A new 2D-3D registration gold-standard dataset for the hip joint based on uncertainty modeling

Estimation of the accuracy of 2D-3D registration is paramount for a correct evaluation of its outcome in both research and clinical studies. Publicly available datasets with standardized evaluation methodology are necessary for validation and comparison of 2D-3D registration techniques. Given the large use of 2D-3D registration in biomechanics, we introduced the first gold standard validation dataset for computed tomography (CT)-to-x-ray registration of the hip joint, based on fluoroscopic images with large rotation angles. As the ground truth computed with fiducial markers is affected by localization errors in the image datasets, we proposed a new methodology based on uncertainty propagation to estimate the accuracy of a gold standard dataset.

The gold standard dataset included a 3D CT scan of a female hip phantom and 19 2D fluoroscopic images acquired at different views and voltages. The ground truth transformations were estimated based on the corresponding pairs of extracted 2D and 3D fiducial locations. These were assumed to be corrupted by Gaussian noise, without any restrictions of isotropy. We devised the multiple projective points criterion (MPPC) that jointly optimizes the transformations and the noisy 3D fiducial locations for all views. The accuracy of the transformations obtained with the MPPC was assessed in both synthetic and real experiments using different formulations of the target registration error (TRE), including a novel formulation of the TRE (uTRE) derived from the uncertainty analysis of the MPPC.

The proposed MPPC method was statistically more accurate compared to the validation methods for 2D-3D registration that did not optimize the 3D fiducial positions or wrongly assumed the isotropy of the noise. The reported results were comparable to previous published works of gold standard datasets. However, a formulation of the TRE commonly found in these gold standard datasets was found to significantly miscalculate the true TRE computed in synthetic experiments with known ground truths. In contrast, the uncertainty-based uTRE was statistically closer to the true TRE.

We proposed a new gold standard dataset for the validation of CT-to-X-ray registration of the hip joint. The gold standard transformations were derived from a novel method modeling the uncertainty in extracted 2D and 3D fiducials. Results showed that considering possible noise anisotropy and including corrupted 3D fiducials in the optimization resulted in improved accuracy of the gold standard. A new uncertainty-based formulation of the TRE also appeared as a good alternative to the unknown true TRE that has been replaced in previous works by an alternative TRE not fully reflecting the gold standard accuracy.