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Memetic electromagnetism algorithm for surface reconstruction with rational bivariate Bernstein basis functions

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Abstract

Surface reconstruction is a very important issue with outstanding applications in fields such as medical imaging (computer tomography, magnetic resonance), biomedical engineering (customized prosthesis and medical implants), computer-aided design and manufacturing (reverse engineering for the automotive, aerospace and shipbuilding industries), rapid prototyping (scale models of physical parts from CAD data), computer animation and film industry (motion capture, character modeling), archaeology (digital representation and storage of archaeological sites and assets), virtual/augmented reality, and many others. In this paper we address the surface reconstruction problem by using rational Bézier surfaces. This problem is by far more complex than the case for curves we solved in a previous paper. In addition, we deal with data points subjected to measurement noise and irregular sampling, replicating the usual conditions of real-world applications. Our method is based on a memetic approach combining a powerful metaheuristic method for global optimization (the electromagnetism algorithm) with a local search method. This method is applied to a benchmark of five illustrative examples exhibiting challenging features. Our experimental results show that the method performs very well, and it can recover the underlying shape of surfaces with very good accuracy.

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Acknowledgments

This research is kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project #TIN2012-30768, Toho University, and the University of Cantabria. The authors are particularly grateful to the Department of Information Science of Toho University for all the facilities given to carry out this work. We also thank the Editor and the two anonymous reviewers who helped us to improve our paper with several constructive comments and suggestions.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computational Sciences, E.T.S.I. Caminos, Canales y Puertos, University of Cantabria, Avda. de los Castros, s/n, 39005, Santander, Spain

    Andrés Iglesias & Akemi Gálvez

  2. Department of Information Science, Faculty of Science, Narashino Campus, Toho University, 2-2-1 Miyama, Funabashi, 274-8510, Japan

    Andrés Iglesias & Akemi Gálvez

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  1. Andrés Iglesias
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  2. Akemi Gálvez
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Correspondence to Andrés Iglesias.

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Iglesias, A., Gálvez, A. Memetic electromagnetism algorithm for surface reconstruction with rational bivariate Bernstein basis functions. Nat Comput 16, 511–525 (2017). https://doi.org/10.1007/s11047-016-9562-5

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