Variational Implicit Point Set Surface

ACM Transactions on Graphics (Proc. ACM Siggraph 2019)
Zhiyang Huang*, Nathan Carr^, Tao Ju*
*Washington University in St. Louis,  ^Adobe


Teaser: Given sparse, non-uniform, noisy and un-oriented points (bottom left) sampled from a set of unstructured 3D curves (top left), our variational definition  simultaneously produces oriented normals (top middle) and a smooth approximating surface (top right). The input is challenging for state-of-the-art normal estimation methods such as Wang's method, which fails around sparsely sampled thin features (the flippers) (bottom middle). Incorrect normals lead to poor reconstructions using existing implicit methods such as Screened Poisson (bottom right).

Gallery: Our vectors (b) and surface (c) for samples from an unstructured sketch (a). The inserts take a closer look between the index and ring fingers (the line segments in the insert of (b) indicate -g).


Gallery: Top row: sampling a torus surface with decreasing density (a,b,c,d with 500, 200, 50, 25 points respectively), varying sampling density (e), missing samples (f,g), and along 1-dimensional curves (h,i). Middle row: optimized vectors $\bg$ visualized as oriented disks (green/blue: front/back side). Bottom row: the VIPSS (lambda=0) colored by distance from the original torus surface(see color bar; the percentages are of the largest dimension of the shape).


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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