Layered Graph Match with Graph Editing

Many vision tasks are posed as either graph partitioning (coloring) or graph matching (correspondence) problems. The former include segmentation and grouping, and the latter include wide baseline stereo, large motion, object tracking and recognition. In this paper, we present an integrated solution for both graph matching and graph partition using an effective sampling algorithm in a Bayesian framework. Given two images for matching, we extract two graphs using a primal sketch algorithm [4]. The graph nodes are linelets and primitives (junctions). Both graphs are automatically partitioned into an unknown number of K + 1 layers of subgraphs so that K pairs of subgraphs are matched and the remaining layer contains unmatched backgrounds. Each matched pair represent a "moving object" with a TPS (thin-plate-spline) transform to account for its deformations and a set of graph operators to edit the pair of subgraphs to achieve perfect structural match. The matching energy between two subgraphs includes geometric deformations, appearance dissimilarities, and the cost of graph editing operators. We demonstrate its application on two tasks: (i) large motion with occlusion, and (ii) automatic detection and recognition of common objects in a pair of images.