3d Mesh Geometry Filtering Algorithms For Progressive Transmission Schemes

3D Mesh Geometry Filtering Algorithms for Progressive Transmission Schemes

Abstract: "A number of static and multi-resolution methods have been introduced in recent years to compress 3D meshes. In most of these methods the connectivity information is encoded without loss of information, but user-controllable loss of information is tolerated while compressing the geometry and property data. All these methods are very efficient at compressing the connectivity information, in some cases to a fraction of a bit per vertex, but the geometry and property data typically occupies much more room in the compressed bitstream than the compressed connectivity data. In this paper we investigate the use of polynomial linear filtering as studied in [Taubin95, TaZhGo96], as a global predictor for the geometry data of a 3D mesh in multi-resolution 3D geometry compression schemes. Rather than introducing a new method to encode the multi-resolution connectivity information, we choose one of the efficient existing schemes depending on the structure of the multi-resolution data. After encoding the geometry of the lowest level of detail with an existing scheme, the geometry of each subsequent level of detail is predicted by applying a polynomial filter to the geometry of its predecesor [sic] lifted to the connectivity of the current level. The polynomial filter is designed to minimize the l2-norm of the approximation error but other norms can be used as well. Three properties of the filtered mesh are studied next: accuracy, robustness and compression ratio. The Zeroth Order Filter (unit polynomial) is found to have the best compression ratio. But higher order filters achieve better accuracy and robustness properties at the price of a slight decrease of the compression ratio."

Dissertation Abstracts International

Handbook of Discrete and Computational Geometry, Second Edition

While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies