Nonlinearly constrained MRFs: exploring the intrinsic dimensions of higher-order cliques

Yun Zeng Chaohui Wang Stefano Soatto Shing-Tung Yau

Statistics Theory and Methods mathscidoc:1912.43695

1706-1713, 2013
This paper introduces an efficient approach to integrating non-local statistics into the higher-order Markov Random Fields (MRFs) framework. Motivated by the observation that many non-local statistics (eg, shape priors, color distributions) can usually be represented by a small number of parameters, we reformulate the higher-order MRF model by introducing additional latent variables to represent the intrinsic dimensions of the higher-order cliques. The resulting new model, called NC-MRF, not only provides the flexibility in representing the configurations of higher-order cliques, but also automatically decomposes the energy function into less coupled terms, allowing us to design an efficient algorithmic framework for maximum a posteriori (MAP) inference. Based on this novel modeling/inference framework, we achieve state-of-the-art solutions to the challenging problems of class-specific image segmentation and template-based 3D facial expression tracking, which demonstrate the potential of our approach.
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@inproceedings{yun2013nonlinearly,
  title={Nonlinearly constrained MRFs: exploring the intrinsic dimensions of higher-order cliques},
  author={Yun Zeng, Chaohui Wang, Stefano Soatto, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205034079988259},
  pages={1706-1713},
  year={2013},
}
Yun Zeng, Chaohui Wang, Stefano Soatto, and Shing-Tung Yau. Nonlinearly constrained MRFs: exploring the intrinsic dimensions of higher-order cliques. 2013. pp.1706-1713. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205034079988259.
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