Edge-Preserving Smoothers for Image Processing

Abstract

Classical smoothers have limited usefulness in image processing, because sharp “edges” tend to be blurred. There is a literature on edge-preserving smoothers, but these all require moderately large “smooth stretches.” Here we discuss an approach to this problem called “sigma filtering” and propose an improvement based on running M estimation. Both computational and theoretical aspects are developed. For image processing, the methods have a niche between standard filtering approaches and Bayes–Markov random-field analysis.

Key Words:

• Image processing
• Jump-preserving smoothing
• Robust M estimation.