M.A. Duchaineau, Dyadic Splines, Ph.D. Thesis, Department of Computer Science, University of California, Davis, 1996. http://graphics.cs.ucdavis.edu/duchaine/dyadic.html  Home/Search   Document Not in Database   Summary   Related Articles   Check

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M.A. Duchaineau, Dyadic Splines, Ph.D. Thesis, Department of Computer Science, University of California, Davis, 1996. http://graphics.cs.ucdavis.edu/duchaine/dyadic.html

....subdivision step. For the next subdivision step, all vertices become v vertices again, and the same subdivision rules are applied recursively. 3. 2 Lifted One Dimensional Wavelets A discrete wavelet transform (DWT) can be defined to represent hierarchical uniform B splines under dyadic refinement [6, 10, 36]. The principle is to decompose a B spline control polygon representing a function at a fine resolution into a hierarchy of coarser Bsplines and a set of wavelet coefficients representing the details that were reduced in each coarsening step. This process is called decomposition or analysis. ....

....moments. We use the term lifting throughout this paper to denote local operations for computing the wavelet transform. The subdivision operator S is obtained from these reconstruction rules by assuming zero wavelet coefficients e 0 . The operator S reproduces dyadic B spline subdivision [6, 10]. Vertices of type e 0 and v 0 represent coefficients for wavelets and B spline scaling functions, respectively. A cubic B spline wavelet obtained from our construction is depicted in Figure 5. To construct the corresponding decomposition rules we invert the three individual lifting ....

M.A. Duchaineau, Dyadic Splines, Ph.D. Thesis, Department of Computer Science, University of California, Davis, 1996. http://graphics.cs.ucdavis.edu/duchaine/dyadic.html

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