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<p><b>Abstract</b>—This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a <tmath>$C^2$</tmath>-continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-to-fine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function. Experimental results demonstrate that high-fidelity reconstruction is possible from a selected set of sparse and irregular samples.</p>
Scattered data interpolation, multilevel B-splines, data approximation.
George Wolberg, Seungyong Lee, Sung Yong Shin, "Scattered Data Interpolation with Multilevel B-Splines", IEEE Transactions on Visualization & Computer Graphics, vol. 3, no. , pp. 228-244, July-September 1997, doi:10.1109/2945.620490
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