<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Woodford, Oliver J</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Global Perspective on MAP Inference for Low-Level Vision Supplementary material to ICCV submission \# 1536</style></title><secondary-title><style face="normal" font="default" size="100%">Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2009</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">In recent years the Markov Random Field (MRF) has become the de facto probabilistic model for low-level vision applications. However, in a maximum a posteriori (MAP) framework, MRFs inherently encourage delta function marginal statistics. By contrast, many low-level vision problems have heavy tailed marginal statistics, making the MRF model unsuitable. In this paper we introduce a more general Marginal Probability Field (MPF), of which the MRF is a special, linear case, and show that convex energy MPFs can be used to encourage arbitrary marginal statistics. We introduce a flexible, extensible framework for effectively optimizing the resulting NP-hard MAP problem , based around dual-decomposition and a modified min-cost flow algorithm, and which achieves global optimality in some instances. We use a range of applications, including image denoising and texture synthesis, to demonstrate the benefits of this class of MPF over MRFs.</style></abstract></record></records></xml>