Uncertainty Quantification in Image-based 2D/3D Registration and Its Relationship with Accuracy.

Purpose: Reliable and accurate 2D/3D registration is essential for image-guided navigation and surgical robotics, enabling precise spatial alignment. This work investigates uncertainty quantification and characterization, addressing challenges specific to 2D/3D registration. Despite a few degrees of freedom (DoF), uncertainty in 2D/3D registration is difficult to estimate and interpret since it lacks the dimensional consistency in 2D/2D or 3D/3D registration.

Methods: We model 2D/3D registration as a Maximum A Posteriori (MAP) estimation over the posterior distribution of 3D object poses given 2D fluoroscopic images. Uncertainty is quantified by sampling from an approximate posterior distribution, derived from a similarity function-based likelihood and a prior over the 6DoF pose space, and computing summary statistics and entropy measures from these samples. To characterize this approach, we generate plausible 2D/3D pelvis registrations and conduct experiments to investigate the relationship between uncertainty metrics and registration error.

Results: Ordinary least squares (OLS) regression, a linear model, failed to capture the relationship between uncertainty metrics and registration error (R-squared = 0.023), while XGBoost provided a significantly better fit (R-squared = 0.85). A paired t-test revealed significant differences in prediction accuracy across registration error groups. XGBoost, fit on registrations closer to the correct solution, showed stronger predictive accuracy than the "global" model, which included the full range of errors, and the importance of uncertainty metrics differed between the two models.

Conclusion: This work presents a novel method for uncertainty quantification and characterization in single-view 2D/3D registration. Our results reveal a nonlinear relationship between uncertainty and registration accuracy, with stronger correlations observed in low-error regimes. These insights offer a foundation for better understanding and improving registration reliability in image-guided interventions.