Optimal computation of 3-D similarity

Gauss-Newton vs. Gauss-Helmert

Kenichi Kanatani, Hirotaka Niitsuma

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Because 3-D data are acquired using 3-D sensing such as stereo vision and laser range finders, they have inhomogeneous and anisotropic noise. This paper studies optimal computation of the similarity (rotation, translation, and scale change) of such 3-D data. We first describe two well known methods for this: the Gauss-Newton and the Gauss-Helmert methods, which are often regarded as different techniques. We then point out that they have similar mathematical structures and combine them to define a hybrid, which we call the modified Gauss-Helmert method. Doing stereo vision simulation, we demonstrate that the proposed method is superior to either of the two methods in convergence performance. Finally, we show an application to real GPS geodetic data and point out that the widely used homogeneous and isotropic noise model is insufficient. We also discuss some numerical issues about GPS data.

Original language English 4470-4483 14 Computational Statistics and Data Analysis 56 12 https://doi.org/10.1016/j.csda.2012.03.014 Published - Dec 2012

Fingerprint

Gauss-Newton
Stereo vision
Gauss
3D
Global positioning system
Range finders
Stereo Vision
Lasers
Laser Range Finder
Sensing
Similarity
Demonstrate
Simulation

Keywords

• 3-D similarity estimation
• Gauss-Helmert method
• Gauss-Newton method
• Geodetic sensing
• Inhomogeneous anisotropic noise
• Stereo vision

ASJC Scopus subject areas

• Computational Mathematics
• Computational Theory and Mathematics
• Statistics and Probability
• Applied Mathematics

Cite this

In: Computational Statistics and Data Analysis, Vol. 56, No. 12, 12.2012, p. 4470-4483.

Research output: Contribution to journalArticle

title = "Optimal computation of 3-D similarity: Gauss-Newton vs. Gauss-Helmert",
abstract = "Because 3-D data are acquired using 3-D sensing such as stereo vision and laser range finders, they have inhomogeneous and anisotropic noise. This paper studies optimal computation of the similarity (rotation, translation, and scale change) of such 3-D data. We first describe two well known methods for this: the Gauss-Newton and the Gauss-Helmert methods, which are often regarded as different techniques. We then point out that they have similar mathematical structures and combine them to define a hybrid, which we call the modified Gauss-Helmert method. Doing stereo vision simulation, we demonstrate that the proposed method is superior to either of the two methods in convergence performance. Finally, we show an application to real GPS geodetic data and point out that the widely used homogeneous and isotropic noise model is insufficient. We also discuss some numerical issues about GPS data.",
keywords = "3-D similarity estimation, Gauss-Helmert method, Gauss-Newton method, Geodetic sensing, Inhomogeneous anisotropic noise, Stereo vision",
author = "Kenichi Kanatani and Hirotaka Niitsuma",
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issn = "0167-9473",
publisher = "Elsevier",
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AU - Niitsuma, Hirotaka

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AB - Because 3-D data are acquired using 3-D sensing such as stereo vision and laser range finders, they have inhomogeneous and anisotropic noise. This paper studies optimal computation of the similarity (rotation, translation, and scale change) of such 3-D data. We first describe two well known methods for this: the Gauss-Newton and the Gauss-Helmert methods, which are often regarded as different techniques. We then point out that they have similar mathematical structures and combine them to define a hybrid, which we call the modified Gauss-Helmert method. Doing stereo vision simulation, we demonstrate that the proposed method is superior to either of the two methods in convergence performance. Finally, we show an application to real GPS geodetic data and point out that the widely used homogeneous and isotropic noise model is insufficient. We also discuss some numerical issues about GPS data.

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