Immunological-based approach for accurate fitting of 3D noisy data points with Bézier surfaces

Abstract

Free-form parametric surfaces are common tools nowadays in many applied fields, such as Computer-Aided Design & Manufacturing (CAD/CAM), virtual reality, medical imaging, and many others. A typical problem in this setting is to fit surfaces to 3D noisy data points obtained through either laser scanning or other digitizing methods, so that the real data from a physical object are transformed back into a fully usable digital model. In this context, the present paper describes an immunologicalbased approach to perform this process accurately by using the classical free-form Bézier surfaces. Our method applies a powerful bio-inspired paradigm called Artificial Immune Systems (AIS), which is receiving increasing attention from the scientific community during the last few years because of its appealing computational features. The AIS can be understood as a computational methodology based upon metaphors of the biological immune system of humans and other mammals. As such, there is not one but several AIS algorithms. In this chapter we focus on the clonal selection algorithm (CSA), which explicitly takes into account the affinity maturation of the immune response. The paper describes how the CSA algorithm can be effectively applied to the accurate fitting of 3D noisy data points with Bézier surfaces. To this aim, the problem to be solved as well as the main steps of our solving method are described in detail. Some simple yet illustrative examples show the good performance of our approach. Our method is conceptually simple to understand, easy to implement, and very general, since no assumption is made on the set of data points or on the underlying function beyond its continuity. As a consequence, it can be successfully applied even under challenging situations, such as the absence of any kind of information regarding the underlying function of data.This research has been kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. #TIN2012-30768, and the University of Cantabria (Santander, Spain). This work has been done during the sabbatical stay of second author at Toho University (Funabashi, Japan), whose academic support has been very valuable to produce this paper. We would also like to thank the three anonymous reviewers for their encouraging comments which helped us to improve the first version of the paper