Towards Globally Optimal Normal Orientations for Large Point Clouds

• Published in: Computer graphics forum 2017-01, Vol.36 (1), p.197-208
• Main Authors: Schertler, Nico, Savchynskyy, Bogdan, Gumhold, Stefan
• Format: Article
• Language: English
• Subjects: Algorithms; computational geometry; digital geometry processing; Energy conservation; Graphs; I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling‐Geometric algorithms, languages and systems; Mathematical analysis; modelling; Optimization; Orientation; Patches (structures); Propagation; Reconstruction; Solvers; Tasks; Three dimensional models
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12795

Various processing algorithms on point set surfaces rely on consistently oriented normals (e.g. Poisson surface reconstruction). While several approaches exist for the calculation of normal directions, in most cases, their orientation has to be determined in a subsequent step. This paper generalizes propagation‐based approaches by reformulating the task as a graph‐based energy minimization problem. By applying global solvers, we can achieve more consistent orientations than simple greedy optimizations. Furthermore, we present a streaming‐based framework for orienting large point clouds. This framework orients patches locally and generates a globally consistent patch orientation on a reduced neighbour graph, which achieves similar quality to orienting the full graph. Various processing algorithms on point set surfaces rely on consistently oriented normals (e.g. Poisson surface reconstruction).While several approaches exist for the calculation of normal directions, in most cases, their orientation has to be determined in a subsequent step. This paper generalizes propagation‐based approaches by reformulating the task as a graph‐based energy minimization problem and presents a streaming‐based out‐of‐core implementation.