Stochastic Graduated Graph Approximation Algorithm for MRF optimization

Abstract

Markov random elds have been powerful models in computer vision but tractable algorithms to obtain exact solution for the corresponding energy functions are lim- ited

approximate solutions, in most cases are provided for efficiency. In this work graduated optimization technique is applied in a novel way to develop an efficient al- gorithm for solving general multi-label MRF optimization problem called Stochastic Graduated graph approximation (SGGA) algorithm. The algorithm initially min- imizes a simplied function and progressively transforms that function until it is equivalent to the original function. However, it is hard to nd how to generate the sequence of intermediate functions and what parameter to use for making transition from one problem to another. For this we propose a new iterative method of build- ing the sequence of approximations for the original energy function. We exploit a stochastic method to generate intermediate functions, which guides the intermedi- ate solutions to the near-optimal solution for the original problem. The transition from one intermediate problem to another is controlled by the schedule of gradual addition of edges. In each iteration, a deterministic algorithm such as block ICM is applied to minimize intermediate functions and to generate initial solution for the next problem. The proposed algorithm guarantees the convergence of local mini- mum. We test on a synthetic image deconvolution problem and also on the set of experiments with the OpenGM2 benchmark.