CT系统几何在线标定

BACKGROUND Computed tomography (CT) generates a three-dimensional rendering that can be used to interrogate a given region or desired structure from any orientation. However, in pre-clinical research, its deployment remains limited due to relatively high upfront costs. Existing integrated imaging systems that provide merged planar X-ray also dwarfs CT popularity in small laboratories due to their added versatility. PURPOSE In this paper, we sought to generate CT-like data using an existing small-animal X-ray imager with a specialized specimen rotation system, or MiSpinner. This setup conforms to the cone-beam computed tomography (CBCT) geometry, which demands high spatial calibration accuracy. Therefore, a simple but robust geometry calibration algorithm is necessary to ensure that the entire imaging system works properly and accurately. METHODS Because the rotation system is not permanently affixed, we propose a structure tensor-based two-step online (ST-TSO) geometry calibration algorithm. Specifically, two datasets are needed, namely calibration and actual measurements. A calibration measurement detects the background of the system forward X-ray projections. A study on the background image reveals the characteristics of the X-ray photon distribution and thus provides a reliable estimate of the imaging geometry origin. Actual measurements consisted of an X-ray of the intended object, including possible geometry errors. A comprehensive image processing technique helps to detect spatial misalignment information. Accordingly, the first processing step employs a modified projection matrix-based calibration algorithm to estimate the relevant geometric parameters. Predicted parameters are then fine-tuned in a second processing step by an iterative strategy based on the symmetry property of the sum of projections. Virtual projections calculated from the parameters after two-step processing compensate for the scanning errors and are used for CT reconstruction. Experiments on phantom and mouse imaging data were performed to validate the calibration algorithm. RESULTS Once system correction was conducted, CBCT of a CT bar phantom and a euthanized mouse were analyzed. No obvious structure error or spatial artifacts were observed, validating the accuracy of the proposed geometry calibration method. Digital phantom simulation indicated that compared with the pre-set spatial values, errors in the final estimated parameters could be reduced to 0.05° difference in dominant angle and 0.5-pixel difference in dominant axis bias. The in-plane resolution view of the CT-bar phantom revealed that the resolution approaches 150 μm. CONCLUSIONS A constrained two-step online geometry calibration algorithm has been developed to calibrate an integrated X-ray imaging system, defined by a first-step analytical estimation and a second-step iterative fine-tuning. Test results have validated its accuracy in system correction, thus demonstrating the potential of the described system to be modified and adapted for pre-clinical research. This article is protected by copyright. All rights reserved.

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.

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BACKGROUND Micro-CT (Micro-Computed Tomography) is a high-resolution, non-destructive three-dimensional imaging technology widely applied in biomedical research. However, the long scanning time of micro-CT and its higher sensitivity to small-scale perturbations make focal spot drift a more likely and non-negligible source of geometric artifacts. Focal spot drift is typically stochastic and unrepeatable, which may make offline calibration inaccurate, while conventional online calibration tends to be time-consuming due to iterative operations. METHODS This paper presents a fast, accurate, and convenient online calibration method that overcomes the limitations commonly associated with existing online calibration approaches. To the best of our knowledge, this work is the first to explicitly and quantitatively describe the relationship between 3D focal spot drift and the resulting 2D projection shifts in micro-CT systems. By leveraging the prior geometric information of a specific feature point on the marker, its true spatial location can be precisely determined, which enables the tracking of its ideal trajectory and corresponding ideal projection positions across all views. Consequently, artifacts induced by focal spot drift can be effectively corrected by compensating for the offsets between the measured and ideal projection positions of the point. The entire correction process requires only a single pass of forward and backward projection. RESULTS The effectiveness and applicability of the method were validated through numerical simulation, physical experiments, and supplementary experiments. In numerical simulations, the method remained effective with even fivefold the normal perturbation level. In physical experiments without ground truth, this method achieved the highest level score according to BRISQUE (Blind/Referenceless Image Spatial Quality Evaluator) and completed the correction in the shortest time, making it the most efficient among all methods. Finally, the supplementary experiments were conducted to verify the applicability of the algorithm under certain assumptions and errors, further demonstrating its practicality. CONCLUSIONS The proposed method preserves the high correction accuracy and strong applicability of online calibrations while avoiding the need for frequent iterations or forward/backward projections, thereby achieving high computational efficiency. It is particularly well-suited for micro-CT systems with a large number of scan views and high projection resolution.

