A nonconvex model‐based combined geometric calibration scheme for micro cone‐beam CT with irregular trajectories

Abstract

Background 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. Purpose 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. Methods 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. Results 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. Conclusions 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.

Fully automatic online geometric calibration for non‐circular cone‐beam CT orbits using fiducials with unknown placement

“…These features preserve the advantages of the previously implemented fiducial-based method while addressing the challenge of human-assisted fiducial localization and coordinate labeling in many existing methods. 25,26,42,47,52,65 The only input required from the operator is an estimate of the number of fiducials available in the FOV, minimizing the burden to the clinicians while allowing for workflow flexibility.…”

“…Methods using a known target assume that the 3D structure of the imaging target is precisely known a priori, for example, from a digital model or prior scans, as is the case with aforementioned dedicated calibration phantoms and 3D-2D registration methods. Conversely, methods using an unknown target are suitable for fiducials placed in an unknown configuration and for cases where a patient has not previously been scanned or presents major anatomical changes from prior scans, but these methods typically require precise localization of fiducials in projection images prior to the geometric calibration, which is practically challenging when the fiducials and patient are simultaneously imaged, 26,42,52 or optimization of 3D image metrics. 45 Some newer methods are addressing some of these intrinsic limitations.…”

“…Methods that do not require precisely manufactured calibration phantoms are also well known, 42,[48][49][50]53 but limiting assumptions such as perfect rotations are often made. Recently, Li et al 52 proposed an optimization-based method using unknown fiducials that can accommodate arbitrary orbits, but it assumes reproducible geome-tries. We are unaware of existing methods that address the issue of fiducial localization when the fiducials are imaged against a complex background.…”

Line‐based iterative geometric calibration method for a tomosynthesis system

“…This allows for the correction of the BB coordinates followed by an iterative calibration to compensate for misalignment and inaccuracies of the phantom. Importantly, our method differs from existing approaches 26,27 . Unlike the existing methods, which find midpoints between pairs of BB projections and average the positions, our approach considers all BB projections in a unified cost function.…”

“…Importantly, our method differs from existing approaches. 26,27 Unlike the existing methods, which find midpoints between pairs of BB projections and average the positions, our approach considers all BB projections in a unified cost function. We show that the line-based iterative method is robust to the motions of the NGT system and improves the image quality in magnification tomosynthesis.The validation is performed both virtually via simulations and experimentally on the NGT system.…”