Implicit surface reconstruction with radial basis functions via PDEs

Xiao Yan Liu, Hui Wang, C. S. Chen, Qing Wang, Xiaoshuang Zhou, Yong Wang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We propose a partial differential equations-based algorithm for the 3D implicit surface reconstruction from a set of scattered cloud data. In the solution process, the method of approximate particular solutions with the IMQ radial basis function is employed for solving the modified Helmholtz or Poisson equation with a constant Dirichlet boundary condition. We also consider to repair the surfaces when a certain region of cloud data points are missing. The selection of several parameters is studied for the optimal recovery of the surfaces. Four examples are presented to validate the effectiveness of the proposed method.

Original languageEnglish
Pages (from-to)95-103
Number of pages9
JournalEngineering Analysis with Boundary Elements
StatePublished - Jan 2020


  • Computer graphics
  • Image reconstruction
  • Implicit surface
  • Method of approximate particular solutions
  • Modified Helmholtz equation
  • Radial basis function

Fingerprint Dive into the research topics of 'Implicit surface reconstruction with radial basis functions via PDEs'. Together they form a unique fingerprint.

Cite this