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Intrinsic and Extrinsic Means on the Circle -- a Maximum Likelihood Interpretation
Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Linköpings universitet, Tekniska högskolan.
Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA.
Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0002-9091-4724
2007 (engelsk)Inngår i: ICASSP 2007. IEEE International Conference on Acoustics, Speech and Signal Processing, 2007, New York, USA: IEEE , 2007, s. III-1053-III-1056Konferansepaper, Publicerat paper (Fagfellevurdert)
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

sted, utgiver, år, opplag, sider
New York, USA: IEEE , 2007. s. III-1053-III-1056
Serie
IEEE International Conference on Acoustics, Speech and Signal Processing. Proceedings, ISSN 1520-6149 ; 3
Emneord [en]
Diffusion equations, Maximum likelihood estimation, Signal Processing, Signal representations
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-38748DOI: 10.1109/ICASSP.2007.366864ISI: 000248906600264Lokal ID: 45478ISBN: 1-4244-0727-3 (tryckt)ISBN: e-1-4244-0728-1 OAI: oai:DiVA.org:liu-38748DiVA, id: diva2:259597
Konferanse
IEEE International Conference on Acoustics, Speech and Signal Processing, 2007. Honolulu, HI, USA, APR 15-20, 2007
Tilgjengelig fra: 2009-10-10 Laget: 2009-10-10 Sist oppdatert: 2015-10-09bibliografisk kontrollert

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