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   -> Volume 5, Issue 6

Thesis: Wavelets and the Use of Curvature
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changl@cs.UManitoba.CA (Chang Li)

PostPosted: Sat Aug 10, 1996 9:32 pm    
Subject: Thesis: Wavelets and the Use of Curvature
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Thesis: Wavelets and the Use of Curvature

MS Thesis Abstract

Wavelets and the Use of Curvature

Chang LI
Department of Computer Science
University of Manitoba

By the methods of multiresolution analysis, wavelets, and differential
geometry, I tried to solve the problem of surface selection,
reconstruction, and measurement. The main approach in this thesis is:
given a set of height data on a grid of rectangle field, applying
endpoint- interpolating B-spline wavelets to select and reconstruct an
approximation surface, using curvature to measure the quality of the
surface, and developing a selection strategy based on curvature
metric. The thesis had discussed multiresolutin analysis and wavelet
on vector space with matrix and filter bank representation. The
endpoint- interpolating B-spline wavelets had also been described.
Several selection stritegies are presented and tested with a tooth
image data. A new selection strategy based on location and curvature
metric is developed. The kernel of this strategy is the mapping
algorithms between the original data location and the dependent
wavelets location and the estimation of curvatures. Two methods are
approached to estimate the curvatures by three point circle and four
point parabolic blending on space curves. A method to estimate the
Gaussian curvature at the top vertex of a polyhedron is also
developed. This method can be used to arbitrary topological triangular
meshes. A group of measure criteria included curvature match,
closeness, and rate of compression for approximation surface are
described. Finally, conclusions and future work are discussed in the

[Answer: WD 11.8 Topic 5559 ]
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