Fast and efficient narrow volume reconstruction from scattered data

Yibao Li, Junseok Kim

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


We describe a fast and efficient numerical algorithm for the process of three-dimensional narrow volume reconstruction from scattered data in three dimensions. The present study is an extension of previous research [Li et al., Surface embedding narrow volume reconstruction from unorganized points, Comput. Vis. Image Underst. 121 (2014) 100-107]. In the previous work, we modified the original Allen-Cahn equation by multiplying a control function to restrict the evolution within a narrow band around the given surface data set. The key idea of the present work is to perform the computations only on a narrow band around the given surface data set. In this way, we can significantly reduce the storage memory and CPU time. The proposed numerical method, based on operator splitting techniques, can employ a large time step size and exhibits unconditional stability. We perform a number of numerical experiments in order to demonstrate the efficiency of this method.

Original languageEnglish
Article number5459
Pages (from-to)4057-4069
Number of pages13
JournalPattern Recognition
Issue number12
Publication statusPublished - 2015 Dec 1

Bibliographical note

Funding Information:
Y.B. Li was supported by the Fundamental Research Funds for the Central Universities , China (No. XJJ2015068 ) and supported by China Postdoctoral Science Foundation (No. 2015M572541 ). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2014R1A2A2A01003683 ). The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper.

Publisher Copyright:
© 2015 Elsevier Ltd.


  • Allen-Cahn equation
  • Narrow band domain
  • Offset surface reconstruction
  • Unconditional stability
  • Unsigned distance function

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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