Outlier robust corner-preserving methods for reconstructing noisy images

TL;DR

This paper introduces the TM-smoother, a novel image smoothing method that effectively removes noise while preserving corners and edges, combining differential geometry theory with outlier robustness.

Contribution

The paper develops the TM-smoother by integrating M-smoothing and least-squares-trimming, providing a new approach for robust, corner-preserving image smoothing.

Findings

TM-smoother outperforms existing smoothers in preserving corners.

The method effectively removes noise and preserves image structure.

A software package for TM- and M-smoothers is available online.

Abstract

The ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother. Unfortunately, they usually seem to be at odds with each other; one can only improve one property at the cost of the other. By combining M-smoothing and least-squares-trimming, the TM-smoother is introduced as a means to unify corner-preserving properties and outlier robustness. To identify edge- and corner-preserving properties, a new theory based on differential geometry is developed. Further, robustness concepts are transferred to image processing. In two examples, the TM-smoother outperforms other corner-preserving smoothers. A software package containing both the TM- and the M-smoother can be downloaded from the Internet.