Applying Clonal Selection Theory to Data Fitting with Rational Bézier Curves

Abstract

This paper addresses the problem of obtaining the rational Bezier curve that fits a given set of data points better in the least-squares sense. This is a difficult problem because in addition to compute the control points of the approximating curve, it also requires to obtain their corresponding weights and a suitable parameterization of data points. This leads to a continuous multivariate nonlinear optimization problem that cannot be solved through traditional mathematical optimization techniques. To overcome this limitation, in this work we consider a powerful bio-inspired paradigm called Artificial Immune Systems (AIS), which is receiving increasing attention from the scientific community during the last few years. The AIS is a computational methodology encompassing many different techniques rather than a single method. In this paper we focus on the clonal selection theory principles. The paper describes how they can be effectively applied to solve our problem. The performance of our approach is evaluated through its application to three illustrative examples of freeform shapes. Our experimental results show that our method performs very well, being able to reconstruct the underlying shape of data points with high accuracy.