Using the Split Bregman Algorithm to Solve the Self-Repelling Snake Model

Preserving the contour topology during image segmentation is useful in manypractical scenarios. By keeping the contours isomorphic, it is possible to pre-vent over-segmentation and under-segmentation, as well as to adhere to giventopologies. The self-repelling snake model (SR) is a variational model thatpreserves contour topology by combining a non-local repulsion term with thegeodesic active contour model (GAC). The SR is traditionally solved using theadditive operator splitting (AOS) scheme. Although this solution is stable, thememory requirement grows quickly as the image size increases. In our paper,we propose an alternative solution to the SR using the Split Bregman method.Our algorithm breaks the problem down into simpler subproblems to use lower-order evolution equations and approximation schemes. The memory usage issignificantly reduced as a result. Experiments show comparable performance to the original algorithm with shorter iteration times.

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

In order to separate completely the objects with larger occluded boundaries in an image, we devise a new variational level set model for image segmentation combing the recently proposed Chan-Vese-Euler model with elastica and landmark constraints. For computational efficiency, we deign 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 solved via simple Gauss-Seidel iterative method, or generalized soft thresholding formulas with projection methods respectively. Numerical experiments show that the proposed model not only can recover larger broken boundaries, but also can improve segmentation efficiency, decrease the dependence of segmentation on tuning parameters and initialization.