Fast B-spline Curve Fitting by L-BFGS

TL;DR

This paper introduces a fast B-spline curve fitting method that uses L-BFGS optimization to simultaneously update control points and foot points, significantly reducing computation time compared to traditional approaches.

Contribution

The novel approach applies L-BFGS to optimize control and foot points simultaneously, eliminating costly matrix and projection computations per iteration.

Findings

Method is significantly faster than existing techniques.

Eliminates the need for matrix computation in each iteration.

Reduces overall computational complexity of B-spline fitting.

Abstract

We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to perform either matrix computation or foot point projection in every iteration. As a result, our method is much faster than existing methods.