Exploiting 2D Topology in Labeling Polyhedral Images

Abstract

A polyhedral image is a segmentation of the image plane into connected regions, called faces, joined by vertices and edges. The segmentation is represented by a planar network of nodes (vertices, edges, faces) linked by adjacency links. The labeling constraints at a node are all local labelings of the node consistent with itself and all its adjacent neighbors. The locallabelings are represented by junctions, junction-pairs, and junction-loops respectively for the vertices, edges, and face boundaries of the image. Constraint satisfaction and propagation is done uniformly over all nodes in the image, from each node to its adjacent neighbors. The result is local consistency or inconsistency at all the nodes in the planar network. We show that globally consistent labelings of the image exist, if and only if all the nodes in the network have locally consistent labelings. The planar network of nodes, with labels and locallabelings attached to each node, represents all locally /globally consistent labelings of the polyhedral image.