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Mathematical Problems in Engineering
Volume 2018, Article ID 7090186, 9 pages
Research Article

Efficient 3D Volume Reconstruction from a Point Cloud Using a Phase-Field Method

1Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
2School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
3ROKIT Inc., Seoul 08512, Republic of Korea

Correspondence should be addressed to Junseok Kim;

Received 22 November 2017; Accepted 1 January 2018; Published 6 February 2018

Academic Editor: Costică Moroșanu

Copyright © 2018 Darae Jeong et al. 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.


We propose an explicit hybrid numerical method for the efficient 3D volume reconstruction from unorganized point clouds using a phase-field method. The proposed three-dimensional volume reconstruction algorithm is based on the 3D binary image segmentation method. First, we define a narrow band domain embedding the unorganized point cloud and an edge indicating function. Second, we define a good initial phase-field function which speeds up the computation significantly. Third, we use a recently developed explicit hybrid numerical method for solving the three-dimensional image segmentation model to obtain efficient volume reconstruction from point cloud data. In order to demonstrate the practical applicability of the proposed method, we perform various numerical experiments.