Voronoi-based variational reconstruction of unoriented point sets
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets
Journal of Mathematical Imaging and Vision
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We discuss the problem of fitting an implicit shape model to a set of points sampled from a co-dimension one manifold of arbitrary topology. The method solves a non-convex optimisation problem in the embedding function that defines the implicit by way of its zero level set. By assuming that the solution is a mixture of radial basis functions of varying widths we attain the globally optimal solution by way of an equivalent eigenvalue problem, without using or constructing as an intermediate step the normal vectors of the manifold at each data point. We demonstrate the system on two and three dimensional data, with examples of missing data interpolation and set operations on the resultant shapes.