An efficient iterative thresholding method for image segmentation

TL;DR

This paper introduces an efficient iterative thresholding algorithm for multi-phase image segmentation that minimizes a Mumford-Shah functional approximation, featuring simple convolutions, thresholding, and proven energy decay.

Contribution

The paper presents a novel, computationally efficient iterative method for multi-phase image segmentation based on a non-local energy approximation of the Mumford-Shah functional.

Findings

Algorithm has optimal $O(N \, log N)$ complexity per iteration.

Iterative method demonstrates energy decay property.

Numerical results confirm high efficiency and effectiveness.

Abstract

We proposed an efficient iterative thresholding method for multi-phase image segmentation. The algorithm is based on minimizing piecewise constant Mumford-Shah functional in which the contour length (or perimeter) is approximated by a non-local multi-phase energy. The minimization problem is solved by an iterative method. Each iteration consists of computing simple convolutions followed by a thresholding step. The algorithm is easy to implement and has the optimal complexity $O(N \log N)$ per iteration. We also show that the iterative algorithm has the total energy decaying property. We present some numerical results to show the efficiency of our method.