On optimizing knot positions for multidimensional B-spline models

Xiang Deng; Thomas S. Denney Jr.

doi:10.1117/12.527245

21 May 2004 On optimizing knot positions for multidimensional B-spline models

Xiang Deng, Thomas S. Denney Jr.

Proceedings Volume 5299, Computational Imaging II; (2004) https://doi.org/10.1117/12.527245
Event: Electronic Imaging 2004, 2004, San Jose, California, United States

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 L^∞error 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: L^∞global 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.

Citation Download Citation

Xiang Deng and Thomas S. Denney Jr. "On optimizing knot positions for multidimensional B-spline models", Proc. SPIE 5299, Computational Imaging II, (21 May 2004); https://doi.org/10.1117/12.527245

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