Computing aspect graphs of curved objects for object recognition.

Abstract

The aspect graph is a viewer-centered object representation that describes the shape of the object by its qualitatively distinct views as seen from various viewpoints. The aspect graph is very useful for generating effective object recognition strategies, since it provides the information about all possible image feature configurations. Several researchers have proposed different algorithms for computing the aspect graphs of polyhedral objects, solids of revolution, and objects bounded by quadric surfaces. In this thesis, we present an algorithm to compute the exact aspect graph of a piecewise smooth curved object bounded by rational algebraic surfaces under orthographic projection. Each view is qualitatively characterized by the topological structure of image contours corresponding to depth and surface normal discontinuities. Computing the aspect graph requires partitioning the viewpoint space into regions, in each of which the structure of the image contours is stable. Region boundaries represent visual events, which are sudden changes in the structure of the image contours. Partitioning the viewpoint space is based on the understanding of all visual events and the viewpoints where they occur. For piecewise smooth objects, a catalogue of visual events was prepared using tools from singularity theory. However, the catalogue is incomplete. In this thesis, we present a complete analysis of events that are not previously studied, and formulate a mathematical framework for computing viewpoints where the visual events occur. Based on the visual event analysis, we also show that the size of the aspect graph is $O(d\sp{24}n\sp6$) under orthographic projection and $O(d\sp{36}n\sp9$) under perspective projection, where n is the number of object surfaces and d is the maximum parametric degree of the surfaces.