We propose an adaptive semi-regular remeshing algorithm for surface meshes. Our algorithm uses Voronoi tessellations during both simplification and refinement stages. During simplification, the algorithm constructs a first centroidal Voronoi tessellation of the vertices of the input mesh. The sites of the Voronoi cells are the vertices of the base mesh of the semi-regular output. During refinement, the new vertices added at each resolution level by regular subdivision are considered as new Voronoi sites. We then use the Lloyd relaxation algorithm to update their position, and finally we obtain uniform semi-regular meshes. Our algorithm also enables adaptive remeshing by tuning a threshold based on the mass probability of the Voronoi sites added by subdivision. Experimentation shows that our technique produces semi-regular meshes of high quality, with significantly less triangles than state of the art techniques.

International audienceThis paper describes how to optimize two popular wavelet transforms for semi-regular meshes, using a lifting scheme. The objective is to adapt multiresolution analysis to the input mesh to improve its subsequent coding. Considering either the Butterfly- or the Loop-based lifting schemes, our algorithm finds at each resolution level an optimal prediction operator P such that it minimizes the L1 norm of the wavelet coefficients. The update operator U is then recomputed in order to take into account the modifications to P. Experimental results show that our algorithm improves on state-of-the-art wavelet coders

To cite this version: ABSTRACTIn this paper, we propose an optimization of the lifted Butterfly scheme for semi-regular meshes. This optimization consists in adapting the predict and update steps at each level of resolution for a given semi-regular mesh. The motivation is the improvement of the multiresolution analysis in order to increase the compression performances of the subsequent geometry coder. We first compute an optimized prediction scheme that minimizes the L1-norm of the wavelet coefficients for each level of resolution, independently. We then compute the update scheme in order to preserve the data average (0 th moment) at the lower resolution. Experimental results shows that our technique globally reduces the entropy of the wavelet coefficients of any semi-regular mesh. Consequently our contribution also improves the compression performances of the zerotree coder PGC.

Abstract. In this paper, we propose a compression scheme for animated semi-regular meshes. This scheme includes a spatio-temporal wavelet filtering to exploit the coherence both in time and space. In order to optimize the quantization of both spatial and temporal wavelet coefficients, the proposed compression scheme also includes a model-based bit allocation. The experimental results show that this approach significantly improves the compression performances, when comparing with previous similar approaches.