Using the Split Bregman Algorithm to Solve the Self-repelling Snake Model
This work addresses the challenge of preventing over- and under-segmentation in image processing for applications requiring topological consistency, though it is incremental as it improves an existing model.
The paper tackles the problem of preserving contour topology in image segmentation by proposing a new solution to the Self-repelling Snake model using the Split Bregman method, resulting in faster convergence and reduced memory requirements compared to the traditional additive operator splitting scheme.
Preserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snake model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model (GAC). The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform (FFT) or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.