Multi-Reconstruction from Points Cloud by Using a Modified Vector-Valued Allen–Cahn Equation

Jin Wang and Zhengyuan Shi
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Jin Wang: School of Humanities and Social Science, Xi’an Jiaotong University, Xi’an 710049, China
Zhengyuan Shi: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China

Mathematics, 2021, vol. 9, issue 12, 1-15

Abstract: The Poisson surface reconstruction algorithm has become a very popular tool of reconstruction from point clouds. If we reconstruct each region separately in the process of multi-reconstruction, then the reconstructed objects may overlap with each other. In order to reconstruct multicomponent surfaces without self-intersections, we propose an efficient multi-reconstruction algorithm based on a modified vector-valued Allen–Cahn equation. The proposed algorithm produces smooth surfaces and closely preserves the original data without self-intersect. Based on operator splitting techniques, the numerical scheme is divided into one linear equation and two nonlinear equations. The linear equation is discretized using an implicit method, and the resulting discrete system of equation is solved by a fast Fourier transform. The two nonlinear equations are solved analytically due to the availability of a closed-form solution. The numerical scheme has merit in that it can be straightforwardly applied to a graphics processing unit, allowing for accelerated implementation that performs much faster than central processing unit alternatives. Various experimental, numerical results demonstrate the effectiveness and robustness of the proposed method.

Keywords: multimaterial; surface reconstruction; Allen–Cahn equation; mean curvature flow (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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