CINAPACT-Splines: A Family of Infnite Smooth, Accurate and Compactly Supported Splines
We introduce a class of compactly supported C infinite kernels (CINAPACT-splines) whose integer translates form a shift-invariant reconstruction space that can be tuned to achieve any order of accuracy. CINAPACT-splines resemble traditional B-splines in that higher orders of accuracy are achieved by successive convolutions with a B-spline of degree zero. Unlike B-splines however, the starting point for CINAPACT-splines is a compactly supported bump function that has been properly normalized so that it fulfills the partition of unity criterion. We explore the properties of CINAPACT-splines in reconstructing volumetric data sampled on regular grids. We show that CINAPACT-splines provide similar reconstruction quality and cost compared to some well-established filters, while being infinitely smooth. We further explore the advantages of our filter by implementing a curvature-based transfer function using second derivatives of the filter to demonstrate feature lines of a function. We apply the same technique using filters of smaller support and less cost.
Akram, B. (2015). CINAPACT-Splines: A Family of Infnite Smooth, Accurate and Compactly Supported Splines (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25328