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This thesis investigates advanced signal processing concepts and their application to geometric processing and transformations of images and volumes. In the first part, we discuss the class of transformations that project volume data onto a plane using par ...
We present an explicit formula for B-spline convolution kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. We apply our results to derive spline-convolution-based algorithms for two closely related prob ...
We define texture mapping as an optimization problem for which the goal of preserving the maximum amount of information in the mapped texture. We derive a solution that is optimal in the least-squares sense and that corresponds to the pseudo-inverse of a r ...
We develop a spline calculus for dealing with fractional derivatives. After a brief review of fractional splines, we present the main formulas for computing the fractional derivatives of the underlying basis functions. In particular, we show that the $ γ ^ ...
