Stable Segmentation of Digital Image

TL;DR

This paper presents a method for stable, optimal image segmentation using piecewise constant approximations, combining a generalized Mumford-Shuh model with the Otsu multi-thresholding method, validated through analytical and experimental results.

Contribution

It introduces a novel approach that ensures stability in optimal image segmentation by integrating a generalized Mumford-Shuh model with Otsu's method.

Findings

The method achieves stable segmentation results.

It effectively minimizes total squared error.

Experimental validation confirms its robustness.

Abstract

In the paper the optimal image segmentation by means of piecewise constant approximations is considered. The optimality is defined by a minimum value of the total squared error or by equivalent value of standard deviation of the approximation from the image. The optimal approximations are defined independently on the method of their obtaining and might be generated in different algorithms. We investigate the computation of the optimal approximation on the grounds of stability with respect to a given set of modifications. To obtain the optimal approximation the Mumford-Shuh model is generalized and developed, which in the computational part is combined with the Otsu method in multi-thresholding version. The proposed solution is proved analytically and experimentally on the example of the standard image.