1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Image Analysis and Computer Graphics, Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark
Analysis and processing of 3D digital shapes is a significant research area with numerous medical, industrial, and entertainment applications which has gained enormously in importance as optical scanning modalities have started to make acquired 3D geometry commonplace. The area holds many challenges. One such challenge, which is addressed in this thesis, is to develop computational methods for classifying shapes which are in agreement with the human way of understanding and classifying shapes. In this dissertation we first present a shape descriptor based on the process of diffusion on the surface of the shape – the auto diffusion function. When all heat is inserted at a single point, the function describes how much of that heat will remain at the same point after a period of time. This method allows for finding shape features at different scales related to time parameter. For instance, in conjunction with the method of Reeb graphs for skeletonization, it is an effective tool for generating scale dependent skeletons of shapes represented as 3D triangle meshes. The second part of the thesis aims at capturing the style phenomenon. The style of an object is easily recognized by humans but a computational method for finding the style of an object is elusive. Instead of codifying the style explicitly, which can be only done within a specific context, we develop a general method for dealing with both style and function which uses the supervision provided by a set of training examples and can be evaluated using any shape descriptor, that produces dissimilarity measures between different shapes. Our methods decouple the effect of style from the effect of function and assess how suitable a descriptor is to a specific problem.