Format

Send to

Choose Destination
IEEE Trans Med Imaging. 2015 Dec;34(12):2632-44. doi: 10.1109/TMI.2015.2451513.

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

Abstract

The Cramér-Rao lower bound for the estimation of the affine transformation parameters in a multivariate heteroscedastic errors-in-variables model is derived. The model is suitable for feature-based image registration in which both sets of control points are localized with errors whose covariance matrices vary from point to point. With focus given to the registration of fluorescence microscopy images, the Cramér-Rao lower bound for the estimation of a feature's position (e.g., of a single molecule) in a registered image is also derived. In the particular case where all covariance matrices for the localization errors are scalar multiples of a common positive definite matrix (e.g., the identity matrix), as can be assumed in fluorescence microscopy, then simplified expressions for the Cramér-Rao lower bound are given. Under 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 data.

PMID:
26641728
PMCID:
PMC4673898
DOI:
10.1109/TMI.2015.2451513
[Indexed for MEDLINE]
Free PMC Article

Supplemental Content

Full text links

Icon for IEEE Engineering in Medicine and Biology Society Icon for PubMed Central
Loading ...
Support Center