Iterative two-step genetic-algorithm-based method for efficient polynomial B-spline surface reconstruction |
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| Authors: | Akemi Gálvez Andrés Iglesias Jaime Puig-Pey |
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| Affiliation: | 1. Center for Engineering and Scientific Computation, and School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China;2. Zienkiewicz Centre for Computational Engineering, and Energy Safety Research Institute, Swansea University, Swansea SA2 8PP, UK;1. School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China;2. School of Business Administration, Northeastern University, Shenyang 110819, China;3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton T6R 2V4 AB, Canada;4. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia;5. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland;1. Center for Mathematics, Computation and Cognition, Federal University of ABC, R. Santa Adélia 166, Santo André, SP 09210-170, Brazil;2. Department of Earth and Exact Sciences, Federal University of São Paulo, R. Arthur Ridel 275, Diadema, SP 09972-270, Brazil;3. Institute of Mathematics and Statistics, University of São Paulo, R. do Matão 1010, São Paulo, SP 05508-090, Brazil;4. Brazilian Bioethanol Science and Technology Laboratory, Campinas, SP 13083-970, Brazil;5. Genomic Signal Processing Lab, Texas A&M University, College Station, TX 77843-3128, USA;1. School of Mathematical Sciences, University of Science and Technology of China, China;2. School of Mathematical Sciences, Soochow University, China;1. School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, 224051, China;2. College of Mathematics and Information Science, Wenzhou University, 325035 Wenzhou, China;3. School of Mathematics and Statistics, Xi''an Jiaotong University, Xi''an, 710049, China |
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| Abstract: | Surface reconstruction is a very challenging problem arising in a wide variety of applications such as CAD design, data visualization, virtual reality, medical imaging, computer animation, reverse engineering and so on. Given partial information about an unknown surface, its goal is to construct, to the extent possible, a compact representation of the surface model. In most cases, available information about the surface consists of a dense set of (either organized or scattered) 3D data points obtained by using scanner devices, a today’s prevalent technology in many reverse engineering applications. In such a case, surface reconstruction consists of two main stages: (1) surface parameterization and (2) surface fitting. Both tasks are critical in order to recover surface geometry and topology and to obtain a proper fitting to data points. They are also pretty troublesome, leading to a high-dimensional nonlinear optimization problem. In this context, present paper introduces a new method for surface reconstruction from clouds of noisy 3D data points. Our method applies the genetic algorithm paradigm iteratively to fit a given cloud of data points by using strictly polynomial B-spline surfaces. Genetic algorithms are applied in two steps: the first one determines the parametric values of data points; the later computes surface knot vectors. Then, the fitting surface is calculated by least-squares through either SVD (singular value decomposition) or LU methods. The method yields very accurate results even for surfaces with singularities, concavities, complicated shapes or nonzero genus. Six examples including open, semi-closed and closed surfaces with singular points illustrate the good performance of our approach. Our experiments show that our proposal outperforms all previous approaches in terms of accuracy and flexibility. |
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