Bayesian inference for layer representation with mixed Markov random field

This paper presents a Bayesian inference algorithm for image layer representation [26], 2.1D sketch [6], with mixed Markov random field. 2.1D sketch is an very important problem in low-middle level vision with a synthesis of two goals: segmentation and 2.5D sketch, in other words, it is to consider 2D segmentation by incorporating occulision/ depth explicitly to get the partial order of final segmented regions and contour completion in the same layer. The inference is based on Swendsen-Wang Cut (SWC) algorithm [4] where there are two types of nodes, instead of all nodes being the same type in traditional MRF model, in the graph representation: atomic regions and their open bonds desribed by address variables. These makes the problem a mixed random field. Therefore, two kinds of energies should be simultaneously minimized by maximizing a joint posterior probability: one is for region coloring/layering, the other is for the assignments of address variables. Given an image, its primal sketch is computed firstly, then some atomic regions can be obtained by completing some sketches into a closed contour. At the same time, T-junctions are detected and broken into terminators as the open bonds of atomic regions after being assigned the ownership between them and atomic regions. With this graph representation, the presented inference algorithm is performed and satisfactory results are shown in the experiments.