Particle-based meta-model for continuous breakpoint optimization in smooth local-support curve fitting

• We compute a smooth meta-model of a given set of data points based on local-support free-form parametric curves.
• Our method applies a particle-based metaheuristic approach to determine optimal values of unknowns of the fitting curve.
• The method does not assume any knowledge about the underlying function of data beyond the data points.
• Our approach performs well and in a fully automatic way even for underlying functions exhibiting challenging features.
• Our experiments show that our approach outperforms previous approaches in terms of generality and fitting error accuracy.

This paper concerns the process of computing the underlying function of a given set of data points. In many cases, it is not possible to obtain an analytical solution for this problem so the goal is transformed into that of computing a meta-model instead. In this paper we seek to compute a smooth meta-model of such points based on local-support free-form parametric curves. Given an initial parameterization, our method applies a particle-based metaheuristic approach to determine optimal values for the breakpoints and poles of the fitting curve, which is well-known to be a continuous nonlinear optimization problem. The performance of our approach is evaluated by its application to two illustrative examples: a synthetic academic shape and a real-world shape. Our experimental results show that the proposed scheme performs very well, even for shapes with underlying functions exhibiting challenging features, such as self-intersections and sharp changes of curvature. Comparative results show that our approach outperforms previous approaches in terms of generality and fitting error accuracy.