A Fast Algorithm for Implementation of Koul's Minimum Distance Estimators and Their Application to Image Segmentation

TL;DR

This paper introduces a fast, practical algorithm for Koul's minimum distance estimators and applies it to complex image segmentation tasks, notably improving performance on real-world images like MR scans.

Contribution

It extends minimum distance estimation to image segmentation by developing a novel, efficient algorithm and integrating it with a segmenting-together strategy for complex images.

Findings

Successfully segments complex real images such as MRI scans

Provides a computationally efficient solution for Koul's estimators

Enhances segmentation accuracy with the segmenting-together strategy

Abstract

Minimum distance estimation methodology based on an empirical distribution function has been popular due to its desirable properties including robustness. Even though the statistical literature is awash with the research on the minimum distance estimation, the most of it is confined to the theoretical findings: only few statisticians conducted research on the application of the method to real world problems. Through this paper, we extend the domain of application of this methodology to various applied fields by providing a solution to a rather challenging and complicated computational problem. The problem this paper tackles is an image segmentation which has been used in various fields. We propose a novel method based on the classical minimum distance estimation theory to solve the image segmentation problem. The performance of the proposed method is then further elevated by integrating it with the ``segmenting-together" strategy. We demonstrate that the proposed method combined with the segmenting-together strategy successfully completes the segmentation problem when it is applied to the complex, real images such as magnetic resonance images.