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The Cramer-Rao lower bound for the estimation of the affine transformationparameters in a multivariate heteroscedastic errors-in-variables model isderived. The model is suitable for feature-based image registration in whichboth sets of control points are localized with errors whose covariance matricesvary from point to point. With focus given to the registration of fluorescencemicroscopy images, the Cramer-Rao lower bound for the estimation of a feature'sposition (e.g. of a single molecule) in a registered image is also derived. Inthe particular case where all covariance matrices for the localization errorsare scalar multiples of a common positive definite matrix (e.g. the identitymatrix), as can be assumed in fluorescence microscopy, then simplifiedexpressions for the Cramer-Rao lower bound are given. Under certain simplifyingassumptions these expressions are shown to match asymptotic distributions for apreviously presented set of estimators. Theoretical results are verified withsimulations and experimental data.

Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy