Learned adaptive nonlinear filtering for anisotropic diffusion approximation in image processing

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