article

Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes

Authors:

Helmut Pottmann,

Yong-Liang Yang,

Shi-Min HuAuthors Info & Claims

International Journal of Computer Vision, Volume 67, Issue 3

Pages 277 - 296

https://doi.org/10.1007/s11263-006-5167-2

Published: 01 May 2006 Publication History

Abstract

The computation of a rigid body transformation which optimally aligns a set of measurement points with a surface and related registration problems are studied from the viewpoint of geometry and optimization. We provide a convergence analysis for widely used registration algorithms such as ICP, using either closest points (Besl and McKay, 1992) or tangent planes at closest points (Chen and Medioni, 1991) and for a recently developed approach based on quadratic approximants of the squared distance function (Pottmann et al., 2004). ICP based on closest points exhibits local linear convergence only. Its counterpart which minimizes squared distances to the tangent planes at closest points is a Gauss---Newton iteration; it achieves local quadratic convergence for a zero residual problem and--if enhanced by regularization and step size control--comes close to quadratic convergence in many realistic scenarios. Quadratically convergent algorithms are based on the approach in (Pottmann et al., 2004). The theoretical results are supported by a number of experiments; there, we also compare the algorithms with respect to global convergence behavior, stability and running time.

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Cited By

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Inza VRist FWallner JPottmann H(2023)Developable Quad Meshes and Contact Element NetsACM Transactions on Graphics10.1145/361835542:6(1-13)Online publication date: 5-Dec-2023
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Index Terms

Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Image and video acquisition
        3D imaging
  2. Computer graphics
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

cover image International Journal of Computer Vision

International Journal of Computer Vision Volume 67, Issue 3

May 2006

113 pages

ISSN:0920-5691

Issue’s Table of Contents

Copyright © Copyright © 2006 Springer Science + Business Media, Inc.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 May 2006

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Cited By

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https://dl.acm.org/doi/10.1145/3687906
Yang JZhao MWu YJia X(2024)Accurate and robust registration of low overlapping point cloudsComputers and Graphics10.1016/j.cag.2023.12.003118:C(146-160)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1016/j.cag.2023.12.003
Inza VRist FWallner JPottmann H(2023)Developable Quad Meshes and Contact Element NetsACM Transactions on Graphics10.1145/361835542:6(1-13)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618355
Sun JGong YZhao JZhang HJin L(2023)Matching based on variance minimization of component distances using edges of free-form surfacesPattern Recognition10.1016/j.patcog.2023.109729143:COnline publication date: 1-Nov-2023
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Hruda LKolingerová IVáša L(2022)Robust, fast and flexible symmetry plane detection based on differentiable symmetry measureThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-020-02034-w38:2(555-571)Online publication date: 1-Feb-2022
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Jiang CWang HCeballos Inza VDellinger FRist FWallner JPottmann H(2021)Using isometries for computational design and fabricationACM Transactions on Graphics10.1145/3450626.345983940:4(1-12)Online publication date: 19-Jul-2021
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Huang XLiang ZHuang Q(2020)Uncertainty quantification for multi-scan registrationACM Transactions on Graphics10.1145/3386569.339240239:4(130:1-130:24)Online publication date: 12-Aug-2020
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