Edge Detection Using Topological Gradients: A Scale-Space Approach

被引:11
作者
Amstutz, Samuel [1 ]
Fehrenbach, Jerome [2 ,3 ]
机构
[1] Univ Avignon, Lab Math Avignon, Avignon, France
[2] CNRS, Inst Math Toulouse, Toulouse, France
[3] Univ Toulouse 3, F-31062 Toulouse, France
关键词
Edge detection; Topological gradient; Heat equation; Scale space; SENSITIVITY-ANALYSIS;
D O I
10.1007/s10851-015-0558-z
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
We provide in this paper a link between two methods of edge detection: edge detection using scale-space analysis, and edge detection using topological asymptotic analysis. More precisely, we show that the topological gradient associated with an image u is given by a combination of the gradients of two smoothed versions of the image u at two different scales, namely phi star u and (phi star phi) star u, where phi is the fundamental solution of the elliptic restoration equation. In the same setting, we propose a new edge detector based on the maximization of the variance of the image. Then we extend our approach to Gaussian kernels through a topological asymptotic analysis of the parabolic heat equation. A numerical comparison of these detectors together with the Canny edge detector is presented.
引用
收藏
页码:249 / 266
页数:18
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