Voronoi-based Variational Reconstruction of Unoriented Point Sets

1. Briefly summarize the paper’s contributions. Does it address a new problem? Does it present a new approach? Does it show new types of results?  [AS] This paper presents a new approach to estimating unoriented normals from an unoriented set of input points, and using this tensor field to find an implicit function representing the surface defined by the input point set.  [DS] The paper presents an algorithm for reconstructing (debatably) watertight surfaces from unoriented point sets. They use the Voronoi diagram of the point set to compute a tensor field that represents the most likely direction of the normal to the surface and the confidence of the estimate. An implicit function is found by solving a generalized eigenvalue problem so that the gradient is aligned with the normal direction estimates. The approach is resilient to noise, and provides parameters to adjust data fitting and smoothness of the reconstructed surface.  [FP] Implicit surface methods (e.g., Othake 2003, Kazhdan 2006, Shen 2004) require of accurate surface normal at sample position. When this normal is not provided, traditional approaches to compute it are based in PCA (e.g. Hoppe 1992), or Voronoi Poles. Global orientation of normal is then attained using MST on a normal propagation graph. This paper looks for a simultaneous solution of the implicit surface and the normal orientation problems, by minimizing a global energy on a tensor field. This tensor field is given by the covariance matrix on expanded Voronoi regions. The optimization step compute an implicit function whose gradient align with the principal directions of the tensor field and is constrained both in smoothness of the gradient field and data fitting (i.e., sample positions at zero level).  [JD]  [LF] The paper presents a new technique for approximating unoriented normals that combines qualities of the PCA and Voronoi pole approaches for doing so and outperforms those two approaches.  [MK] The paper proposes a new variational approach to surface reconstruction that does not require knowing, or even estimating, surface normals.