Multiresolution analysis on irregular surface meshes

Wavelet-based methods have proven their efficiency for 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...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics 1998-10, Vol.4 (4), p.365-378
Main Author: Bonneau, G.-P.
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Artificial intelligence
Computer errors
Computer graphics
Computer Science
Computer science
control theory
systems
Data visualization
Exact sciences and technology
Graphics
Multiresolution analysis
Pattern recognition. Digital image processing. Computational geometry
Reconstruction algorithms
Surface reconstruction
Surface waves
Theoretical computing
Wavelet analysis
Wavelet domain
Wavelet transforms
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Summary:Wavelet-based methods have proven their efficiency for 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 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.
ISSN:1077-2626
1941-0506
DOI:10.1109/2945.765329