Fast least-squares curve fitting using quasi-orthogonal splines

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...

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Bibliographic Details
Main Authors: Flickner, M., Hafner, J., Rodriguez, E.J., Sanz, J.L.C.
Format: Conference Proceeding
Language:English
Subjects:
Computer graphics
Convolution
Curve fitting
Least squares approximation
Least squares methods
Optical character recognition software
Polynomials
Size control
Solid modeling
Spline
Online Access:Request full text
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Summary: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.< >
DOI:10.1109/ICIP.1994.413402