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Analysis of point based image registration errors with applications in single molecule microscopy

Analysis of point based image registration errors with applications in single molecule microscopy
Analysis of point based image registration errors with applications in single molecule microscopy

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data.

Errors-in-variable, fluorescence microscopy, generalized least squares, image registration
1053-587X
6291-6306
Cohen, E. A.K.
97c75d1e-6c18-4e03-8e7a-29472b32d9c2
Ober, R. J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Cohen, E. A.K.
97c75d1e-6c18-4e03-8e7a-29472b32d9c2
Ober, R. J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36

Cohen, E. A.K. and Ober, R. J. (2013) Analysis of point based image registration errors with applications in single molecule microscopy. IEEE Transactions on Signal Processing, 61 (24), 6291-6306, [6616646]. (doi:10.1109/TSP.2013.2284154).

Record type: Article

Abstract

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data.

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More information

Published date: 2013
Keywords: Errors-in-variable, fluorescence microscopy, generalized least squares, image registration

Identifiers

Local EPrints ID: 423645
URI: http://eprints.soton.ac.uk/id/eprint/423645
ISSN: 1053-587X
PURE UUID: 093ec2ed-03bc-4402-a4c6-f0cd54ba52a2
ORCID for R. J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

Catalogue record

Date deposited: 27 Sep 2018 16:30
Last modified: 16 Mar 2024 04:37

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Contributors

Author: E. A.K. Cohen
Author: R. J. Ober ORCID iD

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