Robust anisotropic diffusion

被引:905
作者
Black, MJ
Sapiro, G
Marimont, DH
Heeger, D
机构
[1] Xerox Corp, Palo Alto Res Ctr, Palo Alto, CA 94304 USA
[2] Univ Minnesota, Dept Elect & Comp Engn, Minneapolis, MN 55455 USA
[3] Stanford Univ, Dept Psychol, Stanford, CA 94305 USA
基金
美国国家科学基金会;
关键词
anisotropic diffusion; line processes; robust statistics;
D O I
10.1109/83.661192
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
Relations between anisotropic diffusion and robust statistics are described in this paper, Specifically, we show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image, The "edge-stopping" function in the anisotropic diffusion equation is closely related to the error norm and influence function in the robust estimation framework, This connection leads to a new "edge-stopping" function based an Tukey's biweight robust estimator that preserves sharper boundaries than previous formulations and improves the automatic stopping of the diffusion. The robust statistical interpretation also provides a means for detecting the boundaries (edges) between the piecewise smooth regions in an image that has been smoothed with anisotropic diffusion, Additionally, we derive a relationship between anisotropic diffusion and regularization with Line processes. Adding constraints on the spatial organization of the line processes allows us to develop new anisotropic diffusion equations that result in a qualitative improvement in the continuity of edges.
引用
收藏
页码:421 / 432
页数:12
相关论文
共 51 条
[1]   IMAGE SELECTIVE SMOOTHING AND EDGE-DETECTION BY NONLINEAR DIFFUSION .2. [J].
ALVAREZ, L ;
LIONS, PL ;
MOREL, JM .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1992, 29 (03) :845-866
[2]  
AUBERT G, IN PRESS SIAM J APPL
[3]  
BESL PJ, P INT C COMP VIS ICC, P591
[4]  
Black M. J., 1991, Proceedings 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (91CH2983-5), P296, DOI 10.1109/CVPR.1991.139705
[5]   On the unification of line processes, outlier rejection, and robust statistics with applications in early vision [J].
Black, MJ ;
Rangarajan, A .
INTERNATIONAL JOURNAL OF COMPUTER VISION, 1996, 19 (01) :57-91
[6]  
BLACK MJ, 1993, P 4 INT C COMP VIS, P231, DOI DOI 10.1109/ICCV.1993.378214
[7]  
Blake A., 1987, Visual Reconstruction
[9]   IMAGE SELECTIVE SMOOTHING AND EDGE-DETECTION BY NONLINEAR DIFFUSION [J].
CATTE, F ;
LIONS, PL ;
MOREL, JM ;
COLL, T .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1992, 29 (01) :182-193
[10]   Deterministic edge-preserving regularization in computed imaging [J].
Charbonnier, P ;
BlancFeraud, L ;
Aubert, G ;
Barlaud, M .
IEEE TRANSACTIONS ON IMAGE PROCESSING, 1997, 6 (02) :298-311