style ante + complexite canny

[canny.git] / complexity.tex

diff --git a/complexity.tex b/complexity.tex
index 6e108f80c1c69feebc2c9dbb44e3b5211a43b6fa..4da4291e06709364d21e1031dab2eea250962166 100644 (file)
--- a/complexity.tex
+++ b/complexity.tex
@@ -24,13 +24,15 @@ 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}
 $O(2.n^2(343^2 + \ln(n)))$.
 
 $O(n^2 +2.343^2 + 2\times 343^2 \times n^2 + 2.n^2 \ln(n))$, \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.
+Our edge selection is based on a Canny  Filter. When applied on a 
+$n \times n$ square image the Noise reduction steps is in $O(5^3 n^2)n$.
+Next, let $T$ be the size of the canny mask.
+Computing gradients is in $O(4Tn)$ since derivatives of each direction (vertical or horizontal) 
+are in $O(2Tn)$.
+Finally, thresholding with hysteresis is in $O(n^2)$.
+The overall complexity is thus in $O((5^3+4T+1)n^2)$.

 To summarize, for the embedding map construction, the complexity of Hugo is
 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.
+dramatically higher than our scheme.

 
 We are then left to express the complexity of the STC algorithm.
 According to~\cite{DBLP:journals/tifs/FillerJF11}, it  is 
 
 We are then left to express the complexity of the STC algorithm.
 According to~\cite{DBLP:journals/tifs/FillerJF11}, it  is