A Phase Space Approach to Minimax Entropy Learning and the Minutemax Approximations

There has been much recent work on measuring image statistics and on learning probability distributions on images. We observe that the mapping from images to statistics is many-to-one and show it can be quantified by a phase space factor. This phase space approach throws light on the Minimax Entropy technique for learning Gibbs distributions on images with potentials derived from image statistics and elucidates the ambiguities that are inherent to determining the potentials. In addition, it shows that if the phase factor can be approximated by an analytic distribution then the computation time for Minimax entropy learning can be vastly reduced. An illustration of this concept, using a Gaussian to approximate the phase factor, leads to a new algorithm called "Minutemax," which gives a good approximation to the results of Zhu and Mumford in just seconds of CPU time. The phase space approach also gives insight into the multi-scale potentials found by Zhu and Mumford and suggest...

• Type: Conference
• Year: 1998
• Where: NIPS
• Authors: James M. Coughlan, Alan L. Yuille
• Keywords: Minimax Entropy, NIPS 1998, NIPS 2007, Phase Factor, Phase Space