  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.
