Surface embedding narrow volume reconstruction from unorganized points

Yibao Li, Dongsun Lee, Chaeyoung Lee, Jihu Lee, Sanha Lee, Junseok Kim, Jisu Kim, Shinwoo Ahn

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


In this paper, we present a novel fast and accurate numerical method for the surface embedding narrow volume reconstruction from unorganized points in R3. Though the level set method prevails in the image processing, it requires a redistancing procedure to maintain a desired shape of the level set function. On the other hand, our method is based on the Allen-Cahn equation, which has been applied in image segmentation due to its motion by mean curvature property. We modify the original Allen-Cahn equation by multiplying a control function to restrict the evolution within a narrow band around the given surface data set. To improve the numerical stability of our proposed model, we split the governing equation into linear and nonlinear terms and use an operator splitting technique. The linear equation is solved by the multigrid method which is a fast solver and the nonlinear equation is solved analytically. The unconditional stability of the proposed scheme is also proved. Various numerical results are presented to demonstrate the robustness and accuracy of the proposed method.

Original languageEnglish
Pages (from-to)100-107
Number of pages8
JournalComputer Vision and Image Understanding
Publication statusPublished - 2014 Apr


  • Allen-Cahn equation
  • Multigrid method
  • Unconditional stability
  • Unsigned distance function
  • Volume reconstruction

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition


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