Provable surface reconstruction from noisy samples

By Tamal K. Dey, Samrat Goswami. SCG '04, 2004

369 citations recorded by the source corpus.

We present an algorithm for surface reconstruction in presence of noise. We show that, under a reasonable noise model, the algorithm has theoretical guarantees. Actual performance of the algorithm is illustrated by our experimental results.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/7d2e90ea450583e526f074d5d15c1d1c9b20b6d5

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

On the Geometry of Adversarial Examples (2018, methodology): “Soon after algorithms were developed for surface reconstruction in R 3 , both in the noise-free setting (Amenta and Bern (1999); Amenta et al. (2002)) and in the presence of noise (Dey and Goswami (2004)).”
A Closed-Form Expression of the Positional Uncertainty for 3D Point Clouds (2009, background): “HE positional uncertainty of a point in an unorganized pointcloudmeasuredbyarangefinderisimportantsince it provides the confidence level of parametric estimations suchasthesurfacenormalvectorandtheregistrationofpoint clouds from such instruments [6], [24], [21], [ 10 ], [11], [3], [1], [4], [2].”
Consolidation of unorganized point clouds for surface reconstruction (2009, methodology): “These methods often provide provable guarantees under prescribed sampling criteria [Amenta and Bern 1998] or noise models [Dey and Goswami 2006] that are generally not realizable by real-world data.”
Provably good sampling and meshing of surfaces (2005, methodology): “P1 If E is a good sample of S, in the sense of [1] or in the sense of [20], then we can compute an approximation of the tangent plane of S in each point of E.”
Stability of Persistence Diagrams (2005, background): “How can we exploit the new insights to get improved algorithms for problems like the medial axis [5], surface reconstruction [1, 10], and alike? How far can we relax the requirements on the input data and still guarantee correct construction?”
Delaunay Triangulation Based Surface Reconstruction: Ideas and Algorithms (2004, methodology): “This extension called Robust Cocone was also developed by Dey and Goswami [DG04].”