Wiles Andrew D, Peters Terry M
Medical Biophysics Department, The University of Western Ontario, London, ON, Canada.
IEEE Trans Med Imaging. 2009 Sep;28(9):1384-98. doi: 10.1109/TMI.2009.2016336. Epub 2009 Mar 24.
Target registration error (TRE) has become a widely accepted error metric in point-based registration since the error metric was introduced in the 1990s. It is particularly prominent in image-guided surgery (IGS) applications where point-based registration is used in both image registration and optical tracking. In point-based registration, the TRE is a function of the fiducial marker geometry, location of the target and the fiducial localizer error (FLE). While the first two items are easily obtained, the FLE is usually estimated using an a priori technique and applied without any knowledge of real-time information. However, if the FLE can be estimated in real-time, particularly as it pertains to optical tracking, then the TRE can be estimated more robustly. In this paper, a method is presented where the FLE statistics are estimated from the latest measurement of the fiducial registration error (FRE) statistics. The solution is obtained by solving a linear system of equations of the form Ax=b for each marker at each time frame where x are the six independent FLE covariance parameters and b are the six independent estimated FRE covariance parameters. The A matrix is only a function of the tool geometry and hence the inverse of the matrix can be computed a priori and used at each instant in which the FLE estimation is required, hence minimizing the level of computation at each frame. When using a good estimate of the FRE statistics, Monte Carlo simulations demonstrate that the root mean square of the FLE can be computed within a range of 70-90 microm. Robust estimation of the TRE for an optically tracked tool, using a good estimate of the FLE, will provide two enhancements in IGS. First, better patient to image registration will be obtained by using the TRE of the optical tool as a weighting factor of point-based registration used to map the patient to image space. Second, the directionality of the TRE can be relayed back to the surgeon giving the surgeon the option of changing their strategy in order to improve the overall system accuracy and, in turn, the quality of procedure.
自20世纪90年代引入误差度量以来，目标配准误差（TRE）已成为基于点的配准中广泛接受的误差度量。它在图像引导手术（IGS）应用中尤为突出，在图像配准和光学跟踪中都使用了基于点的配准。在基于点的配准中，TRE是基准标记几何形状、目标位置和基准定位器误差（FLE）的函数。虽然前两项很容易获得，但FLE通常使用先验技术进行估计，并且在没有任何实时信息的情况下应用。然而，如果可以实时估计FLE，特别是与光学跟踪相关的FLE，那么TRE可以更稳健地估计。在本文中，提出了一种方法，其中从基准配准误差（FRE）统计的最新测量中估计FLE统计。通过在每个时间帧为每个标记求解形式为Ax = b的线性方程组来获得解，其中x是六个独立的FLE协方差参数，b是六个独立估计的FRE协方差参数。A矩阵仅是工具几何形状的函数，因此可以先验计算矩阵的逆，并在需要FLE估计的每个时刻使用，从而最小化每个帧的计算量。当使用FRE统计的良好估计时，蒙特卡罗模拟表明FLE的均方根可以在70 - 90微米的范围内计算。使用FLE的良好估计对光学跟踪工具的TRE进行稳健估计，将在IGS中提供两个改进。首先，通过将光学工具的TRE用作用于将患者映射到图像空间的基于点的配准的加权因子，可以获得更好的患者到图像配准。其次，TRE的方向性可以反馈给外科医生，使外科医生可以选择改变他们的策略，以提高整个系统的准确性，进而提高手术质量。
