Title: Multiresolution Analysis on Irregular Surface Meshes (G.P. Bonneau)
Published in IEEE TVCG, Volume 4, Number 4, 1998.
© 1998 IEEE. Personal use of this material is permitted. However, permission
to reprint/republish this material for advertising or promotional purposes or
for creating new collective works for resale or redistribution to servers or
lists, or to reuse any copyrighted component of this work in other works must
be obtained from the IEEE.
This material is presented to ensure timely dissemination of scholarly and technical
work. Copyright and all rights therein are retained by authors or by other
copyright holders. All persons copying this information are expected to adhere
to the terms and constraints invoked by each author's copyright. In most cases,
these works may not be reposted without the explicit permission of the copyright
holder.
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 {\it 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 non-regular triangulations,
-
it extents previous results on Haar-wavelets over 4-to-1 split triangulations.
Postscript files:
Links to color plates (HTML + Jpeg images):
Return to
George-Pierre Bonneau's homepage.