Rate-distortion optimal mesh simplification for communications

The thesis studies the optimization of a specific type of computer graphic representation: polygon-based, textured models. More precisely, we focus on meshes having 4-8 connectivity. We study a progressive and adaptive representation for textured 4-8 meshes suitable for transmission. Our results are valid for 4-8 meshes built from matrices of amplitudes, or given as approximations of a subdivision surface. In the latter case, the models can have arbitrary topology. In order to clarify our goals, we first describe a transmission system for computer graphics models (Chapter 1). Then, we review approximation techniques (Chapter 2) and study the computational properties of 4-8 meshes (Chapter 3). We provide an efficient method to store and access our dataset (Chapter 4). We address the problem of 4-8 mesh simplification and give an efficient θ(n log n) algorithm to compute progressive and adaptive representations of 4-8 meshes using global error (Chapter 5). We study the joint optimization of mesh and texture (Chapter 6). Finally, we conclude and give future research directions (Chapter 7)