Adaptive B-spline knot selection using multi-resolution basis set

Abstract

B-splines are commonly used to fit complicated functions in Computer Aided Design and signal processing because they are simple yet flexible. However, how to place the knots appropriately in B-spline curve fitting remains a difficult problems. This article discusses a two-stage knot placement method to place knots adapting to the curvature structures of unknown function. In the first stage, a subset of basis functions is selected from the pre-specified multi-resolution basis set using a statistical variable selection method: Lasso. In the second stage, a vector space that is spanned by the selected basis functions is constructed and a concise knot vector is identified that is sufficient to characterize the vector space to fit the unknown function. The effectiveness of the proposed method is demonstrated using numerical studies on multiple representative functions.

Keywords:

• B-splines
• Lasso
• knot selection
• free knot splines

Acknowledgements

The authors gratefully thank the editor and the referees for their valuable comments and suggestions. This research was supported by the National Science Foundation under grant CMMI-0856222 and Singapore AcRF Tier 1 Funding R-266-000-057-133.