  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.
