Article

Provably good moving least squares

Author:

Ravikrishna KolluriAuthors Info & Claims

SIGGRAPH '05: ACM SIGGRAPH 2005 Courses

Pages 213 - es

https://doi.org/10.1145/1198555.1198652

Published: 31 July 2005 Publication History

Abstract

We analyze a moving least squares algorithm for reconstructing a surface from point cloud data. Our algorithm defines an implicit function I whose zero set U is the reconstructed surface. We prove that I is a good approximation to the signed distance function of the sampled surface F and that U is geometrically close to and homeomorphic to F. Our proof requires sampling conditions similar to ε-sampling, used in Delaunay reconstruction algorithms.

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Cited By

Bouchiba HSantoso SDeschaud JRocha-Da-Silva LGoulette FCoupez T(2020)Computational Fluid Dynamics on 3D Point Set SurfacesJournal of Computational Physics: X10.1016/j.jcpx.2020.100069(100069)Online publication date: Aug-2020
https://doi.org/10.1016/j.jcpx.2020.100069
Williams FSchneider TSilva CZorin DBruna JPanozzo D(2019)Deep Geometric Prior for Surface Reconstruction2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR.2019.01037(10122-10131)Online publication date: Jun-2019
https://doi.org/10.1109/CVPR.2019.01037
Menon H(2017)Issues involved in automatic selection and intensity based matching of feature points for mls registration of medical images2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI)10.1109/ICACCI.2017.8125938(787-792)Online publication date: Sep-2017
https://doi.org/10.1109/ICACCI.2017.8125938
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Provably good moving least squares
1. Computing methodologies
  1. Computer graphics
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Conferences

SIGGRAPH '05: ACM SIGGRAPH 2005 Courses

July 2005

7157 pages

ISBN:9781450378338

DOI:10.1145/1198555

Editor:
John Fujii
Hewlett-Packard Company

Copyright © 2005 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 31 July 2005

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Cited By

Bouchiba HSantoso SDeschaud JRocha-Da-Silva LGoulette FCoupez T(2020)Computational Fluid Dynamics on 3D Point Set SurfacesJournal of Computational Physics: X10.1016/j.jcpx.2020.100069(100069)Online publication date: Aug-2020
https://doi.org/10.1016/j.jcpx.2020.100069
Williams FSchneider TSilva CZorin DBruna JPanozzo D(2019)Deep Geometric Prior for Surface Reconstruction2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR.2019.01037(10122-10131)Online publication date: Jun-2019
https://doi.org/10.1109/CVPR.2019.01037
Menon H(2017)Issues involved in automatic selection and intensity based matching of feature points for mls registration of medical images2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI)10.1109/ICACCI.2017.8125938(787-792)Online publication date: Sep-2017
https://doi.org/10.1109/ICACCI.2017.8125938
Shi BLiang J(2016)An integration method for scanned multi-view range images (MRIs) based on local weighted least squares (LWLS) surface fittingOptics and Lasers in Engineering10.1016/j.optlaseng.2015.07.01177(64-78)Online publication date: Feb-2016
https://doi.org/10.1016/j.optlaseng.2015.07.011
Berger MLevine JNonato LTaubin GSilva C(2013)A benchmark for surface reconstructionACM Transactions on Graphics10.1145/2451236.245124632:2(1-17)Online publication date: 30-Apr-2013
https://dl.acm.org/doi/10.1145/2451236.2451246
Pfaff TThuerey NGross M(2012)Lagrangian vortex sheets for animating fluidsACM Transactions on Graphics10.1145/2185520.218560831:4(1-8)Online publication date: 1-Jul-2012
https://dl.acm.org/doi/10.1145/2185520.2185608
Park TLee SKim C(2012)Analytic Solutions of Integral Moving Least Squares for Polygon SoupsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2011.28618:10(1638-1649)Online publication date: 1-Oct-2012
https://dl.acm.org/doi/10.1109/TVCG.2011.286
Weber CHahmann SHagen HBonneau G(2012)Sharp feature preserving MLS surface reconstruction based on local feature line approximationsGraphical Models10.1016/j.gmod.2012.04.01274:6(335-345)Online publication date: 1-Nov-2012
https://dl.acm.org/doi/10.1016/j.gmod.2012.04.012
Chen YLai S(2011)An Orientation Inference Framework for Surface Reconstruction From Unorganized Point CloudsIEEE Transactions on Image Processing10.1109/TIP.2010.207629720:3(762-775)Online publication date: 1-Mar-2011
https://dl.acm.org/doi/10.1109/TIP.2010.2076297
Zheng CZhang H(2011)Implicit Surface Reconstruction Based on Adaptive ClusteringProceedings of the 2011 12th International Conference on Computer-Aided Design and Computer Graphics10.1109/CAD/Graphics.2011.64(509-515)Online publication date: 15-Sep-2011
https://dl.acm.org/doi/10.1109/CAD/Graphics.2011.64
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