An efficient volume repairing method by using a modified Allen-Cahn equation

Li, Yibao; Lan, Shouren; Liu, Xin; Lu, Bingheng; Wang, Lisheng

doi:10.1016/j.patcog.2020.107478

Cited by 18 publications

(1 citation statement)

References 21 publications

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“…Under the mean curvature flow, the reconstructed surface is smooth. The Allen-Cahn equation has been applied to a wide range of problems such as crystal growth [12][13][14], image analysis [15][16][17][18], triply-periodic minimal surface [19,20], and volume reconstruction [21][22][23], and topology optimization [24]. In this paper, we use the Allen-Cahn equation in different contexts and applications.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Shi

2021

Mathematics

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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.

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