Please use this identifier to cite or link to this item: http://hdl.handle.net/1993/949

 Title: Wavelets and the use of curvature to approximate surfaces Authors: Li, Chang Issue Date: 1-Jun-1997 Abstract: By using the wavelets and curvature, I tried to get a high quality compact representation of a surface. I get better results than simple Haar wavelets with curvature subdivision and Local Haar wavelets on the mathematical range data surface. To estimate the curvature of a curve represented by discrete data, a three point algorithm is developed. A normal approximation algorithm and an algorithm to estimate the Gaussian curvature are also developed for surface. The latter algorithm has a stable and fast convergence. To present background knowledge, I describe the multiresolution analysis with matrix and filter bank representation, the endpoint-interpolating B-spline wavelets, and basics of differential geometry. Several selection strategies for wavelets such as threshold and $\rm L\sp2$ measurement are presented and tested. A simple location mapping algorithm for Haar wavelets is also studied. Finally I discuss the conclusions and future work. URI: http://hdl.handle.net/1993/949 Appears in Collection(s): FGS - Electronic Theses & Dissertations (Public)

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