Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation

Xiao, Dong, Shi, Zuoqiang, Li, Siyu, Deng, Bailin ORCID: https://orcid.org/0000-0002-0158-7670 and Wang, Bin 2023. Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation. Computer Aided Geometric Design 103 , 102195. 10.1016/j.cagd.2023.102195

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Abstract

Oriented normals are common pre-requisites for many geometric algorithms based on point clouds, such as Poisson surface reconstruction. However, it is not trivial to obtain a consistent orientation. In this work, we bridge orientation and reconstruction in the implicit space and propose a novel approach to orient point cloud normals by incorporating isovalue constraints to the Poisson equation. In implicit surface reconstruction, the reconstructed shape is represented as an isosurface of an implicit function defined in the ambient space. Therefore, when such a surface is reconstructed from a set of sample points, the implicit function values at the points should be close to the isovalue corresponding to the surface. Based on this observation and the Poisson equation, we propose an optimization formulation that combines isovalue constraints with local consistency requirements for normals. We optimize normals and implicit functions simultaneously and solve for a globally consistent orientation. Thanks to the sparsity of the linear system, our method can work on an average laptop with reasonable computational time. Experiments show that our method can achieve high performance in non-uniform and noisy data and manage varying sampling densities, artifacts, multiple connected components, and nested surfaces. The source code is available at https://github.com/Submanifold/IsoConstraints.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QA Mathematics > QA76 Computer software
Date of First Compliant Deposit:	27 April 2023
Date of Acceptance:	29 March 2023
Last Modified:	18 Apr 2024 17:14
URI:	https://orca.cardiff.ac.uk/id/eprint/159075

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