Abstract. 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, it...