A line fiducial method for geometric calibration of cone-beam CT systems with diverse scan trajectories

Investigations into the Geometric Calibration and Systematic Effects of a Micro-CT System

Micro-Computed Tomography (µCT) systems are used for examining the internal structures of various objects, such as material samples, manufactured parts, and natural objects. Resolving fine details or performing accurate geometric measurements in the voxel data critically depends on the precise calibration of the µCT systems geometry. This paper presents a calibration method for µCT systems using projections of a calibration phantom, where the coordinates of the phantom are initially unknown. The approach involves detecting and tracking steel ball bearings and adjusting the unknown system geometry parameters using non-linear least squares optimization. Multiple geometric models are tested to verify their suitability for a self-calibration approach. The implementation is tested using a calibration phantom captured at different magnifications. The results demonstrate the system's capability to determine the geometry model parameters with a remaining error on the detector between 0.27 px and 0.18 px. Systematic errors that remain after calibration, as well as changing parameters due to system instabilities, are investigated. The source code of this work is published to enable further research.

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

BACKGROUND

Cone-beam CT (CBCT) with non-circular scanning orbits can improve image quality for 3D intraoperative image guidance. However, geometric calibration of such scans can be challenging. Existing methods typically require a prior image, specialized phantoms, presumed repeatable orbits, or long computation time.

PURPOSE

We propose a novel fully automatic online geometric calibration algorithm that does not require prior knowledge of fiducial configuration. The algorithm is fast, accurate, and can accommodate arbitrary scanning orbits and fiducial configurations.

METHODS

The algorithm uses an automatic initialization process to eliminate human intervention in fiducial localization and an iterative refinement process to ensure robustness and accuracy. We provide a detailed explanation and implementation of the proposed algorithm. Physical experiments on a lab test bench and a clinical robotic C-arm scanner were conducted to evaluate spatial resolution performance and robustness under realistic constraints.

RESULTS

Qualitative and quantitative results from the physical experiments demonstrate high accuracy, efficiency, and robustness of the proposed method. The spatial resolution performance matched that of our existing benchmark method, which used a 3D-2D registration-based geometric calibration algorithm.

CONCLUSIONS

We have demonstrated an automatic online geometric calibration method that delivers high spatial resolution and robustness performance. This methodology enables arbitrary scan trajectories and should facilitate translation of such acquisition methods in a clinical setting.

Line-based iterative geometric calibration method for a tomosynthesis system

BACKGROUND

A next generation tomosynthesis (NGT) system, capable of two-dimensional source motion, detector motion in the perpendicular direction, and magnification tomosynthesis, was constructed to investigate different acquisition geometries. Existing position-based geometric calibration methods proved ineffective when applied to the NGT geometries.

PURPOSE

A line-based iterative calibration method is developed to perform accurate geometric calibration for the NGT system.

METHODS

The proposed method calculates the system geometry through virtual line segments created by pairs of fiducials within a calibration phantom, by minimizing the error between the line equations computed from the true and estimated fiducial projection pairs. It further attempts to correct the 3D fiducial locations based on the initial geometric calibration. The method's performance was assessed via simulation and experimental setups with four distinct NGT geometries: X, T, XZ, and TZ. The X geometry resembles a conventional DBT acquisition along the chest wall. The T geometry forms a "T"-shaped source path in mediolateral (ML) and posteroanterior (PA) directions. A descending detector motion is added to both X and T geometries to form the XZ and TZ geometries, respectively. Simulation studies were conducted to assess the robustness of the method to geometric perturbations and inaccuracies in fiducial locations. Experimental studies were performed to assess the impact of phantom magnification and the performance of the proposed method for various geometries, compared to the traditional position-based method. Star patterns were evaluated for both qualitative and quantitative analyses; the Fourier spectral distortions (FSDs) graphs and the contrast transfer function (CTF) were extracted. The limit of spatial resolution (LSR) was measured at 5% modulation of the CTF.

RESULTS

The proposed method presented is highly robust to geometric perturbation and fiducial inaccuracies. After the line-based iterative method, the mean distance between the true and estimated fiducial projections was [X, T, XZ, TZ]: [0.01, 0.01, 0.02, 0.01] mm. The impact of phantom magnification was observed; a contact-mode acquisition of a calibration phantom successfully provided an accurate geometry for 1.85× magnification images of a star pattern, with the X geometry. The FSD graphs for the contact-mode T geometry acquisition presented evidence of super-resolution, with the LSR of [0°-quadrant: 8.57, 90°-quadrant: 8.47] lp/mm. Finally, a contact-mode XZ geometry acquisition and a 1.50× magnification TZ geometry acquisition were reconstructed with three calibration methods-position-based, line-based, and iterative line-based. As more advanced methods are applied, the CTF becomes more isotropic, the FSD graphs demonstrate less spectral leakage as super-resolution is achieved, and the degree of blurring artifacts reduces significantly.

CONCLUSIONS

This study introduces a robust calibration method tailored to the unique requirements of advanced tomosynthesis systems. By employing virtual line segments and iterative techniques, we ensure accurate geometric calibration while mitigating the limitations posed by the complex acquisition geometries of the NGT system. Our method's ability to handle various NGT configurations and its tolerance to fiducial misalignment make it a superior choice compared to traditional calibration techniques.

