A parameterization method for B-spline curve interpolation via supervised regression

Abstract

Parameterization plays a crucial role in the quality of B-spline curve interpolation, but automatically selecting an appropriate method for diverse data distributions remains challenging. A recent classification-based hybrid parameterization approach addresses this issue, statistically outperforming alternative methods, but it comes with relatively high computational costs. In this work, an automatic parameterization method via supervised regression is proposed for B-spline curve interpolation. A regressor is first trained on a dataset of randomly generated data point sequences (each of length four), with optimal parameters from those given by classical methods used as labels. The regressor then estimates the optimal local parameters for each set of four consecutive data points based on their local geometric distribution. Global parameters that closely match the local ones are computed through a merging process. Since local parameters are directly generated by the regressor, the proposed method is more efficient than the classification-based hybrid approach. Additionally, since regressors are inherently more flexible than classifiers, the proposed regression-based method is compatible with any existing or new parameterization method — rather than being limited to just the three representative methods used in the classification-based approach — and is capable of producing better results. Experimental results demonstrate that the proposed method efficiently produces superior interpolation curves compared to existing techniques, even outperforming the previous classification-based approach with an idealized theoretical classifier.