A Nonlinear Diffusion Equation As A Fast And Optimal Solver Of Edge Detection Problems.

A nonlinear diffusion process known to be effective for image segmentation is analyzed in 1-D. It is shown that it optimally solves certain edge detection problems. A fast implementation of the algorithm is introduced. 1. INTRODUCTION. The recent years have seen a great number of exciting developments in the field of nonlinear diffusion filtering of images. Many theories have been proposed that result in edge-preserving scale spaces possessing various interesting properties (see [1, 5, 4, 7, 6] and many other references in [9]). One striking feature uniting many of these frameworks--including our own [6]--is that they are deterministic. Usually, one starts with a set of "common-sense" principles which an image smoothing operation should satisfy. Examples of these are the axioms in [1] and the observation in [5] that, in order to achieve edge preservation, very little smoothing should be done at points with high gradient. From these principles, a nonlinear scale space is derived, and t..