Point normal orientation and surface reconstruction by incorporating
isovalue constraints to Poisson equation
- URL: http://arxiv.org/abs/2209.15619v3
- Date: Sun, 30 Apr 2023 14:01:45 GMT
- Title: Point normal orientation and surface reconstruction by incorporating
isovalue constraints to Poisson equation
- Authors: Dong Xiao, Zuoqiang Shi, Siyu Li, Bailin Deng, Bin Wang
- Abstract summary: Oriented normals are common pre-requisites for many geometric algorithms based on point clouds.
We propose a novel approach to orient point cloud normals by incorporating isovalue constraints to the Poisson equation.
Our method can achieve high performance in non-uniform and noisy data.
- Score: 16.467735758073363
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- 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
\url{https://github.com/Submanifold/IsoConstraints}.
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