Abstract Trust region is a well-known general iterative 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 fifixed radius around the current solution, a.k.a. trust region. In general, this approach can be used only when some effificient constrained optimization algorithm is available for the selected nonlinear (more accurate) approximation model. In this paper we propose a Fast Trust Region (FTR) approach for optimization of segmentation energies with nonlinear 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