--- _id: '3203' abstract: - lang: eng text: 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 mincost 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. author: - first_name: Oliver full_name: Woodford, Oliver J last_name: Woodford - first_name: Carsten full_name: Rother, Carsten last_name: Rother - first_name: Vladimir full_name: Vladimir Kolmogorov id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Woodford O, Rother C, Kolmogorov V. A global perspective on MAP inference for low level vision. In: IEEE; 2009:2319-2326. doi:10.1109/ICCV.2009.5459434' apa: 'Woodford, O., Rother, C., & Kolmogorov, V. (2009). A global perspective on MAP inference for low level vision (pp. 2319–2326). Presented at the ICCV: International Conference on Computer Vision, IEEE. https://doi.org/10.1109/ICCV.2009.5459434' chicago: Woodford, Oliver, Carsten Rother, and Vladimir Kolmogorov. “A Global Perspective on MAP Inference for Low Level Vision,” 2319–26. IEEE, 2009. https://doi.org/10.1109/ICCV.2009.5459434. ieee: 'O. Woodford, C. Rother, and V. Kolmogorov, “A global perspective on MAP inference for low level vision,” presented at the ICCV: International Conference on Computer Vision, 2009, pp. 2319–2326.' ista: 'Woodford O, Rother C, Kolmogorov V. 2009. A global perspective on MAP inference for low level vision. ICCV: International Conference on Computer Vision, 2319–2326.' mla: Woodford, Oliver, et al. A Global Perspective on MAP Inference for Low Level Vision. IEEE, 2009, pp. 2319–26, doi:10.1109/ICCV.2009.5459434. short: O. Woodford, C. Rother, V. Kolmogorov, in:, IEEE, 2009, pp. 2319–2326. conference: name: 'ICCV: International Conference on Computer Vision' date_created: 2018-12-11T12:01:59Z date_published: 2009-05-01T00:00:00Z date_updated: 2021-01-12T07:41:46Z day: '01' doi: 10.1109/ICCV.2009.5459434 extern: 1 month: '05' page: 2319 - 2326 publication_status: published publisher: IEEE publist_id: '3481' quality_controlled: 0 status: public title: A global perspective on MAP inference for low level vision type: conference year: '2009' ...