Institute for Biomechanics, ETH Zürich, Zürich, Switzerland.
Geneva School of Health Sciences, HES-SO University of Applied Sciences and Arts of Western Switzerland, Geneva, Switzerland.
Med Phys. 2021 Oct;48(10):5991-6006. doi: 10.1002/mp.15124. Epub 2021 Aug 17.
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.
对于 2D-3D 配准结果的正确评估，其准确性的估计至关重要。具有标准化评估方法的公共可用数据集对于 2D-3D 配准技术的验证和比较是必要的。鉴于 2D-3D 配准在生物力学中的广泛应用，我们引入了第一个基于大旋转角度透视图像的髋关节 CT 到 X 射线配准的黄金标准验证数据集。由于使用基准标记计算的地面真实值受到图像数据集定位误差的影响，我们提出了一种基于不确定性传播的新方法来估计黄金标准数据集的准确性。
黄金标准数据集包括女性髋关节的 3D CT 扫描和在不同视图和电压下获取的 19 个 2D 透视图像。地面真实变换是基于提取的 2D 和 3D 基准位置的对应对估计的。这些被假设为受到高斯噪声的污染，没有任何各向同性的限制。我们设计了多个投影点准则（MPPC），该准则联合优化了所有视图的变换和嘈杂的 3D 基准位置。使用不同的目标配准误差（TRE）公式（包括从 MPPC 的不确定性分析得出的新的 TRE 公式（uTRE）），在合成和真实实验中评估了使用 MPPC 获得的变换的准确性。
与不优化 3D 基准位置或错误地假设噪声各向同性的 2D-3D 配准验证方法相比，所提出的 MPPC 方法在统计学上更为准确。报告的结果与以前发表的黄金标准数据集的工作相当。然而，在具有已知地面真实值的合成实验中，发现常用的黄金标准数据集的 TRE 公式会显著计算错误的真实 TRE。相比之下，基于不确定性的 uTRE 在统计学上更接近真实 TRE。
我们提出了一种新的髋关节 CT 到 X 射线配准验证的黄金标准数据集。黄金标准变换是从一种新的方法中得出的，该方法模拟了提取的 2D 和 3D 基准的不确定性。结果表明，考虑到可能的噪声各向异性，并在优化中包含损坏的 3D 基准，可以提高黄金标准的准确性。基于不确定性的 TRE 新公式也是未知真实 TRE 的一个很好的替代方案，在以前的工作中，未知真实 TRE 已被不完全反映黄金标准准确性的替代 TRE 所取代。
