A Topology fixated Shape Gradient Framework for Non Simple Boundary Extraction for CIE Lab color images with Repulsive Energy

TL;DR

This paper introduces a hybrid, topology-aware shape gradient framework for segmenting complex images with multiple and nested boundaries, ensuring precise control over boundary evolution.

Contribution

It presents a novel topology fixated shape gradient method incorporating a multivariable function to handle self-intersections during boundary evolution.

Findings

Effective segmentation of complex images with nested structures.

Precise control over boundary topology and self-intersections.

Successful application to gray scale and color images, including astronomical objects.

Abstract

A levelset free but a hybrid image segmentation approach based on a modified version of the piece wise constant shape gradient of an Mumford Shah shape functional and a repulsive function is considered. The segmentation is performed a non-local shape based through an evolution of discrete curves driven by a non local shape based energy to segment images containing disjoint regions and multiple boundaries. This formulation has a novel additional component as a multivariable function dependent on a few sampled points of the curves that handles the occurrence of self intersection during boundary curves evolution. The method is applied to a few gray scale and color images, including images with nested structures and astronomical objects. The results indicate effective segmentation in complex scenarios with absolute control on the topology of the segments and self-intersections of the boundaries