Anisotropic Mesh Adaptation for Image Segmentation Based on Mumford-Shah Functional

TL;DR

This paper introduces a novel anisotropic mesh adaptation algorithm for image segmentation based on the Mumford-Shah functional, achieving faster and higher-quality results without image resizing.

Contribution

It combines anisotropic mesh adaptation with finite element methods to improve image segmentation efficiency and quality over traditional finite difference approaches.

Findings

Faster segmentation compared to finite difference methods

Higher quality segmentation results

Effective multi-region image segmentation

Abstract

As the resolution of digital images increase significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this paper, we consider image segmentation by solving a partial differentiation equation (PDE) model based on the Mumford-Shah functional. We develop a new algorithm by combining anisotropic mesh adaptation for image representation and finite element method for solving the PDE model. Comparing to traditional algorithms solved by finite difference method, our algorithm provides faster and better results without the need to resizing the images to lower quality. We also extend the algorithm to segment images with multiple regions.