Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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THREE-DIMENSIONAL VOLUME RECONSTRUCTION BASED ON MODIFIED FRACTIONAL CAHN-HILLIARD EQUATION

  • CHOI, YONGHO (DEPARTMENT OF MATHEMATICS AND BIG DATA, DAEGU UNIVERSITY) ;
  • LEE, SEUNGGYU (DEPARTMENT OF MATHEMATICS AND RESEARCH INSTITUTE OF NATURAL SCIENCE, GYEONGSANG NATIONAL UNIVERSITY)
  • Received : 2019.09.03
  • Accepted : 2019.09.14
  • Published : 2019.09.25
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Abstract

We present the three-dimensional volume reconstruction model using the modified Cahn-Hilliard equation with a fractional Laplacian. From two-dimensional cross section images such as computed tomography, magnetic resonance imaging slice data, we suggest an algorithm to reconstruct three-dimensional volume surface. By using Laplacian operator with the fractional one, the dynamics is changed to the macroscopic limit of Levy process. We initialize between the two cross section with linear interpolation and then smooth and reconstruct the surface by solving modified Cahn-Hilliard equation. We perform various numerical experiments to compare with the previous research.

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References

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