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.

Compared to single source systems, stereo X-ray CT systems allow acquiring projection data within a reduced amount of time, for an extended field-of-view, or for dual X-ray energies. To exploit the benefit of a dual X-ray system, its acquisition geometry needs to be calibrated. Unfortunately, in modular stereo X-ray CT setups, geometry misalignment occurs each time the setup is changed, which calls for an efficient calibration procedure. Although many studies have been dealing with geometry calibration of an X-ray CT system, little research targets the calibration of a dual cone-beam X-ray CT system. In this work, we present a phantom-based calibration procedure to accurately estimate the geometry of a stereo cone-beam X-ray CT system. With simulated as well as real experiments, it is shown that the calibration procedure can be used to accurately estimate the geometry of a modular stereo X-ray CT system thereby reducing the misalignment artifacts in the reconstruction volumes.

Conventional intraoperative computed tomography (CT) has a long scan time, degrading the image quality. Its large size limits the position of a surgeon during surgery. Therefore, this study proposes a CT system comprising of eight carbon-nanotube (CNT)-based x-ray sources and 16 detector modules to solve these limitations. Gantry only requires 45° of rotation to acquire the whole projection, reducing the scan time to 1/8 compared to the full rotation. Moreover, the volume and scan time of the system can be significantly reduced using CNT sources with a small volume and short pulse width and placing a heavy and large high-voltage generator outside the gantry. We divided the proposed system into eight subsystems and sequentially devised a geometry calibration method for each subsystem. Accordingly, a calibration phantom consisting of four polytetrafluoroethylene beads, each with 15 mm diameter, was designed. The geometry calibration parameters were estimated by minimizing the difference between the measured bead projection and the forward projection of the formulated subsystem. By reflecting the estimated geometry calibration parameters, the projection data were obtained via rebinning to be used in the filtered-backprojection reconstruction. The proposed calibration and reconstruction methods were validated by computer simulations and real experiments. Additionally, the accuracy of the geometry calibration method was examined by computer simulation. Furthermore, we validated the improved quality of the reconstructed image through the mean-squared error (MSE), structure similarity (SSIM), and visual inspections for both the simulated and experimental data. The results show that the calibrated images, reconstructed by reflecting the calibration results, have smaller MSE and higher SSIM values than the uncalibrated images. The calibrated images were observed to have fewer artifacts than the uncalibrated images in visual inspection, demonstrating that the proposed calibration and reconstruction methods effectively reduce artifacts caused by geometry misalignments.

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The geometric parameters of the CT system significantly influence the quality of reconstructed images and the accuracy of dimensional measurements. To achieve precise calibration of these parameters, this study develops a self-calibration method for spiral CT geometry based on data redundancy conditions. Theoretical analysis is conducted to identify the geometric relationships that satisfy data redundancy under spiral scanning trajectories. Using simulation data, we investigate the effects of three key geometric parameters-the source-to-sample distance, the horizontal offset of the detector, and the rotation angle in detector plane-on data redundancy. Additionally, we examine how varying noise levels impact the accuracy of geometric parameter estimation. Finally, the proposed method is validated through spiral CT scanning experiments with real samples. Results show that the calculation accuracy for the detector's horizontal offset is better than 1 pixel, the rotation angle in detector plane accuracy exceeds 0.1°, and the source-to-sample distance accuracy surpasses 0.42%. These findings confirm the effectiveness of the proposed method in practical applications.

