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One of the areas of research that has achieved tremendous importance over the recent past is the problem of reconstructing a surface of a solid polyhedral object. This problem has found vast applications in human anatomy, automobile design, medical imaging and therapy, etc. One of the foremost techniques used to solve this problem included constructing the solid from a series of slices parallel to each other. This slice data was obtained by taking horizontal cross-sections passing through the interior of the solid like slicing an apple through a number of thin horizontal planes. The piecewise linear interpolation technique was one of the traditional algorithms based on the above slicing technique. One of the problems with this algorithm was that the running time of the algorithm was large and it required fine-tuning of certain external parameters. In the 1980s, multiresolution methods using wavelets emerged as an alternative to solve problems then solved by the windowed Fourier transforms. Wavelets were basically useful for sparse representations of various functions. Our thesis aims at implementing the multiresolution tiling algorithm using wavelets for the purpose of surface reconstruction. This technique also uses data from slices taken through the surface being reconstructed. In this thesis, we have discussed the pros and cons of using either algorithm and our implementation provides a stable workbench for surface reconstruction using wavelets to enable further research. Experiments show that the running time of the multiresolution tiling algorithm is much lesser than that of the piecewise linear technique. Experiments also show that both algorithms show good resemblances with that of the original. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .I94. Source: Masters Abstracts International, Volume: 42-02, page: 0615. Adviser: Asish Mukopadhyay. Thesis (M.Sc.)--University of Windsor (Canada), 2003.
Iyer, Shobha., "Wavelet-based multiresolution method for surface reconstruction." (2003). Electronic Theses and Dissertations. 4552.