Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation
This work addresses a key challenge in geometric processing for applications like 3D modeling and computer graphics, offering an incremental improvement over existing Poisson-based methods.
The authors tackled the problem of obtaining consistent normal orientations for point clouds, which is crucial for surface reconstruction, by proposing a method that incorporates isovalue constraints into the Poisson equation to simultaneously optimize normals and implicit functions, achieving high performance on non-uniform and noisy data.
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}.