+
+
+
+\section{Complexity Analysis}\label{sub:complexity}
+This section aims at justifying the leightweight 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 folllows, 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 Feature,
+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
+$O(2\time 343^2)$ and this mdification is thus in $O(2\time 343^2 \time n^2)$.
+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
+$O(n^2 +2.343^2 + 2\time 343^2 \time n^2 + 2.n^2 \ln(n))$, \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.
+The complexity of Hugo is at least $343^2/\ln{n}$ times higher than our scheme.
+
+
+
+
+
