Curvature Regularized Surface Reconstruction from Point Clouds

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

16 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)1834-1859
Journal / PublicationSIAM Journal on Imaging Sciences
Volume13
Issue number4
Online published27 Oct 2020
Publication statusPublished - 2020
Externally publishedYes

Abstract

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. © 2020 Society for Industrial and Applied Mathematics.

Research Area(s)

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

Citation Format(s)

Curvature Regularized Surface Reconstruction from Point Clouds. / He, Yuchen; Kang, Sung Ha; Liu, Hao.
In: SIAM Journal on Imaging Sciences, Vol. 13, No. 4, 2020, p. 1834-1859.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review