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Point Normal Orientation and Surface Reconstruction by Incorporating Isovalue Constraints to Poisson Equation

Dong XiaoZuoqiang ShiSiyu LiBailin DengBin Wang
Sep 2022
摘要
Oriented normals are common pre-requisites for many geometric algorithmsbased on point clouds, such as Poisson surface reconstruction. However, it isnot trivial to obtain a consistent orientation. In this work, we bridgeorientation and reconstruction in implicit space and propose a novel approachto orient point clouds by incorporating isovalue constraints to the Poissonequation. Feeding a well-oriented point cloud into a reconstruction approach,the indicator function values of the sample points should be close to theisovalue. Based on this observation and the Poisson equation, we propose anoptimization formulation that combines isovalue constraints with localconsistency requirements for normals. We optimize normals and implicitfunctions simultaneously and solve for a globally consistent orientation. Owingto the sparsity of the linear system, an average laptop can be used to run ourmethod within reasonable time. Experiments show that our method can achievehigh performance in non-uniform and noisy data and manage varying samplingdensities, artifacts, multiple connected components, and nested surfaces.
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