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Visual Surface Interpolation: A Comparison of Two Methods

Boult, Terrance E.

We critically compare 2 different methods for visual surface interpolation. One method uses the reproducing kernels of Hilbert spaces to construct a spline interpolating the data, such that this spline is of minimal norm. The other method, presented in Grimson (1981), recovers the surface of minimal norm by direct minimization of the norm with a gradient projection algorithm. We present the problem that each algorithm is attempting to solve, then briefly introduce both methods. The main contribution is an analysis of each algorithm in terms of the worst case running time (serial processor), space complexity, and rough estimates of the running time and space costs for massively parallel implementations. We then conclude with a discussion of the differences in the internal representation of the surface in both algorithms.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-189-85
Published Here
November 1, 2011
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