 2014 10:09:11 +0200 Subject: [PATCH 1/1] =?utf8?q?ajout=20complexit=C3=A9=20WOW=20et=20UNIWARD?= MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit --- complexity.tex | 29 +++++++++++++++++++++++++++-- 1 file changed, 27 insertions(+), 2 deletions(-) diff --git a/complexity.tex b/complexity.tex index e2f0203..e4e6b0e 100644 --- a/complexity.tex +++ b/complexity.tex @@ -4,9 +4,11 @@ To be more precise, we compare the complexity of our schemes to some of current state of the art of steganographic scheme, namely HUGO~\cite{DBLP:conf/ih/PevnyFB10}, WOW~\cite{conf/wifs/HolubF12}, and UNIWARD~\cite{HFD14}. +Each of these scheme starts with the computation of the distortion cost +for each pixel switch and is later followed by the STC algorithm. +Since this last step is shared by all, we do not add its complexity. +In all the rest of this section, we consider a $n \times n$ square image. - -In what follows, we consider a $n \times n$ square image. First of all, HUGO starts with computing the second order SPAM Features. This steps is in $O(n^2 + 2\times 343^2)$ due to the calculation of the difference arrays and next of the 686 features (of size 343). @@ -26,6 +28,29 @@ The overall complexity of the pixel selection is finally $O(n^2 +2.343^2 + 2\times 343^2 \times n^2 + 2.n^2 \ln(n))$, \textit{i.e}, $O(2.n^2(343^2 + \ln(n)))$. + + + +Let us focus now on WOW. +This scheme starts to compute the residual +of the cover as a convolution product which is in $O(n^2\ln(n^2))$. +The embedding suitability $\eta_{ij}$ is then computed for each pixel +$1 \le i,j \le n$ thanks to a convolution product again. +We thus have a complexity of $O(n^2 \times n^2\ln(n^2))$. +Moreover the suitability is computed for each wavelet level +detail (HH, HL, LL). +This distortion computation step is thus in $O(6n^4\ln(n))$. +Finally a norm of these three values is computed for each pixel +which adds to this complexity the complexity of $O(n^2)$. +To summarize, the complixity is in $O(6n^4\ln(n) +n^2)$ + +What follows details the complexity of the distortion evaluation of the +UNIWARD scheme. This one is based to a convolution product $W$ of two elements +of size $n$ and is again in $O(n^2 \times n^2\ln(n^2))$ and a sum $D$ of +these $W$ which is in $O(n^2)$. +This distortion computation step is thus in $O(6n^4\ln(n) + n^2)$. + + Our edge selection is based on a Canny Filter. When applied on a $n \times n$ square image, the noise reduction step is in $O(5^3 n^2)$. Next, let $T$ be the size of the canny mask. -- 2.39.5