From: couchot <jf.couchot@gmail.com>
Date: Tue, 17 Dec 2013 12:29:39 +0000 (+0100)
Subject: kl
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/commitdiff_plain/d67ddfb670a8d832dcf94f66044f3bb2ac8add39?ds=sidebyside;hp=--cc

kl
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+This section aims at justifying the lightweight attribute of our approach.
+To be more precise, we compare the complexity of our schemes to the 
+state of the art steganography, namely HUGO~\cite{DBLP:conf/ih/PevnyFB10}.
+
+
+In what follows, we consider an $n \times n$ square image. 
+First of all, HUGO starts with computing the second order SPAM Features.
+This steps is in  $O(n^2 + 2.343^2)$ due to the calculation 
+of the difference arrays and next of the 686 features (of size 343).
+Next for each pixel, the distortion measure is calculated by +1/-1 modifying
+its value and computing again the SPAM 
+features. Pixels are thus selected according to their ability to provide
+an image whose SPAM features are close to the original one. 
+The algorithm is thus computing a distance between each computed feature, 
+andthe original ones
+which is at least in $O(343)$ and an overall distance between these 
+metrics which is in $O(686)$. Computing the distance is thus in 
+$O(2\times 343^2)$ and this modification
+is thus in $O(2\times 343^2 \times n^2)$.
+Ranking these results may be achieved with a insertion sort which is in 
+$2.n^2 \ln(n)$.
+The overall complexity of the pixel selection is thus 
+$O(n^2 +2.343^2 + 2\times 343^2 \times n^2 + 2.n^2 \ln(n))$, \textit{i.e}
+$O(2.n^2(343^2 + \ln(n)))$.
+
+Our edge selection is based on a Canny  Filter, 
+whose complexity is in $O(2n^2.\ln(n))$ thanks to the convolution step
+which can be implemented with FFT.
+To summarize, for the embedding map construction, the complexity of Hugo is
+at least $343^2/\ln{n}$ times higher than 
+our scheme. For instance, for a squared image with 4M pixel per slide,
+this part of our algorithm is more than 14100 faster than Hugo.
+
+We are then left to express the complexity of the STC algorithm .
+According to~\cite{DBLP:journals/tifs/FillerJF11}, it  is 
+in $O(2^h.n)$ where $h$ is the size of the duplicated 
+matrix. Its complexity is thus negligeable compared with the embedding map
+construction.
+
+Thanks to these complexity result, we claim that STABYLO is lightweight. 
+
+
+
+
+