  Estimating normals with globally consistent orientations for a raw point
cloud has many downstream geometry processing applications. Despite tremendous
efforts in the past decades, it remains challenging to deal with an unoriented
point cloud with various imperfections, particularly in the presence of data
sparsity coupled with nearby gaps or thin-walled structures. In this paper, we
propose a smooth objective function to characterize the requirements of an
acceptable winding-number field, which allows one to find the globally
consistent normal orientations starting from a set of completely random
normals. By taking the vertices of the Voronoi diagram of the point cloud as
examination points, we consider the following three requirements: (1) the
winding number is either 0 or 1, (2) the occurrences of 1 and the occurrences
of 0 are balanced around the point cloud, and (3) the normals align with the
outside Voronoi poles as much as possible. Extensive experimental results show
that our method outperforms the existing approaches, especially in handling
sparse and noisy point clouds, as well as shapes with complex
geometry/topology.
