Image selective smoothing and edge detection by nonlinear diffusion. II

A new version of the Perona and Malik theory for edge detection and image restoration is proposed. This new version keeps all the improvements of the original model and avoids its drawbacks: it is proved to be stable in presence of noise, with existence and uniqueness results. Numerical experiments on natural images are presented.

[1]  A. Rosenfeld,et al.  Edge and Curve Detection for Visual Scene Analysis , 1971, IEEE Transactions on Computers.

[2]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[3]  P. Lions Generalized Solutions of Hamilton-Jacobi Equations , 1982 .

[4]  K. Höllig,et al.  A Diffusion Equation with a Nonmonotone Constitutive Function , 1983 .

[5]  J. Canny Finding Edges and Lines in Images , 1983 .

[6]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[7]  Alan L. Yuille,et al.  Scaling Theorems for Zero Crossings , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  J. Morel,et al.  Segmentation of images by variational methods: a constructive approach. , 1988 .

[9]  Yun-Gang Chen,et al.  Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations , 1989 .

[10]  H. Ishii,et al.  Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains , 1991 .

[11]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  L. Rudin,et al.  Feature-oriented image enhancement using shock filters , 1990 .

[13]  G. Barles,et al.  Convergence of approximation schemes for fully nonlinear second order equations , 1991 .

[14]  L. Evans,et al.  Motion of level sets by mean curvature. II , 1992 .