Filter-based Mean-Field Inference for Random Fields with Higher Order Terms and Product Label-Spaces

Recently, a number of cross bilateral filtering methods have been proposed for solving multi-label problems in computer vision, such as stereo, optical flow and object class segmentation that show an order of magnitude improvement in speed over previous methods. These methods have achieved good results despite using models with only unary and/or pairwise terms. However, previous work has shown the value of using models with higher-order terms e.g. to represent label consistency over large regions, or global co-occurrence relations. We show how these higher-order terms can be formulated such that filter-based inference remains possible. We demonstrate our techniques on joint stereo and object labeling problems, as well as object class segmentation, showing in addition for joint object-stereo labeling how our method provides an efficient approach to inference in product label-spaces. We show that we are able to speed up inference in these models around 10-30 times with respect to competing graph-cut/move-making methods, as well as maintaining or improving accuracy in all cases. We show results on PascalVOC-10 for object class segmentation, and Leuven for joint object-stereo labeling.