Discrete MRF inference of marginal densities for non-uniformly discretized variable space

Masaki Saito, Takayuki Okatani, Koichiro Deguchi

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)


This paper is concerned with the inference of marginal densities based on MRF models. The optimization algorithms for continuous variables are only applicable to a limited number of problems, whereas those for discrete variables are versatile. Thus, it is quite common to convert the continuous variables into discrete ones for the problems that ideally should be solved in the continuous domain, such as stereo matching and optical flow estimation. In this paper, we show a novel formulation for this continuous-discrete conversion. The key idea is to estimate the marginal densities in the continuous domain by approximating them with mixtures of rectangular densities. Based on this formulation, we derive a mean field (MF) algorithm and a belief propagation (BP) algorithm. These algorithms can correctly handle the case where the variable space is discretized in a non-uniform manner. By intentionally using such a non-uniform discretization, a higher balance between computational efficiency and accuracy of marginal density estimates could be achieved. We present a method for actually doing this, which dynamically discretizes the variable space in a coarse-to-fine manner in the course of the computation. Experimental results show the effectiveness of our approach.

Original languageEnglish
Article number6618859
Pages (from-to)57-64
Number of pages8
JournalProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Publication statusPublished - 2013
Event26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2013 - Portland, OR, United States
Duration: 2013 Jun 232013 Jun 28


  • Markov Random Fields
  • belief propagation
  • marginal density
  • mean field approximation


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