Title :
Robust anisotropic diffusion and sharpening of scalar and vector images
Author :
Black, Michael ; Sapiro, Guillermo ; Marimont, David ; Heeger, David
Author_Institution :
Xerox Palo Alto Res. Center, CA, USA
Abstract :
Relations between anisotropic diffusion and robust statistics are described. 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 on 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 the image. We extend the framework to vector-valued images and show applications to robust image sharpening
Keywords :
edge detection; image enhancement; image segmentation; noise; parameter estimation; statistical analysis; anisotropic diffusion equation; automatic stopping; biweight robust estimator; edge-stopping function; error norm; image boundaries detection; image enhancement; influence function; noisy input image; piecewise smooth image estimation; piecewise smooth regions; robust anisotropic diffusion; robust anisotropic sharpening; robust estimation; robust image sharpening; robust statistics; scalar images; vector images; Anisotropic magnetoresistance; Color; Degradation; Geometry; Image edge detection; Linear approximation; Partial differential equations; Pixel; Robustness; Statistics;
Conference_Titel :
Image Processing, 1997. Proceedings., International Conference on
Conference_Location :
Santa Barbara, CA
Print_ISBN :
0-8186-8183-7
DOI :
10.1109/ICIP.1997.647755