Abstract

The enclosing surface, or boundary, of a well-behaved 3-D rigid solid unambiguously specifies the object. More importantly, the boundary captures the notation of a shape, which is an intrinsic property of solid objects. There are numerous data acquisition techniques which provide geometrically explicit image information in the form of depth maps. It is of great interest to be able to extract compact, canonical shape features of an object from the geometry of the bounding surface. The so-called 3-D shape descriptors provide a viewer-independent image representation that greatly simplifies the recognition task. New 3-D shape descriptors are calculated from the differential characteristics of a solid's bounding surface. First, the bounding surface is represented by a hierarchy of bivariate functions projected on a sphere. The representation, at the top level, is an intrinsic surface function independent of the object that is embedded in its 3-D coordinate space. A subsequent Fourier transformation maps significant features for a correct classification of solids. The notation of similarity of objects, based on their shape characteristics, is simplified to a measurement of distance in a multidimensional feature space. Similar objects cluster naturally in the multidimensional descriptor space.

© 1989 Optical Society of America