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 separately eavluate this complexity.
+we separately evaluate this complexity.
In all the rest of this section, we consider a $n \times n$ square image.
First of all, HUGO starts with computing the second order SPAM Features.
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 $\theta(4Tn)$ since derivatives of each direction (vertical or horizontal)
-are in $\theta(2Tn)$.
+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 $\theta((5^3+4T+1)n^2)$.
construction.
The Fig.~\ref{fig:compared}
-summarizes the complexity of the embedding map construction, for Hugo, Wow
-and Uniward. It deals with square images
+summarizes the complexity of the embedding map construction, for
+WOW/UNIWARD, HUGO, and STABYLO. It deals with square images
of size $n \times n$ when $n$ ranges from
512 to 4096. The $y$-coordinate is expressed in a logarithm scale.
-It shows that the complexity of all algorithms
+It shows that the complexity of all the algorithms
is dramatically larger than the one of the STABYLO scheme.
-Thanks to these complexity results, we claim that STABYLO is lightweight.
+Thanks to these complexity results, we claim that our approach is lightweight.
\begin{figure}
\begin{center}
\includegraphics[scale=0.4]{complexity}
\end{center}
-\caption{Complexity evaluation of Wow/Uniward, Hugo, and Stabylo}
+\caption{Complexity evaluation of WOW/UNIWARD, HUGO, and STABYLO}
\label{fig:compared}
\end{figure}
