(with Guillermo Sapiro)
Edges are viewed as statistical outliers with respect to local image gradient magnitudes. Within local image regions we compute a robust statistical measure of the gradient variation and use this in an anisotropic diffusion framework to determine a spatially varying ``edge-stopping'' parameter "sigma". We show how to determine this parameter for two edge-stopping functions described in the literature (Perona-Malik and Tukey). Smoothing of the image is related the local texture and in regions of low texture, small gradient values may be treated as edges whereas in regions of high texture, large gradient magnitudes are necessary before an edge is preserved. Intuitively these results have similarities with human perceptual phenomena such as masking and ``popout''. Results are shown on a variety of standard images.
Black, M. J. and Sapiro, G., Edges as outliers: Anisotropic smoothing using local image statistics, Scale-Space Theories in Computer Vision, Second Int. Conf., Scale-Space '99, Corfu, Greece, LNCS 1682, Springer, Sept. 1999, pp. 259-270. (postscript, 1.3MB)(pdf, 0.3MB).
Black, M. J., Sapiro, G., Marimont, D., Heeger, D., Robust anisotropic diffusion, IEEE Transactions on Image Processing, Special issue on Partial Differential Equations and Geometry Driven Diffusion in Image Processing and Analysis, 7(3), pp. 421-432, March 1998. (pdf), (postscript)
Black, M. J., Sapiro, G., Marimont, D., Heeger, D., Robust anisotropic diffusion and sharpening of scalar and vector images. Int. Conf. on Image Processing, ICIP, Vol. 1, Santa Barbara, CA, Oct. 1997, pp. 263-266.
Black, M. J., Sapiro, G., Marimont, D., Heeger, D., Robust anisotropic diffusion: Connections between robust statistics, line processing, and anisotropic diffusion, in Scale-Space Theory in Computer Vision, Scale-Space'97, B. ter Haar Romeny, L. Florack, J. Koenderink, and M. Viergever (Eds.), Springer Verlag, LNCS 1252, Utrecht, the Netherlands, July 1997, pp. 323-326. (postscript)