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Intrinsic and Extri...
Intrinsic and Extrinsic Means on the Circle -- a Maximum Likelihood Interpretation
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- Brun, Anders, 1976- (författare)
- Linköpings universitet,Medicinsk informatik,Centrum för medicinsk bildvetenskap och visualisering, CMIV,Tekniska högskolan
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- Westin, Carl-Fredrik (författare)
- Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA
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- Herberthson, Magnus, 1963- (författare)
- Linköpings universitet,Tillämpad matematik,Tekniska högskolan
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- Knutsson, Hans, 1950- (författare)
- Linköpings universitet,Medicinsk informatik,Centrum för medicinsk bildvetenskap och visualisering, CMIV,Tekniska högskolan
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(creator_code:org_t)
- New York, USA : IEEE, 2007
- 2007
- Engelska.
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Ingår i: ICASSP 2007. IEEE International Conference on Acoustics, Speech and Signal Processing, 2007. - New York, USA : IEEE. - 1424407273 ; , s. III-1053-III-1056
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- 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
Nyckelord
- Diffusion equations
- Maximum likelihood estimation
- Signal Processing
- Signal representations
- TECHNOLOGY
- TEKNIKVETENSKAP
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