Li Guang, Chen Xue, You Chenyu, Huang Xinhai, Deng Zhenhao, Luo Shouhua
Jiangsu Key Laboratory for Biomaterials and Devices, Department of Biomedical Engineering, Southeast University, Nanjing, China.
Image Processing and Analysis Group (IPAG), Yale University, New Haven, Connecticut, USA.
Med Phys. 2023 May;50(5):2759-2774. doi: 10.1002/mp.16257. Epub 2023 Feb 11.
Many dedicated cone-beam CT (CBCT) systems have irregular scanning trajectories. Compared with the standard CBCT calibration, accurate calibration for CBCT systems with irregular trajectories is a more complex task, since the geometric parameters for each scanning view are variable. Most of the existing calibration methods assume that the intrinsic geometric relationship of the fiducials in the phantom is precisely known, and rarely delve deeper into the issue of whether the phantom accuracy is adapted to the calibration model.
A high-precision phantom and a highly robust calibration model are interdependent and mutually supportive, and they are both important for calibration accuracy, especially for the high-resolution CBCT. Therefore, we propose a calibration scheme that considers both accurate phantom measurement and robust geometric calibration.
Our proposed scheme consists of two parts: (1) introducing a measurement model to acquire the accurate intrinsic geometric relationship of the fiducials in the phantom; (2) developing a highly noise-robust nonconvex model-based calibration method. The measurement model in the first part is achieved by extending our previous high-precision geometric calibration model suitable for CBCT with circular trajectories. In the second part, a novel iterative method with optimization constraints based on a back-projection model is developed to solve the geometric parameters of each view.
The simulations and real experiments show that the measurement errors of the fiducial ball bearings (BBs) are within the subpixel level. With the help of the geometric relationship of the BBs obtained by our measurement method, the classic calibration method can achieve good calibration based on far fewer BBs. All metrics obtained in simulated experiments as well as in real experiments on Micro CT systems with resolutions of 9 and 4.5 μm show that the proposed calibration method has higher calibration accuracy than the competing classic method. It is particularly worth noting that although our measurement model proves to be very accurate, the classic calibration method based on this measurement model can only achieve good calibration results when the resolution of the measurement system is close to that of the system to be calibrated, but our calibration scheme enables high-accuracy calibration even when the resolution of the system to be calibrated is twice that of the measurement system.
The proposed combined geometrical calibration scheme does not rely on a phantom with an intricate pattern of fiducials, so it is applicable in Micro CT with high resolution. The two parts of the scheme, the "measurement model" and the "calibration model," prove to be of high accuracy. The combination of these two models can effectively improve the calibration accuracy, especially in some extreme cases.
许多专用锥形束CT（CBCT）系统具有不规则的扫描轨迹。与标准CBCT校准相比，对具有不规则轨迹的CBCT系统进行精确校准是一项更为复杂的任务，因为每个扫描视图的几何参数都是可变的。现有的大多数校准方法都假定体模中基准标记的内在几何关系是精确已知的，并且很少深入探讨体模精度是否适用于校准模型的问题。
高精度体模和高度稳健的校准模型相互依存、相互支持，对于校准精度都很重要，尤其是对于高分辨率CBCT。因此，我们提出一种兼顾精确体模测量和稳健几何校准的校准方案。
我们提出的方案由两部分组成：（1）引入测量模型以获取体模中基准标记的精确内在几何关系；（2）开发一种基于非凸模型的高度抗噪声校准方法。第一部分中的测量模型是通过扩展我们先前适用于圆形轨迹CBCT的高精度几何校准模型来实现的。在第二部分中，开发了一种基于反投影模型的具有优化约束的新型迭代方法来求解每个视图的几何参数。
模拟和实际实验表明，基准滚珠轴承（BBs）的测量误差在亚像素级别内。借助我们的测量方法获得的BBs的几何关系，经典校准方法基于少得多的BBs就能实现良好的校准。在模拟实验以及分辨率为9μm和4.5μm的微型CT系统的实际实验中获得的所有指标均表明，所提出的校准方法比竞争的经典方法具有更高的校准精度。特别值得注意的是，尽管我们的测量模型证明非常准确，但基于此测量模型的经典校准方法只有在测量系统的分辨率与待校准系统的分辨率相近时才能获得良好的校准结果，而我们的校准方案即使在校准系统的分辨率是测量系统分辨率的两倍时也能实现高精度校准。
所提出的组合几何校准方案不依赖于具有复杂基准标记图案的体模，因此适用于高分辨率微型CT。该方案的两个部分，即“测量模型”和“校准模型”，证明具有很高的精度。这两个模型的组合可以有效提高校准精度，尤其是在一些极端情况下。
