Learning Contour-Fragment-based Shape Model with And-Or Tree Representation

Abstract: This paper proposes a simple yet effective method to learn the hierarchical object shape model consisting of local contour fragments, which represents a category of shapes in the form of an And-Or tree. This model extends the traditional hierarchical tree structures by introducing the "switch" variables (i.e. the or-nodes) that explicitly specify production rules to capture shape variations. We thus define the model with three layers: the leaf-nodes for detecting local contour fragments, the or-nodes specifying selection of leaf-nodes, and the root-node encoding the holistic distortion. In the training stage, for optimization of the And-Or tree learning, we extend the concave-convex procedure (CCCP) by embedding the structural clustering during the iterative learning steps. The inference of shape detection is consistent with the model optimization, which integrates the local testings via the leaf-nodes and or-nodes with the global verification via the root-node. The advantages of our approach are validated on the challenging shape databases (i.e., ETHZ and INRIA Horse) and summarized as follows. (1) The proposed method is able to accurately localize shape contours against unreliable edge detection and edge tracing. (2) The And-Or tree model enables us to well capture the intraclass variance.