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Uncertainty characterization of the orthogonal Procrustes problem with arbitrary covariance matrices
Pedro Lourenço1; Bruno J. Guerreiro1,2; Pedro Batista1,2; Paulo Oliveira1,3,4; Carlos Silvestre1,5
2016-07-28
Source PublicationPATTERN RECOGNITION
ISSN0031-3203
Volume61Pages:210-220
Abstract

This paper addresses the weighted orthogonal Procrustes problem of matching stochastically perturbed point clouds, formulated as an optimization problem with a closed-form solution. A novel uncertainty characterization of the solution of this problem is proposed resorting to perturbation theory concepts, which admits arbitrary transformations between point clouds and individual covariance and cross covariance matrices for the points of each cloud. The method is thoroughly validated through extensive Monte Carlo simulations, and particularly interesting cases where nonlinearities may arise are further analyzed. 

KeywordWeighted Procrustes Statistics Perturbation Theory Uncertainty Characterization Map Transformation
DOI10.1016/j.patcog.2016.07.037
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS IDWOS:000385899400015
PublisherELSEVIER SCI LTD
The Source to ArticleWOS
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Cited Times [WOS]:7   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorPedro Lourenço
Affiliation1.Institute for Systems and Robotics, Laboratory for Robotics and Engineering Systems, Portugal
2.Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
3.Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
4.Institute of Mechanical Engineering, Associated Laboratory for Energy, Transports and Aeronautics, Lisbon, Portugal
5.Department of Electrical and Computer Engineering, Faculty of Science and Technology of the University of Macau, China
Recommended Citation
GB/T 7714
Pedro Lourenço,Bruno J. Guerreiro,Pedro Batista,et al. Uncertainty characterization of the orthogonal Procrustes problem with arbitrary covariance matrices[J]. PATTERN RECOGNITION,2016,61:210-220.
APA Pedro Lourenço,Bruno J. Guerreiro,Pedro Batista,Paulo Oliveira,&Carlos Silvestre.(2016).Uncertainty characterization of the orthogonal Procrustes problem with arbitrary covariance matrices.PATTERN RECOGNITION,61,210-220.
MLA Pedro Lourenço,et al."Uncertainty characterization of the orthogonal Procrustes problem with arbitrary covariance matrices".PATTERN RECOGNITION 61(2016):210-220.
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