| Geometry compression concerns the representation of three-dimensional objects. The goal of geometry compression is to find an efficient way to express models created from both the physical world and virtual reality applications. The benefits of geometry compression include the saving of storage and network bandwidths, among others. In this thesis, we first review related techniques that have been extensively used in 3D model compression and coding algorithms. Then we present a novel structure to organize a general class of polygonal mesh surfaces. Our compressed representation prevents error accumulation through careful numerical analysis. In order to obtain optimal compression results, we make full use of and improve existing 2D image compression and coding techniques so as to remove the redundancy within 3D objects to the maximum extent. In our compression framework, a new second-order prediction scheme is introduced to locate and remove possible redundant geometric information, as well as provide a compact representation to organize connectivity information. The embedded bit stream supports resilience and error recovery. To support progressive transmission, two approaches are taken. First, geometry progressive transmission is achieved by using the successive quantization technique. Second, a two-phase scheme is designed to construct multiresolution surfaces. The latter approach gives a compact progressive connectivity representation, while displaying the ability of both topology preserving and topology non-preserving decomposition and reconstruction, demonstrating the efficiency and flexibility of our approach. |
