University of Oulu

Yibao Li, Shouren Lan, Xin Liu, Bingheng Lu, Lisheng Wang, An efficient volume repairing method by using a modified Allen-Cahn equation, Pattern Recognition, Volume 107, 2020, 107478, ISSN 0031-3203,

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

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Author: Li, Yibao1; Lan, Shouren2; Liu, Xin3,4;
Organizations: 1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
2Department of Automation, Shanghai Jiaotong University, Shanghai, 200240, China
3School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
4The Center for Machine Vision and Signal Analysis, University of Oulu, Finland
5Collaborative Innovation Center of High-End Manufacturing Equipment, Xi’an Jiaotong University, Xi’an 710049, China
6National Institue of Additive Manufacturing, Xi’an 710049, China
7School of Mechanical Engineering, Dongguan University of Technology, Dongguan 523808, China
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 2.5 MB)
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Language: English
Published: Elsevier, 2020
Publish Date: 2022-05-30


Classifying and rendering volumes of the structure are two essential goals of the visualization process. However, loss of some voxels can cause poor visualization results, such as small holes or non-smooth patches in visualized volumes. Beginning with the classified volumes, we propose a modified Allen-Cahn equation, which has the motion of mean curvature, to recover lost voxels and to fill holes. Consequently, a probability function can be obtained, which indicates the probability of each voxel being a volume voxel. Usually, the obtained probability function is smooth due to the motion of the mean curvature flow. Therefore visualization quality of volumes can be significantly improved. The equation is numerically computed by the unconditional stable operator splitting method with a large time step size. Thus the numerical scheme is fast and can be straightforwardly applied to GPU-accelerated DCT implementation that performs up to many times faster than CPU-only alternatives. Many experimental results have been performed to demonstrate the efficiency of the proposed method.

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Series: Pattern recognition
ISSN: 0031-3203
ISSN-E: 1873-5142
ISSN-L: 0031-3203
Volume: 107
Issue: November 2020
Article number: 107478
DOI: 10.1016/j.patcog.2020.107478
Type of Publication: A1 Journal article – refereed
Field of Science: 113 Computer and information sciences
Funding: Y.B. Li is supported by the China Postdoctoral Science Foundation (No. 2018M640968). B.H. Lu is supported by Shaanxi Provincial Science and Technology Planning Project (2017KTZD6-01) and by Dongguan University of Technology High-level Talents Research Project (KCYCXPT2016003). L. Wang is supported in part by Shanghai Intelligent Medicine Project (2018ZHYL0217), Construction project of Shanghai Key Laboratory of Molecular Imaging (18DZ2260400), Shanghai Municipal Education Commission (Class II Plateau Disciplinary Construction Program of Medical Technology of SUMHS, 2018–2020). The authors thank the reviewers for the constructive and helpful comments on the revision of this article.
Copyright information: © 2020 Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license