TY - JOUR
T1 - Optimal computation of 3-D similarity
T2 - Gauss-Newton vs. Gauss-Helmert
AU - Kanatani, Kenichi
AU - Niitsuma, Hirotaka
N1 - Funding Information:
The authors thank Orhan Akyilmaz of Istanbul Institute of Technology, Turkey for providing the GPS data and doing helpful discussions. They also thank Takuto Honda of Okayama University and Hiroki Hara of SANYO Electric Co. Ltd for helping our numerical experiments. This work was supported in part by JSPS Grant-in-Aid for Challenging Exploratory Research ( 24650086 ).
PY - 2012/12
Y1 - 2012/12
N2 - 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.
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.
KW - 3-D similarity estimation
KW - Gauss-Helmert method
KW - Gauss-Newton method
KW - Geodetic sensing
KW - Inhomogeneous anisotropic noise
KW - Stereo vision
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U2 - 10.1016/j.csda.2012.03.014
DO - 10.1016/j.csda.2012.03.014
M3 - Article
AN - SCOPUS:84864143860
SN - 0167-9473
VL - 56
SP - 4470
EP - 4483
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 12
ER -