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Intrinsic and Extrinsic Means on the Circle -- a Maximum Likelihood Interpretation
Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.
Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9091-4724
2007 (English)In: ICASSP 2007. IEEE International Conference on Acoustics, Speech and Signal Processing, 2007, New York, USA: IEEE , 2007, III-1053-III-1056 p.Conference paper, Published paper (Refereed)
Abstract [en]

For data samples in Rn, the mean is a well known estimator. When the data set belongs to an embedded manifold M in Rn, e.g. the unit circle in R2, the definition of a mean can be extended and constrained to M by choosing either the intrinsic Riemannian metric of the manifold or the extrinsic metric of the embedding space. A common view has been that extrinsic means are approximate solutions to the intrinsic mean problem. This paper study both means on the unit circle and reveal how they are related to the ML estimate of independent samples generated from a Brownian distribution. The conclusion is that on the circle, intrinsic and extrinsic means are maximum likelihood estimators in the limits of high SNR and low SNR respectively

Place, publisher, year, edition, pages
New York, USA: IEEE , 2007. III-1053-III-1056 p.
Series
IEEE International Conference on Acoustics, Speech and Signal Processing. Proceedings, ISSN 1520-6149 ; 3
Keyword [en]
Diffusion equations, Maximum likelihood estimation, Signal Processing, Signal representations
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-38748DOI: 10.1109/ICASSP.2007.366864ISI: 000248906600264Local ID: 45478ISBN: 1-4244-0727-3 (print)ISBN: e-1-4244-0728-1 OAI: oai:DiVA.org:liu-38748DiVA: diva2:259597
Conference
IEEE International Conference on Acoustics, Speech and Signal Processing, 2007. Honolulu, HI, USA, APR 15-20, 2007
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2015-10-09Bibliographically approved

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Brun, AndersHerberthson, MagnusKnutsson, Hans

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  • apa
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