Curvature Regularized Surface Reconstruction from Point Clouds

Yuchen He, Sung Ha Kang, Hao Liu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

18 Citations (Scopus)
55 Downloads (Pure)


We propose a variational functional with a curvature constraint to reconstruct implicit surfaces from point cloud data. In the point cloud data, only locations are assumed to be given, without any normal direction or any curvature estimation. The minimizing functional balances two terms: the distance function from the point cloud to the surface and the mean curvature of the surface itself. We explore both the L1 and L2 norms for the curvature constraint. With the added curvature constraint, the computation becomes particularly challenging. We propose two efficient algorithms. The first algorithm is a novel operator splitting method. It replaces the original high-order PDEs by a decoupled PDE system, which is solved by a semi-implicit method. We also discuss an approach based on an augmented Lagrangian method. The proposed model shows robustness against noise and recovers concave features and corners better compared to models without curvature constraint. Numerical experiments on two- and three-dimensional data sets, noisy data and sparse data, are presented to validate the model. Experiments show that the operator splitting semi-implicit method is flexible and robust.
Original languageEnglish
Pages (from-to)1834-1859
Number of pages26
JournalSIAM Journal on Imaging Sciences
Issue number4
Publication statusPublished - Sept 2020

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Augmented lagrangian method
  • Curvature minimization
  • Level set method
  • Operator splitting method
  • Surface reconstruction


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