Smoothing-based Optimization

Abstract

We propose an efficient method for complex optimization problems that often arise in computer vision. While our method is general and could be applied to various tasks, it was mainly inspired from problems in computer vision, and it borrows ideas from scale space theory. One of the main motivations for our approach is that searching for the global maximum through the scale space of a function is equivalent to looking for the maximum of the original function, with the advantage of having to handle fewer local optima. Our method works with any non-negative, possibly non-smooth function, and requires only the ability of evaluating the function at any specific point. The algorithm is based on a growth transformation, which is guaranteed to increase the value of the scale space function at every step, unlike gradient methods. To demonstrate its effectiveness we present its performance on a few computer vision applications, and show that in our experiments it is more effective than some well established methods such as MCMC, Simulated Annealing and the more local Nelder-Mead optimization method.