This work aims at computing multiresolution analysis on 3D triangular meshes
Figure 1 : Multiresolution hierarchy build from the original mesh (left). This representation enables efficient progressive transmission.
Based on the inversion of an irregular subdivision scheme, our algorithm is able to construct a complete hierarchy of meshes from one original mesh (see figure 1). This simplification is reversible, and the information to reconstruct the original mesh connectivity from the lowest resolution mesh is a compact code, well suited for connectivity compression. The subdivision paradigm allows our approach to apply the wavelet decomposition on the mesh geometry (the vertices coordinates), the filter bank being constructed by applying the lifting scheme on the “lazy” wavelets filter bank (see figure 2).
Figure 2 : a “lazy” wavelet (left) and its lifted version (right)
Using this wavelet scheme, two compression approaches were proposed : compression with progressive resolution  (the mesh connectivity is refined during transmission) or compression with progressive precision  (the mesh geometry is refined during transmission).
Sébastien Valette and Rémy Prost, Wavelet Based Multiresolution Analysis Of Irregular Surface Meshes, IEEE Transactions on Visualization and Computer Graphics, Vol. 10, No. 2, March/April 2004, pp. 113-122.
Abstract: This paper extends Lounsbery s multiresolution analysis wavelet-based theory for triangular 3D meshes, which can only be applied to regularly subdivided meshes and thus involves a remeshing of the existing 3D data. Based on a new irregular subdivision scheme, the proposed algorithm can be applied directly to irregular meshes, which can be very interesting when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. This is very convenient in CAD (Computer-Assisted Design), when the mesh has attributes such as texture and color information, or when the 3D mesh is used for simulations, and where a different connectivity could lead to simulation errors. The algorithm faces an inverse problem for which a solution is proposed. For each level of resolution, the simplification is processed in order to keep the mesh as regular as possible. In addition, a geometric criterion is used to keep the geometry of the approximations as close as possible to the original mesh. Several examples on various reference meshes are shown to prove the efficiency of our proposal. [Preprint]
Sébastien Valette and Rémy Prost, A Wavelet-Based Progressive Compression Scheme For Triangle Meshes : Wavemesh, IEEE Transactions on Visualization and Computer Graphics, Vol. 10, No. 2, March/April 2004, pp. 123-129.
Abstract: This paper proposes a new lossy to lossless progressive compression scheme for triangular meshes, based on a wavelet multiresolution theory for irregular 3D meshes. Although remeshing techniques obtain better compression ratios for geometric compression, this approach can be very effective when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. The simplification is based on the solving of an inverse problem. Optimization of both the connectivity and geometry of the processed mesh improves the approximation quality and the compression ratio of the scheme at each resolution level. We show why this algorithm provides an efficient means of compression for both connectivity and geometry of 3D meshes and it is illustrated by experimental results on various sets of reference meshes, where our algorithm performs better than previously published approaches for both lossless and progressive compression. [Preprint]
Sébastien Valette, Alexandre Gouaillard and Rémy Prost, Compression of 3D triangular meshes with progressive precision, Computers & Graphics, Vol. 28, No. 1, February 2004, pp. 35-42.
Abstract: In this paper we introduce a novel approach for progressive transmission of three-dimensional (3D) triangular meshes. This algorithm is based on a new reversing approach of the irregular mesh subdivision that enables a wavelet representation of any mesh geometry. In this paper, we show how to achieve progressive compression of 3D models by transmitting more and more wavelet coef cients computed from the original mesh vertices coordinates. The connectivity of the reconstructed mesh remains the same as the original one, but its geometry is progressively re ned by means of bitplane encoding. This approach processes directly oating point coordinates which is the most common representation for 3D meshes, and does not need quantization, which is a lossy transformation. Experimental results are given and demonstrate the efficiency of our encoding scheme versus other approaches. [Preprint]
Sébastien Valette, Yun-Sang Kim, Ho-Youl Jung, Isabelle Magnin, Rémy Prost, A multiresolution wavelet scheme for irregularly subdivided 3D triangular mesh, IEEE Int. Conf on Image Processing ICIP’99, October 25-28, Kobe, Japan, Vol. 1, pp 171-174.Abstract: We propose a new subdivision scheme derived from the Lounsbery's 1:4 face split, allowing multiresolution analysis of irregularly subdivided triangular meshes by the wavelet transforms. Some experimental results on real medical meshes prove the efficiency of this approach in multiresolution schemes. In addition we show the effectiveness of the proposed algorithm for lossless compression. [Preprint]
Source code and executableSource code is available on github . This code is distributed under the GPL license. CNRS, INSA-Lyon, UCBL, INSERM.
This code uses: A (rather old...) pre-compiled window$ executable is available here. Note that only the github source code contains the last version.
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