Skeletal Shape Abstraction from Examples

Learning a class prototype from a set of exemplars is an important challenge facing researchers in object categorization. Although the problem is receiving growing interest, most approaches assume a one-to-one correspondence among local features, restricting their ability to learn true abstractions of a shape. In this paper, we present a new technique for learning an abstract shape prototype from a set of exemplars whose features are in many-to-many correspondence. Focusing on the domain of 2D shape, we represent a silhouette as a medial axis graph whose nodes correspond to "parts" defined by medial branches and whose edges connect adjacent parts. Given a pair of medial axis graphs, we establish a many-to-many correspondence between their nodes to find correspondences among articulating parts. Based on these correspondences, we recover the abstracted medial axis graph along with the positional and radial attributes associated with its nodes. We evaluate the abstracted prototypes in the context of a recognition task.