Point-based rigid registration (PBRR) techniques are widely used in many aspects of image-guided surgery (IGS). Accurately estimating target registration error (TRE) statistics is of essential value for medical applications such as optically surgical tool-tip tracking and image registration. For example, knowing the TRE distribution statistics of surgical tool tip can help the surgeon make right decisions during surgery. In the meantime, the pose of a surgical tool is usually reported relative to a second rigid body whose local frame is called coordinate reference frame (CRF). In an n-ocular tracking system, fiducial localization error (FLE) should be considered inhomogeneous, that means FLE is different between fiducials, and anisotropic that indicates FLE is different in all directions. In this paper, we extend the TRE estimation algorithm relative to a CRF from homogeneous and anisotropic to heterogeneous FLE cases. Arbitrary weightings can be assumed in solving the registration problems in the proposed TRE estimation algorithm. Monte Carlo simulation results demonstrate the proposed algorithm’s effectiveness for both homogeneous and inhomogeneous FLE distributions. The results are further compared with those using the other two algorithms. When FLE distribution is anisotropic and homogeneous, the proposed TRE estimation algorithm’s performance is comparable with that of the first one. When FLE distribution is heterogeneous, proposed TRE estimation algorithm outperforms the other two classical algorithms in all test cases when ideal weighting scheme is adopted in solving two registrations. Possible clinical applications include the online estimation of surgical tool-tip tracking error with respect to a CRF in IGS.

基于点的刚性配准 (PBRR) 技术广泛用于图像引导手术 (IGS) 的许多方面。准确估计目标配准误差 (TRE) 统计数据对于光学手术工具提示跟踪和图像配准等医疗应用具有重要价值。例如，了解手术刀尖的 TRE 分布统计数据可以帮助外科医生在手术过程中做出正确的决定。同时，手术工具的姿态通常是相对于第二个刚体报告的，其局部框架称为坐标参考框架（CRF）。在单目跟踪系统中，基准定位误差 (FLE) 应该被认为是不均匀的，这意味着 FLE 在基准之间是不同的，而各向异性则表明 FLE 在各个方向上都是不同的。在本文中，我们将相对于 CRF 的 TRE 估计算法从均质和各向异性扩展到异质 FLE 案例。在解决所提出的 TRE 估计算法中的配准问题时，可以假设任意权重。蒙特卡罗模拟结果证明了所提出的算法对均匀和非均匀 FLE 分布的有效性。结果进一步与使用其他两种算法的结果进行比较。当FLE分布各向异性且均匀时，所提出的TRE估计算法的性能与第一种算法相当。当 FLE 分布是异构的时，当采用理想的加权方案解决两个配准时，所提出的 TRE 估计算法在所有测试用例中都优于其他两种经典算法。