In this section
Most of the members of this group are from the Statistics Section and Biomaths research group of the Department of Mathematics. Below you can find a list of research areas that members of this group are currently working on and/or would like to work on by applying their developed mathematical and statistical methods.
@article{Cohen:2013:10.1109/TSP.2013.2284154,
author = {Cohen, EAK and Ober, RJ},
doi = {10.1109/TSP.2013.2284154},
journal = {IEEE Transactions on Signal Processing},
pages = {6291--6306},
title = {Analysis of point based image registration errors with applications in single molecule microscopy},
url = {http://dx.doi.org/10.1109/TSP.2013.2284154},
volume = {61},
year = {2013}
}
TY - JOUR
AB - We present an asymptotic treatment of errors involvedin point-based image registration where control point (CP)localization is subject to heteroscedastic noise; a suitable modelfor image registration in fluorescence microscopy. Assuming anaffine transform, CPs are used to solve a multivariate regressionproblem. With measurement errors existing for both sets of CPsthis is an errors-in-variable problem and linear least squaresis inappropriate; the correct method being generalized leastsquares. To allow for point dependent errors the equivalence of ageneralized maximum likelihood and heteroscedastic generalizedleast squares model is achieved allowing previously publishedasymptotic results to be extended to image registration. For aparticularly useful model of heteroscedastic noise where covariancematrices are scalar multiples of a known matrix (includingthe case where covariance matrices are multiples of the identity)we provide closed form solutions to estimators and derive theirdistribution. We consider the target registration error (TRE) anddefine a new measure called the localization registration error(LRE) believed to be useful, especially in microscopy registrationexperiments. Assuming Gaussianity of the CP localization errors,it is shown that the asymptotic distribution for the TRE and LREare themselves Gaussian and the parameterized distributions arederived. Results are successfully applied to registration in singlemolecule microscopy to derive the key dependence of the TRE andLRE variance on the number of CPs and their associated photoncounts. Simulations show asymptotic results are robust for lowCP numbers and non-Gaussianity. The method presented here isshown to outperform GLS on real imaging data.
AU - Cohen,EAK
AU - Ober,RJ
DO - 10.1109/TSP.2013.2284154
EP - 6306
PY - 2013///
SN - 1053-587X
SP - 6291
TI - Analysis of point based image registration errors with applications in single molecule microscopy
T2 - IEEE Transactions on Signal Processing
UR - http://dx.doi.org/10.1109/TSP.2013.2284154
UR - http://hdl.handle.net/10044/1/24483
VL - 61
ER -
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