X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/b04e55fbbcdcbca04098f1bf05ec4473e47b5c51..ebe8c2f159425cf2a2f7a696eedb593305fd19b7:/complexity.tex?ds=inline

diff --git a/complexity.tex b/complexity.tex
index d19f6e2..a5904a7 100644
--- a/complexity.tex
+++ b/complexity.tex
@@ -7,7 +7,7 @@ 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 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.
@@ -55,8 +55,8 @@ 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 $\theta(4Tn)$ 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 $\theta((5^3+4T+1)n^2)$.
 
@@ -71,18 +71,18 @@ matrix. Its complexity is thus negligible compared with the embedding map
 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}