# The Chan-Vese Model with Elastica and Landmark Constraints for Image Segmentation

## TL;DR

This paper introduces a new variational level set model for image segmentation that combines the Chan-Vese model with elastica and landmark constraints, improving boundary recovery and segmentation efficiency.

## Contribution

It proposes a novel model integrating elastica and landmark constraints with the Chan-Vese framework, along with an efficient ALM/ADMM optimization algorithm.

## Key findings

- Enhanced boundary recovery in occluded regions
- Improved segmentation efficiency and robustness
- Reduced dependence on parameter tuning and initialization

## Abstract

In order to completely separate objects with large sections of occluded boundaries in an image, we devise a new variational level set model for image segmentation combining the Chan-Vese model with elastica and landmark constraints. For computational efficiency, we design its Augmented Lagrangian Method (ALM) or Alternating Direction Method of Multiplier (ADMM) method by introducing some auxiliary variables, Lagrange multipliers, and penalty parameters. In each loop of alternating iterative optimization, the sub-problems of minimization can be easily solved via the Gauss-Seidel iterative method and generalized soft thresholding formulas with projection, respectively. Numerical experiments show that the proposed model can not only recover larger broken boundaries but can also improve segmentation efficiency, as well as decrease the dependence of segmentation on parameter tuning and initialization.