The (MAP) assignment for general structure Markov random fields (MRFs) is computationally intractable. In this paper, we exploit tree-based methods to efficiently address this problem. Our novel method, named Tree-based Iterated Local Search (T-ILS) takes advantage of the tractability of tree-structures embedded within MRFs to derive strong local search in an ILS framework. The method efficiently explores exponentially large neighborhood and does so with limited memory without any requirement on the cost functions. We evaluate the T-ILS in a simulation of Ising model and two real-world problems in computer vision: stereo matching, image denoising. Experimental results demonstrate that our methods are competitive against state-of-the-art rivals with a significant computational gain.
A method is presented to approximate optimally an n -dimensional discrete probability distribution by a product of second-order distributions, or the distribution of the first-order tree dependence. The problem is to find an optimum set of n - 1 first order dependence relationship among the n variables. It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information. It is further shown that when this procedure is applied to empirical observations from an unknown distribution of tree dependence, the procedure is the maximum-likelihood estimate of the distribution. Reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts-in particular, making ties to topics such as wavelets and multigrid methods. A third goal is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for self-similar and 1 f processes. We also illustrate how these methods have been used in practice. 