Variable-conductance, level-set curvature for image denoising

This paper describes a partial differential equation for denoising images. The proposed method is demonstrably superior to anisotropic diffusion (and its many variations) for denoising images that are approximately piecewise constant. The method relies on an equation that is the level-set equivalent of the anisotropic diffusion equation proposed by Perona and Malik (1990). This proposed equation has come up in the literature, but has failed to be fully utilized due to a lack of analysis and the need for a stable, accurate numerical implementation. Our analysis shows that the proposed method is more aggressive than anisotropic diffusion at enhancing and preserving edges, and is less sensitive to the edge contrast parameter. Empirical results confirm these advantages, and show that for certain classes of images, one should always prefer the proposed method over anisotropic diffusion.

[1]  Scott T. Acton,et al.  Multigrid anisotropic diffusion , 1998, IEEE Trans. Image Process..

[2]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[3]  Stanley Osher,et al.  Explicit Algorithms for a New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal , 2000, SIAM J. Sci. Comput..

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

[5]  Guido Gerig,et al.  Vector-Valued Diffusion , 1994, Geometry-Driven Diffusion in Computer Vision.

[6]  Ross T. Whitaker,et al.  A multi-scale approach to nonuniform diffusion , 1993 .

[7]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[8]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[9]  Jean-Michel Morel,et al.  Morphological Approach to Multiscale Analysis: From Principles to Equations , 1994, Geometry-Driven Diffusion in Computer Vision.

[10]  Guillermo Sapiro,et al.  Anisotropic diffusion of multivalued images with applications to color filtering , 1996, IEEE Trans. Image Process..

[11]  Guillermo Sapiro,et al.  Color Snakes , 1997, Comput. Vis. Image Underst..

[12]  P. Lions,et al.  Image selective smoothing and edge detection by nonlinear diffusion. II , 1992 .

[13]  Anthony J. Yezzi,et al.  Modified curvature motion for image smoothing and enhancement , 1998, IEEE Trans. Image Process..

[14]  Guillermo Sapiro,et al.  Robust anisotropic diffusion , 1998, IEEE Trans. Image Process..

[15]  Ron Kimmel,et al.  A general framework for low level vision , 1998, IEEE Trans. Image Process..

[16]  Jayant Shah.  Segmentation by nonlinear diffusion. II , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.