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Mathematical Problems in Engineering
Volume 2014, Article ID 351648, 13 pages
Research Article

Hybrid Functional-Neural Approach for Surface Reconstruction

1Department of Applied Mathematics and Computational Sciences, E.T.S.I. Caminos, Canales y Puertos, University of Cantabria, Avenida de los Castros, s/n, 39005 Santander, Spain
2Department of Information Science, Faculty of Sciences, Toho University, 2-2-1 Miyama, Funabashi 274-8510, Japan

Received 28 July 2013; Accepted 8 December 2013; Published 16 January 2014

Academic Editor: Yudong Zhang

Copyright © 2014 Andrés Iglesias and Akemi Gálvez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper introduces a new hybrid functional-neural approach for surface reconstruction. Our approach is based on the combination of two powerful artificial intelligence paradigms: on one hand, we apply the popular Kohonen neural network to address the data parameterization problem. On the other hand, we introduce a new functional network, called NURBS functional network, whose topology is aimed at reproducing faithfully the functional structure of the NURBS surfaces. These neural and functional networks are applied in an iterative fashion for further surface refinement. The hybridization of these two networks provides us with a powerful computational approach to obtain a NURBS fitting surface to a set of irregularly sampled noisy data points within a prescribed error threshold. The method has been applied to two illustrative examples. The experimental results confirm the good performance of our approach.