Estimating 3-D rigid body transformations: a comparison of four major algorithms

Eggert, Daniel; Lorusso, Adele; Fisher, Robert B.

doi:10.1007/s001380050048

Cited by 698 publications

(417 citation statements)

References 15 publications

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“…This problem has not been addressed, and we ignore if an analytic solution exists to solve it. It can be viewed as a generalization of the orthogonal Procrustes problem [9,10,11,12], which usually deals with the registration of a single pattern. In our study, the shift-invariant case will be considered hereafter.…”

Section: The Organizationmentioning

confidence: 99%

“…Eggert et al [10] reviewed the main methods that give an analytical solution to this rigid 3D registration problem: singular value decomposition (SVD) [9,19], unit quaternions [20], orthonormal matrix [21], and dual quaternions [22]. In [11], Gower and Dijksterhuis reviewed multiple different Procrustes problems and many generalizations.…”

Section: Rigid 3d Registration or Orthogonal Procrustes Problemmentioning

confidence: 99%

“…For solving this 3D registration equation, the SVD method is chosen among the other possible methods because it is the cheapest and it simply deals with the particular cases of noise and planar patterns [10]. Introduced by [9] to solve the orthogonal Procrustes problem, the SVD method fails in the particular cases mentioned above.…”

Section: Registration By Svdmentioning

confidence: 99%

“…(10). Otherwise, it is suboptimal, since atom overlaps generate cross terms that are not treated by 3DRI-MP, as observed in [8].…”

Section: Comments On the 3dri-mpmentioning

confidence: 99%

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Decomposition and dictionary learning for 3D trajectories

2014

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A new model for describing a three-dimensional (3D) trajectory is proposed in this article. The studied trajectory is viewed as a linear combination of rotatable 3D patterns. The resulting model is thus 3D rotation invariant (3DRI). Moreover, the temporal patterns are considered as shift-invariant. This article is divided into two parts based on this model. On the one hand, the 3DRI decomposition estimates the active patterns, their coefficients, their rotations and their shift parameters. Based on sparse approximation, this is carried out by two non-convex optimizations: 3DRI matching pursuit (3DRI-MP) and 3DRI orthogonal matching pursuit (3DRI-OMP). On the other hand, a 3DRI learning method learns the characteristic patterns of a database through a 3DRI dictionary learning algorithm (3DRI-DLA). The proposed algorithms are first applied to simulation data to evaluate their performances and to compare them to other algorithms. Then, they are applied to real motion data of cued speech, to learn the 3D trajectory patterns characteristic of this gestural language.

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Section: The Organizationmentioning

confidence: 99%

Section: Rigid 3d Registration or Orthogonal Procrustes Problemmentioning

confidence: 99%

Section: Registration By Svdmentioning

confidence: 99%

“…(10). Otherwise, it is suboptimal, since atom overlaps generate cross terms that are not treated by 3DRI-MP, as observed in [8].…”

Section: Comments On the 3dri-mpmentioning

confidence: 99%

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Decomposition and dictionary learning for 3D trajectories

2014

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“…(6) and (8) For the equation like (13), C fix can be uniquely solved by an optimization method using the singular value decomposition (SVD) [16] as…”

Section: Calibration Algorithmmentioning

confidence: 99%

A fast in-situ SINS and Doppler sensor calibration algorithm for underwater vehicle navigation

Song

2014

IEICE Electron. Express

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This paper reports the development and experimental evaluation of an in-situ calibration algorithm of the misalignment mounting angle matrix between the Strapdown inertial navigation system (SINS) and Doppler sensor which are practically used for accurate underwater navigation. Most previously reported methods required the SINS to be aligned first to output accurate attitude before the calibration. By separately treating the body frame and the navigation frame attitude update, the algorithm in this paper could be simultaneously carried out during the SINS attitude alignment stage. Simulation and experiment results show that the calibration could be done in 300 s and the position error during the navigation is less than 0.8% of the voyage distance.

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Protein Structure Classification

Koehl

2006

Reviews in Computational Chemistry

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Years of research in biology have established that all cellular functions are deeply connected to the shape of their molecular actors. As a response, structural molecular biology has emerged as a new line of experimental research focused on revealing the structure of bio-molecules. This branch of biology has recently experienced a major uplift through the development of high-throughput structural studies aimed at developing a comprehensive view of the protein structure universe. While these studies are generating a wealth of information, stored into protein structure databases, the key to their success lies in our ability to organize and analyze the information contained in these databases, and integrate it with other biological efforts aimed at solving the mysteries behind cell functions. In this survey, I focus on the first step behind any such organization scheme, namely the classification of protein structures. I review the properties of protein structures, with a special interest on their geometry. Computer methods for the automatic comparison and classification of these structures are then reviewed. In parallel, I describe the existing classifications of protein structures, and their applications in biology, with a special focus on computational biology. I conclude the review with a discussion on the future of these classifications.

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Estimating 3-D rigid body transformations: a comparison of four major algorithms

Cited by 698 publications

References 15 publications

Decomposition and dictionary learning for 3D trajectories

Decomposition and dictionary learning for 3D trajectories

A fast in-situ SINS and Doppler sensor calibration algorithm for underwater vehicle navigation

Protein Structure Classification

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