Variational Implicit Point Set Surfaces

ACM Transactions on Graphics (Proc. SIGGRAPH)

Published July 28, 2019

Zhiyang Huang, Nathan Carr, Tao Ju

We propose a new method for reconstructing an implicit surface from an un-oriented point set. While existing methods often involve non-trivial heuristics and require additional constraints, such as normals or labelled points, we introduce a direct definition of the function from the points as the solution to a constrained quadratic optimization problem. The definition has a number of appealing features: it uses a single parameter (parameter-free for exact interpolation), applies to any dimensions, commutes with similarity transformations, and can be easily implemented without discretizing the space. More importantly, the use of a global smoothness energy allows our definition to be much more resilient to sampling imperfections than existing methods, making it particularly suited for sparse and non-uniform inputs.

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Research Area:  Graphics (2D & 3D)