A critical issue in recognizing 3D objects and in registering surfaces is the definition of a ound measure of similarity between 3D shapes. Although shape similarity metrics have been proposed in the case of 2D shapes, only partial results have been obtained for 3D shapes. Part of the problem is that it is difficult to define the necessary pose-independent reference frame on a 3D surface. This research investigates representations of 3D shapes that lead to a natural definition of shape similarity that can be built directly from point sets without requiring feature extraction, segmentation, or surface fitting. These representations may be adjusted to be either a global representation of a surface (e.g., for object recognition) or a more local representation (e.g., for tracking of local surface patches.) They lead naturally to 3D shape matching algorithms directly applicable to object recognition problems. Beyond their application to 3D object recognition, these representations will provide a framework for the analysis of 3D shapes. Of particular interest is the study of shape classes and generic object recognition. The shape representations and the associated matching algorithms are validated through scenarios motivated by real applications. In one application, object recognition is used for building and identifying geometric models of industrial parts. In a second application, the shape similarity technique is used for registering views of terrain and landmark surfaces in a natural environment for mobile robot navigation and mapping.
