Implicit B-spline fitting using the 3L algorithm

Abstract

This paper proposes a novel extension of the 3L algorithm to the B-Splines solution space. The 3L algorithm is a fast algebraic method for fitting a set of points through implicit curves or surfaces. It was originally proposed for Implicit Polynomials, which although simple and attractive are not flexible representations. In this paper Implicit B-Splines (IBSs) are used to define the solution space of the 3L algorithm. IBSs offer flexible representations, which can be locally controlled. These properties are exploited for regularizing the solution space. The experimental results illustrate that the proposed framework outperforms previous formulation.