Three-dimensional volume reconstruction from slice data using phase-field models

Yibao Li, Jaemin Shin, Yongho Choi, Junseok Kim

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


Abstract We propose the application of a phase-field framework for three-dimensional volume reconstruction using slice data. The proposed method is based on the Allen-Cahn and Cahn-Hilliard equations, and the algorithm consists of two steps. First, we perform image segmentation on the given raw data using a modified Allen-Cahn equation. Second, we reconstruct a three-dimensional volume using a modified Cahn-Hilliard equation. In the modified Cahn-Hilliard equation, a fidelity term is introduced to keep the solution close to the slice data. The numerical methods use a hybrid method and an unconditionally stable nonlinear splitting scheme. The resulting discrete equations are solved using a multigrid method. The experiments on synthetic and real medical images are performed to demonstrate the accuracy and efficiency of the proposed method.

Original languageEnglish
Article number2215
Pages (from-to)115-124
Number of pages10
JournalComputer Vision and Image Understanding
Publication statusPublished - 2015 Jun 2

Bibliographical note

Funding Information:
Y.B. Li is supported by the Fundamental Research Funds for the Central Universities, China . The author (J. Shin) is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), which is funded by the Ministry of Education ( 2009-0093827 ). 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 anonymous referees, whose valuable suggestions and comments significantly improved the quality of this paper.

Publisher Copyright:
© 2015 Elsevier Inc.


  • Allen-Cahn equation
  • Cahn-Hilliard equation
  • Image inpainting
  • Image segmentation
  • Multigrid method
  • Volume reconstruction

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition


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