Color Edge Preserving Smoothing

The creation of a successively smoother image that retains the edge information of the original is a problem that has attracted researchers and resulted in many different algorithms. Most methods share the same fundamental steps where a measure of the strength of the edge is defined and as a second step diffusion is allowed along the edge but not across it. Moreover, these algorithms are either designed for monochromatic images or developed to consider the color values in their spatial space and thus treat the color image as a single function rather than n different channels. In this paper, we introduce an edge preserving smoothing method which defines an edge by diffusing two color vectors and considering the effect of that operation on the local gradients. We argue that diffusing in the direction of strong gradients results in an increase of small neighboring gradients. This simple observation is shown to result in accurate edge detection and preservation. Our operation is performed in a local color space where we decompose all color values into a component that is along the pixel value under consideration and another that is orthogonal to it thus allowing us to control the level of allowable color change.