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


The Cramér-Rao lower sure for the estimation of the affine transformation parameters during a multivariate heteroscedastic errors-in-variables model springs. The model is appropriate for feature-based mostly image registration in that each sets of control points are localized with errors whose covariance matrices vary from purpose to purpose. With focus given to the registration of fluorescence microscopy pictures, the Cramér-Rao lower sure for the estimation of a feature’s position (e.g., of one molecule) during a registered image is additionally derived. In the actual case where all covariance matrices for the localization errors are scalar multiples of a standard positive definite matrix (e.g., the identity matrix), as can be assumed in fluorescence microscopy, then simplified expressions for the Cramér-Rao lower sure are given. Beneath certain simplifying assumptions these expressions are shown to match asymptotic distributions for a previously presented set of estimators. Theoretical results are verified with simulations and experimental knowledge.

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