Towards globally optimal normal orientations for thin surfaces

• Published in: Computers & graphics Vol. 75; pp. 36 - 43
• Main Authors: Xu, Minfeng, Xin, Shiqing, Tu, Changhe
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2018; Elsevier Science Ltd
• Subjects: Consistent normal orientation; Geometric optimization; Geometry; Image reconstruction; Mapping; Optimization; Orientations; Studies; Surface reconstruction; Texture mapping; Thin surface; Three dimensional models; Surface reconstruction; Geometric optimization; Consistent normal orientation; Thin surface
• ISSN: 0097-8493; 1873-7684
• DOI: 10.1016/j.cag.2018.06.002

•We propose a novel framework to generate globally consistent orientations from an un-organized point cloud.•Different than previous approaches, we use the offset surface to guide/refine the orientations based on optimal mass transport of normal vectors.•Rather than explicitly compute the offset surface, we use a set of moveable particles, following a uniform distribution, to potentially represent the offset surface.•We develop a particle system based implementation that requires only the MLS projection operation and doesn’t depend on additional numeric solvers. [Display omitted] Globally unified normal orientations for unorganized point set are essential for reconstruction, rendering, texture mapping etc. Although there is a large body of literature on dealing with various difficult cases to get consistent normal orientation, effective approaches are not available yet to handle a point cloud with thin surfaces, to our best knowledge. The difficulty lies in that thin structure doesn’t have a strong coherence between locations of surface points and their normal orientations. In this paper, we propose a novel approach for computing globally optimal normal orientations to facilitate high-quality surface reconstruction from a point cloud with thin structures. The key idea is to generate an uniform particle set constrained on an offset surface that is topologically identical to the real target surface and further use the particle set to compute and refine the normal vector at each primitive point. Our strategy for inferring the globally consistent orientation is much different from the conventional paradigm that computes unoriented normal vectors and then re-orients them coherently. Experimental results on natural and man-made models with noise and thin parts show that our algorithm outperforms existing approaches on normal consistence and is able to produce a desirable global optimal normal orientations with which a structurally sound thin shape can be finally reconstructed by the well known screened Poisson reconstruction approach.