{"id":157936,"date":"2009-01-01T00:00:00","date_gmt":"2009-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/a-global-perspective-on-map-inference-for-low-level-vision\/"},"modified":"2018-10-16T20:07:01","modified_gmt":"2018-10-17T03:07:01","slug":"a-global-perspective-on-map-inference-for-low-level-vision","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/a-global-perspective-on-map-inference-for-low-level-vision\/","title":{"rendered":"A Global Perspective on MAP Inference for Low-Level Vision"},"content":{"rendered":"<div class=\"asset-content\">\n<p>TR should come soon &#8230;<\/p>\n<p>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.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>TR should come soon &#8230; 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. 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