Drift correction in laboratory nanocomputed tomography using joint feature correlation

Laboratory nanocomputed tomography (nano-CT), which can provide a spatial resolution of up to 100 nm, has been widely used due to its volume advantage. However, the drift of the x-ray source focal spot and the thermal expansion of the mechanical system can cause projection drift during long-time scanning. The three-dimensional result reconstructed from the drifted projections contains severe drift artifacts, which reduce the spatial resolution of nano-CT. Registering the drifted projections using rapidly acquired sparse projections is one of the mainstream correction methods, but the high noise and contrast differences of projections in nano-CT affect the correction effectiveness of existing methods. Herein, we propose a rough-to-refined projection registration method, which fully combines the information of the features in the gray and frequency domains of the projections. Simulation data show that the drift estimation accuracy of the proposed method is improved by 5× and 16× compared with the mainstream random sample consensus and locality preserving matching based on features. The proposed method can effectively improve the imaging quality of nano-CT.

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

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.

Online Calibration of a Linear Micro Tomosynthesis Scanner

In a linear tomosynthesis scanner designed for imaging histologic samples of several centimeters size at 10 µm resolution, the mechanical instability of the scanning stage (±10 µm) exceeded the resolution of the image system, making it necessary to determine the trajectory of the stage for each scan to avoid blurring and artifacts in the images that would arise from the errors in the geometric information used in 3D reconstruction. We present a method for online calibration by attaching a layer of randomly dispersed micro glass beads or calcium particles to the bottom of the sample stage. The method was based on a parametric representation of the rigid body motion of the sample stage-marker layer assembly. The marker layer was easy to produce and proven effective in the calibration procedure.

Online Geometric Calibration of a Hybrid CT System for Ultrahigh-Resolution Imaging

A hybrid imaging system consisting of a standard computed tomography (CT) scanner and a low-profile photon-counting detector insert in contact with the patient's body has been used to produce ultrahigh-resolution images in a limited volume in chest scans of patients. The detector insert is placed on the patient bed as needed and not attached. Thus, its position and orientation in the scanner is dependent on the patient's position and scan settings. To allow accurate image reconstruction, we devised a method of determining the relative geometry of the detector insert and the CT scanner for each scan using fiducial markers. This method uses an iterative registration algorithm to align the markers in the reconstructed volume from the detector insert to that of the concurrent CT scan. After obtaining precise geometric information of the detector insert relative to the CT scanner, the two complementary sets of images are summed together to create a detailed image with reduced artifacts.

Source-detector trajectory optimization in cone-beam computed tomography: a comprehensive review on today’s state-of-the-art

Cone-beam computed tomography (CBCT) imaging is becoming increasingly important for a wide range of applications such as image-guided surgery, image-guided radiation therapy as well as diagnostic imaging such as breast and orthopaedic imaging. The potential benefits of non-circular source-detector trajectories was recognized in early work to improve the completeness of CBCT sampling and extend the field of view (FOV). Another important feature of interventional imaging is that prior knowledge of patient anatomy such as a preoperative CBCT or prior CT is commonly available. This provides the opportunity to integrate such prior information into the image acquisition process by customized CBCT source-detector trajectories. Such customized trajectories can be designed in order to optimize task-specific imaging performance, providing intervention or patient-specific imaging settings. The recently developed robotic CBCT C-arms as well as novel multi-source CBCT imaging systems with additional degrees of freedom provide the possibility to largely expand the scanning geometries beyond the conventional circular source-detector trajectory. This recent development has inspired the research community to innovate enhanced image quality by modifying image geometry, as opposed to hardware or algorithms. The recently proposed techniques in this field facilitate image quality improvement, FOV extension, radiation dose reduction, metal artifact reduction as well as 3D imaging under kinematic constraints. Because of the great practical value and the increasing importance of CBCT imaging in image-guided therapy for clinical and preclinical applications as well as in industry, this paper focuses on the review and discussion of the available literature in the CBCT trajectory optimization field. To the best of our knowledge, this paper is the first study that provides an exhaustive literature review regarding customized CBCT algorithms and tries to update the community with the clarification of in-depth information on the current progress and future trends.

[Free trajectory cone beam computed tomography reconstruction method for synchronous scanning of geometric calibration phantom and imaging object]

In order to suppress the geometrical artifacts caused by random jitter in ray source scanning, and to achieve flexible ray source scanning trajectory and meet the requirements of task-driven scanning imaging, a method of free trajectory cone-beam computed tomography (CBCT) reconstruction is proposed in this paper. This method proposed a geometric calibration method of two-dimensional plane. Based on this method, the geometric calibration phantom and the imaging object could be simultaneously imaged. Then, the geometric parameters could be obtained by online calibration method, and then combined with the geometric parameters, the alternating direction multiplier method (ADMM) was used for image iterative reconstruction. Experimental results showed that this method obtained high quality reconstruction image with high contrast and clear feature edge. The root mean square errors (RMSE) of the simulation results were rather small, and the structural similarity (SSIM) values were all above 0.99. The experimental results showed that it had lower image information entropy (IE) and higher contrast noise ratio (CNR). This method provides some practical value for CBCT to realize trajectory freedom and obtain high quality reconstructed image.

A method of determining geometry of cone beam CT scanner

The task of determining the geometry of a cone-beam CT scanner with flat panel detector and circular/spiral source trajectory is considered. Accomplishing this task implies analyzing projections of a set of points referred to as calibrating set or calibrating phantom. We take advantage of the fact that observed coordinates of a point’s projection are rational functions of the point’s location. Unknown coefficients of these functions can be recovered exactly from six projections of the point. Location of the source as well as position and orientation of the detector are determined in the scanner reference frame, which is constituted by rotation axis and central plane of the scanner. Two different projections of a calibrating set are enough to solve the task if the source trajectory is a circle. In applications where a shift of an object transversally to the central plane is required, two additional projections have to be collected in order to identify the direction of the shift. The developed formalism becomes especially simple when the detector is aligned with the rotation axis. In this case four projections of a single calibrating point rotated successfully about the rotation axis are sufficient. The error analysis carried out in the paper shows that the magnitude of deviation from the true values is of the order of the magnitude of measurement errors.