3D mesh geometry filtering algorithms for progressive transmission schemes

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 the Refs. [Taubin G. A signal processing approach to fair surface design. Computer Graphics Proc., Annual Conference Series 1995;351–358; Taubin G, Zhang T, Golub G. Optimal surface smoothing as filter design. IBM Research report RC–20,404, 1996], as a global predictor for the geometry data of a 3D mesh in multiresolution 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 predecessor lifted to the connectivity of the current level. The polynomial filter is designed to minimize the l-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. q 2000 Elsevier Science Ltd. All rights reserved.