Article

Robust moving least-squares fitting with sharp features

Authors:

Shachar Fleishman,

Daniel Cohen-Or,

Cláudio T. SilvaAuthors Info & Claims

SIGGRAPH '05: ACM SIGGRAPH 2005 Papers

Pages 544 - 552

https://doi.org/10.1145/1186822.1073227

Published: 01 July 2005 Publication History

Abstract

We introduce a robust moving least-squares technique for reconstructing a piecewise smooth surface from a potentially noisy point cloud. We use techniques from robust statistics to guide the creation of the neighborhoods used by the moving least squares (MLS) computation. This leads to a conceptually simple approach that provides a unified framework for not only dealing with noise, but also for enabling the modeling of surfaces with sharp features.Our technique is based on a new robust statistics method for outlier detection: the forward-search paradigm. Using this powerful technique, we locally classify regions of a point-set to multiple outlier-free smooth regions. This classification allows us to project points on a locally smooth region rather than a surface that is smooth everywhere, thus defining a piecewise smooth surface and increasing the numerical stability of the projection operator. Furthermore, by treating the points across the discontinuities as outliers, we are able to define sharp features. One of the nice features of our approach is that it automatically disregards outliers during the surface-fitting phase.

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Cited By

Zhu XDu DChen WZhao ZNie YHan X(2023)NerVE: Neural Volumetric Edges for Parametric Curve Extraction from Point Cloud2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52729.2023.01307(13601-13610)Online publication date: Jun-2023
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Grimm W(2022)Covariance‐invariant mapping of data points to nonlinear modelsMathematical Methods in the Applied Sciences10.1002/mma.871246:4(3597-3613)Online publication date: 14-Sep-2022
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Reviews

Reviewer: Lars Eldén

A moving least-squares technique is described for reconstructing a piecewise smooth surface using noisy data from a digital scanner. The method is based on the forward-search algorithm used to detect outliers in robust statistics. Some points in the neighborhood of an input point are fitted locally with a low-degree polynomial. If there is a sharp edge within the neighborhood, it is detected by identifying the points on the other side (with respect to the input point) of the edge as outliers in the polynomial fit. A projection operator is defined that projects the data points onto the piecewise smooth surface. The procedure is tested on noisy data. The paper is well written, and the results are promising. Online Computing Reviews Service

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cover image ACM Conferences

SIGGRAPH '05: ACM SIGGRAPH 2005 Papers

July 2005

826 pages

ISBN:9781450378253

DOI:10.1145/1186822

Editor:
Markus Gross
Eidgenössische Technische Hochschule Zürich

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: 01 July 2005

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July 31 - August 4, 2005

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SIGGRAPH '05 Paper Acceptance Rate 98 of 461 submissions, 21%;

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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Cited By

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https://doi.org/10.1109/CVPR52729.2023.01307
Grimm W(2022)Covariance‐invariant mapping of data points to nonlinear modelsMathematical Methods in the Applied Sciences10.1002/mma.871246:4(3597-3613)Online publication date: 14-Sep-2022
https://doi.org/10.1002/mma.8712
Himeur CLejemble TPellegrini TPaulin MBarthe LMellado N(2021)PCEDNet: A Lightweight Neural Network for Fast and Interactive Edge Detection in 3D Point CloudsACM Transactions on Graphics10.1145/348180441:1(1-21)Online publication date: 10-Nov-2021
https://dl.acm.org/doi/10.1145/3481804
Metzer GHanocka RGiryes RCohen-Or D(2021)Self-Sampling for Neural Point Cloud ConsolidationACM Transactions on Graphics10.1145/347064540:5(1-14)Online publication date: 24-Sep-2021
https://dl.acm.org/doi/10.1145/3470645
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Wang XXu YXu KTagliasacchi AZhou BMahdavi-Amiri AZhang HLarochelle HRanzato MHadsell RBalcan MLin H(2020)PIE-NETProceedings of the 34th International Conference on Neural Information Processing Systems10.5555/3495724.3497417(20167-20178)Online publication date: 6-Dec-2020
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Kim SMin DLin SSohn K(2020)Discrete-Continuous Transformation Matching for Dense Semantic CorrespondenceIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2018.287824042:1(59-73)Online publication date: 1-Jan-2020
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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
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Tsuchie S(2019)Mesh simplification accompanied by its denoising of scanned dataEngineering with Computers10.1007/s00366-018-0647-x35:3(993-1008)Online publication date: 1-Jul-2019
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Hu YFang YGe ZQu ZZhu YPradhana AJiang C(2018)A moving least squares material point method with displacement discontinuity and two-way rigid body couplingACM Transactions on Graphics10.1145/3197517.320129337:4(1-14)Online publication date: 30-Jul-2018
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