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Multiresolution Analysis on Irregular Surface Meshes
October-December 1998 (vol. 4 no. 4)
pp. 365-378

Abstract—Wavelet-based methods have proven their efficiency for the visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all wavelet-based methods is a hierarchy of meshes that satisfies subdivision-connectivity: This hierarchy has to be the result of a subdivision process starting from a base mesh. Examples include quadtree uniform 2D meshes, octree uniform 3D meshes, or 4-to-1 split triangular meshes. In particular, the necessity of subdivision-connectivity prevents the application of wavelet-based methods on irregular triangular meshes. In this paper, a "wavelet-like" decomposition is introduced that works on piecewise constant data sets over irregular triangular surface meshes. The decomposition/reconstruction algorithms are based on an extension of wavelet-theory allowing hierarchical meshes without subdivision-connectivity property. Among others, this approach has the following features: It allows exact reconstruction of the data set, even for nonregular triangulations, and it extends previous results on Haar-wavelets over 4-to-1 split triangulations.

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Index Terms:
Wavelets, nonregular triangulations, compression, visualization.
Citation:
Georges-Pierre Bonneau, "Multiresolution Analysis on Irregular Surface Meshes," IEEE Transactions on Visualization and Computer Graphics, vol. 4, no. 4, pp. 365-378, Oct.-Dec. 1998, doi:10.1109/2945.765329
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