Issue No. 04 - October-December (1998 vol. 4)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/2945.765329
<p><b>Abstract</b>—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 <it>subdivision-connectivity</it>: 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 <it>exact reconstruction</it> of the data set, even for nonregular triangulations, and it extends previous results on Haar-wavelets over 4-to-1 split triangulations.</p>
Wavelets, nonregular triangulations, compression, visualization.
G. Bonneau, "Multiresolution Analysis on Irregular Surface Meshes," in IEEE Transactions on Visualization & Computer Graphics, vol. 4, no. , pp. 365-378, 1998.