A Global Perspective on MAP Inference for Low-Level Vision
Abstract
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. 1.
Cite
Text
Woodford et al. "A Global Perspective on MAP Inference for Low-Level Vision." IEEE/CVF International Conference on Computer Vision, 2009. doi:10.1109/ICCV.2009.5459434Markdown
[Woodford et al. "A Global Perspective on MAP Inference for Low-Level Vision." IEEE/CVF International Conference on Computer Vision, 2009.](https://mlanthology.org/iccv/2009/woodford2009iccv-global/) doi:10.1109/ICCV.2009.5459434BibTeX
@inproceedings{woodford2009iccv-global,
title = {{A Global Perspective on MAP Inference for Low-Level Vision}},
author = {Woodford, Oliver J. and Rother, Carsten and Kolmogorov, Vladimir},
booktitle = {IEEE/CVF International Conference on Computer Vision},
year = {2009},
pages = {2319-2326},
doi = {10.1109/ICCV.2009.5459434},
url = {https://mlanthology.org/iccv/2009/woodford2009iccv-global/}
}