Intelligent modeling and manipulation of three dimensional objects in computer vision and animation

In this thesis, the author investigates the use of Attributed Hypergraph Representation (AHR) based on category theory as the supporting framework of a generic 3D object modeling and manipulation methodology. The efficacy of the methodology is illustrated by its applications in computer vision and animation. Compared with the relational graph used in computer vision [79] and the scene graph used in computer graphics [17], AHR has the advantage that it is capable of representing multiple relations by its hyperedge structure. One of the most important contributions of the thesis is the mathematical framework established to examine AHR from a theoretical perspective.; From multiple 2D views of a 3D object or scene, range information is first computed and then a triangular mesh model is built. A net-like data structure of AHR can be configured on this mesh model. The data structure is designed to handle the transformations on the representation corresponding to the object's movements and deformations. In an attributed hypergraph, the attributes associated with the hyperedges and the vertices give it power to model arbitrary shapes with geometrical, physical or behavioral features. As a hierarchical and generic representation, AHR enables pattern matching, recognition, synthesis and manipulation to be carried out at different resolution levels or on different subsets depending on the context. Symbolic computation on knowledge represented in the format of attributed hypergraphs becomes straightforward.; From the mathematical viewpoint, a representation on a feature level with the transformations defined on it, such as physically based modeling [85] with the state transition functions, forms a category; AHR and AHR transformations form another category. Given the features of a 3D object or scene, the procedure of constructing the AHR corresponds to the concept of functor in category theory, which maps one category to another one. The transformations of AHR are in the form of a set of operators defined on attributed by pergraphs, which stand for the motions and deformations of the object.; This representation is applied to various modeling and manipulation tasks on 3D objects: (1) the process of motion analysis of a 3D object is the task of extracting a sequence of AH operators from the AHR of the object; (2) a 3D scene can be modeled by AHR and then altered/augmented with other 3D models, by which an augmented reality can be built; (3) given the AHR's of two different 3D shapes, 3D morphing can be accomplished by matching the two AHR's and then mapping the difference to a sequence of AH operators; (4) model based animation of an object can be accomplished by applying a set of AH operators to its AHR.