<title>Qualitative and quantitative characterization of surface and volumetric properties of objects for recognition</title>

Abstract

Recently advanced computational theories of 3D shape representation for recognition have focused on the alternative of viewer-centered vs. object-centered representation. Both approaches rely on establishing a correspondence between image data and the prototypical knowledge of object shape. This paper discusses the mathematical structures needed for organizing prototypical knowledge of object shape in a way that naturally relies to perceptual categories and thus allows for a flexible and efficient recognition process. The representational schema consists of a configuration of boundary based constituent parts which build the reference frame for qualitative and quantitative shape attributes. The decomposition into constituent parts maximizes convexity regions of the bounding surface and relies on extending the local classification into elliptic, hyperbolic, plane and parabolic to globally convex and nonconvex surface regions. The surface type of the parts guides and is preserved in a subsequent part approximation through generalized cones as volumetric primitives. This approach allows for a consistent characterization of surface and volumetric properties of object shape. A secondary segmentation into sub-parts and associated features is defined by the surface type and the type of change in cross section area along the axis. The two segmentation levels allows for a detailed and elaborate shape description. We show examples of shape description and discuss the representation in relation to the viewer-centered and object centered approaches to recognition.