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Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy.

E A K Cohen1, R J Ober2

  • 1Eric Jonsson School of Electrical Engineering and Computer Science, University of Texas at Dallas, Richardson, TX 75083 USA. He is also with the Department of Mathematics, Imperial College London, SW7 2AZ U.K.

IEEE Transactions on Signal Processing : a Publication of the IEEE Signal Processing Society
|March 18, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for point-based image registration, addressing heteroscedastic noise in control point localization. The approach improves accuracy in fluorescence microscopy by using generalized least squares for better target registration error (TRE) and localization registration error (LRE) estimation.

Keywords:
Errors-in-variablefluorescence microscopygeneralized least squaresimage registration

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Area of Science:

  • Medical Imaging
  • Computational Biology
  • Statistical Modeling

Background:

  • Point-based image registration is crucial for aligning images, particularly in fluorescence microscopy.
  • Heteroscedastic noise in control point (CP) localization presents a significant challenge for traditional methods.
  • Existing methods like linear least squares are inadequate for errors-in-variable problems common in image registration.

Purpose of the Study:

  • To develop an asymptotic treatment for errors in point-based image registration under heteroscedastic noise.
  • To extend existing statistical results to the domain of image registration, specifically for microscopy.
  • To introduce and validate new error metrics for evaluating registration performance.

Main Methods:

  • An asymptotic treatment of errors-in-variable problems using generalized least squares (GLS).
  • Equivalence of generalized maximum likelihood and heteroscedastic GLS models for point-dependent errors.
  • Derivation of closed-form solutions and distributions for estimators under specific noise models.
  • Definition and asymptotic analysis of Target Registration Error (TRE) and Localization Registration Error (LRE).

Main Results:

  • The proposed method, based on heteroscedastic GLS, outperforms standard GLS on real imaging data.
  • Asymptotic distributions for TRE and LRE are derived, assuming Gaussianity of CP localization errors.
  • The variance of TRE and LRE is shown to depend on the number of CPs and photon counts in single molecule microscopy.
  • Simulations demonstrate the robustness of asymptotic results for low CP numbers and non-Gaussian noise.

Conclusions:

  • The developed method provides a statistically rigorous approach to image registration with heteroscedastic noise.
  • The new Localization Registration Error (LRE) metric is valuable for microscopy applications.
  • The findings offer insights into optimizing CP selection and data acquisition for improved registration accuracy.