Multi-source stationary CT is a multi-source multi-detector system where the sources and detectors are mounted on two fixed ring gantries with a constant offset between them. The imaging geometry of this system, encompassing the positional information of all source focal spots and sub-panel detectors, entails a high-dimensional parameter space. Existing geometric calibration methods often neglect the rigid structural constraint of the detector ring as a whole, calibrating each sub-detector individually, which leads to suboptimal results. To address this, this paper proposes a calibration framework based on the holistic structure of the detector ring and distance-truncated regularization constraints. The method establishes detector ring and phantom coordinate systems to formulate a composite loss function leveraging the collinearity constraint among the source focal spot, the center of a phantom sphere, and its projection point. A simplex algorithm combined with simulated annealing is employed to jointly optimize the nine parameters characterizing the spatial pose of each source-detector ring assembly. Furthermore, distance-truncated regularization with an adaptive penalty mechanism confines the distance between each source and its corresponding detector center to a reasonable range. A parameter grouping optimization strategy reduces the number of variables per projection angle from nine to six, enhancing the overall calibration efficacy. Experiments demonstrate significant improvements: on simulated data with injected noise, compared to traditional calibration methods, the proposed method achieves a 77% improvement in PSNR and a 22% improvement in SSIM. Imaging of the Catphan500 quality assurance phantom shows markedly enhanced line-pair resolution.

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This study is devoted to the design and application of algorithms based on planar CT technology. First, we propose a set of accurate calibration algorithms for the CT system, and successfully determine the position of the center of rotation, the inter-detector cell distance, and the direction of rotation of the X-rays through the processing of the projection data of the calibration plate by the least-squares fitting and the optimization of the parameters. Secondly, we applied the calibration parameters to the imaging reconstruction of unknown media and combined the Filtered Back Projection algorithm (FBP) and the Algebraic Reconstruction Technique (ART) to establish two kinds of CT back projection reconstruction models, continuous and discrete, to realize the accurate determination of the media position, geometry, and absorptivity. And meanwhile, it can provide the absorptivity information at the specified position. Further, we analyzed the accuracy and stability of the calibration algorithm and verified the performance of the algorithm under different noise conditions through simulation experiments, and the results showed that the algorithm has high accuracy and stability. Overall, this study has made significant progress in CT system calibration and imaging reconstruction, providing reliable support and guidance for the application of CT technology in medicine and engineering.

BACKGROUND: Geometry calibration for robotic CT system is necessary for obtaining acceptable images under the asynchrony of two manipulators. OBJECTIVE: We aim to evaluate the impact of different types of asynchrony on images and propose a reference-free calibration method based on a simplified geometry model. METHODS: We evaluate the impact of different types of asynchrony on images and propose a novel calibration method focused on asynchronous rotation of robotic CT. The proposed method is initialized with reconstructions under default uncalibrated geometry and uses grid sampling of estimated geometry to determine the direction of optimization. Difference between the re-projections of sampling points and the original projection is used to guide the optimization direction. Images and estimated geometry are optimized alternatively in an iteration, and it stops when the difference of residual projections is close enough, or when the maximum iteration number is reached. RESULTS: In our simulation experiments, proposed method shows better performance, with the PSNR increasing by 2%, and the SSIM increasing by 13.6% after calibration. The experiments reveal fewer artifacts and higher image quality. CONCLUSION: We find that asynchronous rotation has a more significant impact on reconstruction, and the proposed method offers a feasible solution for correcting asynchronous rotation.

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.

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Nanovision static computed tomography (CT), a novel system with a multisource X-ray array and tiled miniature detectors, promises unprecedented temporal resolution but introduces significant geometric calibration challenges due to its high-dimensional parameter space and the difficulty of constraining individual detector poses. Existing approaches rely on strong assumptions, such as high-precision phantoms and ideal circular scanning trajectories, which limit their applicability in practical engineering scenarios. To address these challenges, we propose a robust, local-to-global framework to solve this nonconvex optimization problem. The method first leverages manufacturing priors to perform a local optimization of the overall source and detector ring geometry. It then proceeds to a global stage, using an alternating optimization algorithm to precisely refine the parameters of each small detector. Experiments conducted on both simulation and clinical datasets demonstrate that our approach significantly improves calibration accuracy and subsequent image reconstruction quality. This work provides a robust and scalable calibration solution, unlocking the potential of complex, tiled-detector CT system.

