The representation and matching of categorical shape

We present a framework for categorical shape recognition. The coarse shape of an object is captured by a multiscale blob decomposition, representing the compact and elongated parts of an object at appropriate scales. These parts, in turn, map to nodes in a directed acyclic graph, in which edges encode both semantic relations (parent/child or sibling) as well as geometric relations. Given two image descriptions, each represented as a directed acyclic graph, we draw on spectral graph theory to derive a new algorithm for computing node correspondence in the presence of noise and occlusion. In computing correspondence, the similarity of two nodes is a function of their topological (graph) contexts, their geometric (relational) contexts, and their node contents. We demonstrate the approach on the domain of view-based 3-D object recognition.