3 Part based 3 D representation for the retrieval of 3 D graphical models

3D object representations have become an integral part of modern computer graphics applications, such as computer-aided design, game development and film production. At the same time, 3D data have become very common in domains such as computer vision, computational geometry, molecular biology and medicine. The rapid evolution in graphics hardware and software development, in particular the availability of low cost 3D scanners, has greatly facilitated 3D model acquisition, creation and manipulation, giving the opportunity to experience applications using 3D models to a large user community. As the number of 3D models is continuously growing the problem of creating new 3D models has shifted to the problem of searching for existing 3D models. Thereupon, the development of efficient search mechanisms is required for the effective retrieval of 3D objects from large repositories, both of a single class and across classes. In this dissertation, a graph-based representation of a 3D object is introduced using a novel segmentation algorithm and the attributed relational graph concept. The proposed graph-based representation sets the base for an effective 3D object retrieval methodology of articulated objects. The contribution of this dissertation is two-fold. The first contribution is a 3D mesh segmentation algorithm based on the premise that a 3D object consists of its main body part and its constituent protrusible parts. The proposed segmentation algorithm aims to segment the object into these parts. To achieve this goal, first the salient points of the object are detected. These points are prominent features of the 3D object that guide the rest of the segmentation. Afterwards, the salient points are gathered into groups representing the main protrusible parts of the object. In the sequel, the main body (core) of the object is approximated using the minimum cost paths between the salient points of the object. The key idea of the proposed core approximation is to expand a set of vertices in ascending order of protrusion function value until the expanded set touches a certain percentage of all elements of the minimum cost paths. The core approximation either covers portions of the protrusible part areas or is very close to the neighboring areas where the real boundary between the core component and the protrusible part is situated. Afterwards, the partitioning boundary is detected, that is the boundary between a protrusible part and the main body of the mesh. It is considered that in the area enclosed by the desired