Three-dimensional volume reconstruction from multi-slice data using a shape transformation[Formula presented]

Hyundong Kim, Chaeyoung Lee, Soobin Kwak, Youngjin Hwang, Sangkwon Kim, Yongho Choi, Junseok Kim

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We present a computational method for the 3D volume reconstruction from cross-sectional data. The proposed method is based on the Allen–Cahn (AC) equation with a source term. The source term is related to shape transformation from a source object to a target object. Using the operator splitting method, the governing equation is solved by splitting it into three steps. The numerical solution is obtained explicitly using the Euler's methods and the separation of variables. To reconstruct the 3D object from two slice data, we set one slice as the target data and the other data as the initial data. We solve the governing equation and stack intermediate solutions based on the relative fraction of the symmetric difference of two regions occupied by the target and source data. To demonstrate that the proposed method can reconstruct a 3D model through extracted intermediate slice data during shape transformation, we perform several computational tests. Furthermore, the proposed method is applied to a 3D volume reconstruction from multi-slice data of human vertebra.

Original languageEnglish
Pages (from-to)52-58
Number of pages7
JournalComputers and Mathematics with Applications
Publication statusPublished - 2022 May 1


  • Finite difference method
  • Phase-field model
  • Shape transformation
  • Volume reconstruction

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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