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Proceedings Paper

On optimizing knot positions for multidimensional B-spline models
Author(s): Xiang Deng; Thomas S. Denney Jr.
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Paper Abstract

In this paper, we present a new method for optimizing knot positions for a multi-dimensional B-spline model. Using the results from from univariate polynomial approximation theory, spline approximation theory and multivariate tensor product theory, we develop the algorithm in three steps. First, we derive a local upper bound for the Lerror in a multivariate B-spline tensor product approximation over a span. Second, we use this result to bound the approximation error for a multi-dimensional B-spline tensor product approximation. Third, we developed two knot position optimization methods based on the minimization of two global approximation errors: Lglobal error and L2 global error. We test our method with 2D surface fitting experiments using B-spline models defined in both 2D Cartesian and polar coordinates. Simulation results demonstrate that the optimized knots can fit a surface more accurately than fixed uniformly spaced knots.

Paper Details

Date Published: 21 May 2004
PDF: 12 pages
Proc. SPIE 5299, Computational Imaging II, (21 May 2004); doi: 10.1117/12.527245
Show Author Affiliations
Xiang Deng, Auburn Univ. (United States)
Thomas S. Denney Jr., Auburn Univ. (United States)

Published in SPIE Proceedings Vol. 5299:
Computational Imaging II
Charles A. Bouman; Eric L. Miller, Editor(s)

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