System and method for image segmentation using continuous valued MRFs with normed pairwise distributions

摘要

A method for segmenting a digital image includes initializing object and background seed nodes in an image, where the image is represented as a graph G=(V, E) whose nodes iεV correspond to image points and whose edges eεE connect adjacent points, where set M⊂V contains locations of nodes marked as seeds, set U⊂V contains locations of unmarked nodes, set O⊂M contains locations of object seed nodes, and set B⊂M contains locations of background seed nodes, assigning to each seed node a membership value such that ∀iεO,x_i=1 and ∀iεB,x_i=0, where each node iεV is associated with a membership x_iε[0,1], and finding a membership vector xε, whose i^th entry is given by x_i that minimizes; $$ E_p\left(x\right)=\sum _{\mathrm{eij}\in E}{w}_{\mathrm{ij}}{x_i-x_j}^{\mathrm{pij}},$$where each edge e_ijεE connecting nodes i and j in V is associated with a weight w_ij and an exponent p_ij, and ∀e_ijεE,1≦p_ij∞, such that x_i=1 if iεO and x_i=0 if iεB.