A theoretical comparison of different target registration error estimators.

Area of Science:

• Medical Imaging
• Surgical Navigation
• Computational Geometry

Background:

• Accurate registration is vital for computer-assisted surgery (CAS).
• Target Registration Error (TRE) quantifies registration accuracy.
• Various methods exist to estimate TRE, focusing on mean squared values or distributions under noise.

Purpose of the Study:

• To theoretically demonstrate that proposed algorithms for TRE estimation converge to a general Maximum Likelihood (ML) solution.
• To validate theoretical derivations through numerical simulations.
• To illustrate TRE prediction in anisotropic noise using experimental data.

Main Methods:

• Theoretical analysis of existing TRE estimation algorithms.
• Development of a general Maximum Likelihood (ML) framework.
• Numerical simulations to verify theoretical convergence.
• Application to experimentally measured fiducial localization error data.

Main Results:

• All previously proposed TRE estimation algorithms were shown to converge to a unified Maximum Likelihood (ML) solution.
• Numerical simulations confirmed the theoretical derivations.
• A practical example demonstrated TRE prediction under anisotropic noise conditions using experimental data.

Conclusions:

• The Maximum Likelihood (ML) framework provides a unifying theoretical basis for TRE estimation in CAS.
• The findings simplify the understanding and development of registration accuracy estimation methods.
• This work has implications for improving the reliability of image-guided surgery systems.