Momentum Based Optimization Methods for Level Set Segmentation

Segmentation of images is often posed as a variational problem. As such, it is solved by formulating an energy functional depending on a contour and other image derived terms. The solution of the segmentation problem is the contour which extremizes this functional. The standard way of solving this optimization problem is by gradient descent search in the solution space, which typically suffers from many unwanted local optima and poor convergence. Classically, these problems have been circumvented by modifying the energy functional. In contrast, the focus of this paper is on alternative methods for optimization. Inspired by ideas from the machine learning community, we propose segmentation based on gradient descent with momentum. Our results show that typical models hampered by local optima solutions can be further improved by this approach. We illustrate the performance improvements using the level set framework.