Shape Gradient Based Non-Parametric Mumford-Shah Segmentation Without Level Sets

TL;DR

This paper introduces a non-parametric, level set free segmentation method that uses shape gradients of the Mumford-Shah energy to detect image boundaries, effectively capturing complex and narrow structures without relying on level set representations.

Contribution

It presents a novel shape gradient-based approach for Mumford-Shah segmentation that operates without level sets or parametric models, enabling flexible boundary detection.

Findings

Effective in capturing intricate and narrow boundaries

Demonstrated success on various texture images

Outperforms traditional level set methods

Abstract

A non parametric, level set free method is proposed for detecting image boundaries using the shape gradient of the Mumford Shah energy for segmentation. Minimizing the variance in pixel intensities inside and outside a boundary set of points is the primary pursuit. The boundary set as a polygon of points rather than a parametric form or a level set, evolves under the guidance of a shape gradient of the Mumford Shah piece wise constant segments model. Iteratively updating through the gradient descent method. The proposed method has been tested on various images, demonstrating its effectiveness in capturing intricate and narrow boundaries texture images.