Learned adaptive nonlinear filtering for anisotropic diffusion approximation in image processing

• Published in: Proceedings of 13th International Conference on Pattern Recognition Vol. 4; pp. 276 - 280 vol.4
• Main Authors: Fischl, B., Schwartz, E.L.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 1996
• Subjects: Adaptive filters; Anisotropic magnetoresistance; Convolution; Filtering; Green's function methods; Image analysis; Image enhancement; Integral equations; Kernel; Machine vision
• ISBN: 9780818672828; 081867282X
• ISSN: 1051-4651
• DOI: 10.1109/ICPR.1996.547430

In the machine vision community multi-scale image enhancement and analysis has frequently been accomplished using a diffusion or equivalent process. Linear diffusion can be replaced by convolution with Gaussian kernels, as the Gaussian is the Green's function of such a system. In this paper we present a technique which obtains an approximate solution to a nonlinear diffusion process via the solution of an integral equation which is the nonlinear analog of convolution. The kernel function of the integral equation plays the same role that a Green's function does for a linear PDE, allowing the direct solution of the nonlinear PDE for a specific time without requiring integration through intermediate times. We then use a learning technique to approximate the kernel function for arbitrary input images. The result is an improvement in speed and noise-sensitivity, as well as providing a parallel algorithm.