A Restricted-Domain Dual Formulation for Two-Phase Image Segmentation

TL;DR

This paper introduces a restricted-domain dual formulation for two-phase image segmentation that enhances computational efficiency by leveraging assumptions about the solution, supported by experimental validation.

Contribution

It proposes a novel restricted-domain dual approach for convex relaxation in image segmentation, improving computational performance over existing methods.

Findings

Significant reduction in computation time.

Solution quality remains comparable to unrestricted methods.

Method easily extendable to similar segmentation problems.

Abstract

In two-phase image segmentation, convex relaxation has allowed global minimisers to be computed for a variety of data fitting terms. Many efficient approaches exist to compute a solution quickly. However, we consider whether the nature of the data fitting in this formulation allows for reasonable assumptions to be made about the solution that can improve the computational performance further. In particular, we employ a well known dual formulation of this problem and solve the corresponding equations in a restricted domain. We present experimental results that explore the dependence of the solution on this restriction and quantify imrovements in the computational performance. This approach can be extended to analogous methods simply and could provide an efficient alternative for problems of this type.