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diff --git a/annexePreuvesComplexiteStego.tex b/annexePreuvesComplexiteStego.tex
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+\begin{theorem}\label{th:cplxt:hugo}
+Le schéma HUGO a une complexité de l'ordre de 
+$\theta(2 \times n^2(343^2 + \ln(n)))$
+\end{theorem}
+
+
+First of all, HUGO starts with computing the second order SPAM Features.
+This steps is in  $\theta(n^2 + 2\times 343^2)$ due to the computation
+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 ones. 
+The algorithm thus computes a distance between each feature 
+and the original ones,
+which is at least in $\theta(343)$, and an overall distance between these 
+metrics, which is in $\theta(686)$. Computing the distance is thus in 
+$\theta(2\times 343^2)$ and this modification
+is thus in $\theta(2\times 343^2 \times n^2)$.
+Ranking these results may be achieved with a quick sort, which is in 
+$\theta(2 \times n^2 \ln(n))$ for data of size $n^2$.
+The overall complexity of the pixel selection is finally
+$\theta(n^2 +2 \times 343^2 + 2\times 343^2 \times n^2 + 2 \times n^2 \ln(n))$, \textit{i.e},
+$\theta(2 \times n^2(343^2 + \ln(n)))$.
+
+
+
+
+Let us focus now on WOW.  
+This scheme starts to compute the residual 
+of the cover as a convolution product which is in $\theta(n^2\ln(n^2))$. 
+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 $\theta(n^2 \times n^2\ln(n^2))$.
+Moreover the suitability is computed for each wavelet level
+detail (HH, HL, LL). 
+This distortion computation step is thus in $\theta(6n^4\ln(n))$.
+Finally a norm of these three values is computed for each pixel 
+which adds to this complexity the complexity of $\theta(n^2)$.
+To summarize, the complixity is in $\theta(6n^4\ln(n) +n^2)$
+
+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   $\theta(n^2 \times n^2\ln(n^2))$,
+ and a sum $D$ of 
+these $W$ which is in $\theta(n^2)$. 
+This distortion computation step is thus in $\theta(6n^4\ln(n) + n^2)$.
+
+
+Our edge selection is based on a Canny filter. When applied on a 
+$n \times n$ square image, the noise reduction step is in $\theta(5^3 n^2)$.
+Next, let $T$ be the size of the Canny mask.
+Computing gradients is in $\theta(4Tn^2)$ since derivatives of each direction (vertical or horizontal) 
+are in $\theta(2Tn^2)$.
+Finally, thresholding with hysteresis is in $\theta(n^2)$.
+The overall complexity is thus in $\theta((5^3+4T+1)n^2)$.

diff --git a/images/complexity.eps b/images/complexity.eps
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