Optimal computation of 3-D similarity: Gauss–Newton vs. Gauss–Helmert

Kenichi Kanatani and Hirotaka Niitsuma

Computational Statistics & Data Analysis, 2012, vol. 56, issue 12, 4470-4483

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; Inhomogeneous anisotropic noise; Gauss–Newton method; Gauss–Helmert method; Stereo vision; Geodetic sensing (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947312001405
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:12:p:4470-4483

DOI: 10.1016/j.csda.2012.03.014

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().