Lévy flight-driven simulated annealing for B-spline curve fitting

Abstract

Point cloud approximation by spline models, also called curve and surface reconstruction, is an active research field in computer-aided design and manufacturing (CAD/CAM). Due to the physical and mechanical processes used to obtain the data, the measurements are often affected by noise and other distortions. Obtaining a suitable spline model to reconstruct the underlying shape of the data while maintaining a low design complexity leads to a multivariate and highly non-linear optimization problem, also known to be non-convex and multi-modal. In this work, we propose a method to fit a given point cloud by means of a B-spline curve model. Our approach to solve the optimization problem is based on a powerful thermodynamics-driven metaheuristic known as the Simulated Annealing. We compute the model parameters by combining traditional SA techniques with Lévy flights (random walks based on the Lévy distribution). The ability to perform such a flight allows the algorithm to escape from local minima and energy plateaus, a strong requirement when dealing with highly multi-modal problems. The performance and robustness of our algorithm is tested against three illustrative examples. Our experimental results show that our method is able to reconstruct the underlying shape of the data, even in the presence of noise, with acceptable accuracy and in a completely automated way.