The paper presents a new approach to least-squares spline fitting of curves. A new approximately orthogonal basis, the Q-spline basis, for n-degree uniform spline space is developed. Using the Q-spline basis, it is shown that least squares spline fitting can be approximated via a single fixed sized inner product for each control point. Another convolution maps these Q-spline control points to the classical B-spline control points. Tight error bounds on the approximation induced errors are derived. Finally a procedure for discrete least squares spline fitting via convolution is presented along with several examples. A generalization of the result has relevance to the solution of regularized fitting problems.<>
Fast least-squares curve fitting using quasi-orthogonal splines
Proceedings of 1st International Conference on Image Processing ; 1 ; 686-690 vol.1
1994-01-01
561213 byte
Conference paper
Electronic Resource
English
Fast Least-Squares Curve Fitting using Quasi-Orthogonal Splines
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