Fast Trust Region for Segmentation

Abstract: Trust region is a well-known general approach to optimization which offers many advantages over standard gradient descent techniques. In particular, it allows more accurate nonlinear approximation models. In each iteration this approach computes a global optimum of a suitable approximation model within a fixed radius around the current solution, a.k.a. trust region. In general, this approach can be used only when some efficient constrained optimization algorithm is available for the selected non-linear (more accurate) approximation model.
In this paper we propose a Fast Trust Region (FTR) approach for optimization of segmentation energies with non-linear regional terms, which are known to be challenging for existing algorithms. These energies include, but are not limited to, KL divergence and Bhattacharyya distance between the observed and the target appearance distributions, volume constraint on segment size, and shape prior constraint in a form of L²-distance from target shape moments. Our method is 1-2 orders of magnitude times faster than the existing state-of-the-art methods while converging to comparable or better solutions.