The image quality of C-arm computed tomography (CT) degrades due to the nonideal projection geometry due to mechanical vibrations of the gantry during the CT scan; therefore, geometrical calibration methods need to be applied to derive the view-specific projection matrices, which are incorporated in the reconstruction processes. Previous geometrical calibration methods either require specific calibration phantoms or long computational time due to the 3-D–2-D registration process. This work begins with a theoretical derivation on how the perturbed geometrical parameters impact the projection images. It was found that with small perturbations of the view angle and the altitude angle, the relationship between the projection images under the ideal geometry and those under the perturbed geometry can be related based on a model-based 2-D deformation dependent on the perturbed geometrical parameters. Guided by the theoretical derivations, a new geometrical correction method was proposed, which generates the geometrical parameters based on 2-D–2-D registrations between the ideal projection images and the perturbed projection images. The proposed method was applied to offline and online calibration and was validated by both numerical experiments and physical experiments.

Abstract. Accurate and artifact-free reconstruction of tomographic images requires precise knowledge of the imaging system geometry. A projection matrix-based calibration method to enable C-arm inverse geometry CT (IGCT) is proposed. The method is evaluated for scanning-beam digital x-ray (SBDX), a C-arm mounted inverse geometry fluoroscopic technology. A helical configuration of fiducials is imaged at each gantry angle in a rotational acquisition. For each gantry angle, digital tomosynthesis is performed at multiple planes and a composite image analogous to a cone-beam projection is generated from the plane stack. The geometry of the C-arm, source array, and detector array is determined at each angle by constructing a parameterized three-dimensional-to-two-dimensional projection matrix that minimizes the sum-of-squared deviations between measured and projected fiducial coordinates. Simulations were used to evaluate calibration performance with translations and rotations of the source and detector. The relative root-mean-square error in a reconstruction of a numerical thorax phantom was 0.4% using the calibration method versus 7.7% without calibration. In phantom studies, reconstruction of SBDX projections using the proposed method eliminated artifacts present in noncalibrated reconstructions. The proposed IGCT calibration method reduces image artifacts when uncertainties exist in system geometry.

Conventional industrial computed tomography (CT) systems are constrained in their choice of acquisition trajectories due to their mechanical design. These systems are very precise instruments since they do only move on primarily highly accurate rotational stages. In order to be able to scan an arbitrary Region of Interest (ROI), regardless of the position, size and weight of the specimen, conventional industrial robots can be used as flexible 6 degrees of freedom (DOF) manipulators. For example in a twin robot computed tomography system, acquisition geometries with arbitrary tool poses can be realized. In scientific applications, the quality of the CT volume image is of primary interest, whereas in an industrial environment it is often a matter of balancing quality and acquisition time. Common industrial robots cannot achieve the required positional accuracy without calibration to generate an ideal reconstruction. In the presented study, methods for the geometric correction of CT scans are compared. Image based correction is compared to general machine calibration and full pose tracking by laser trackers. Image quality metrics such as the Modulation Transfer Function, Shannon entropy and Tenengrad variance are utilized to evaluate and compare the reconstruction quality of the various correction and calibration approaches. The assessment of the reconstruction quality revealed a comparable reconstruction quality between the approaches, with the machine calibration approach emerging as one of the best, while also reducing the time-intensive correction overhead.

Multi-segment static computed tomography (MS-staticCT) is a generalized and efficient configuration of static CT systems, achieving high temporal resolution imaging by sequentially firing x-ray sources, instead of rotation. However, it contains numerous geometric parameters. Due to the dense arrangement of both the x-ray sources and detectors within their respective configurations, there are some coupled illumination relationships where some x-ray sources simultaneously illuminate multiple detectors. To address these calibration challenges, we propose a geometric calibration method based on ordered subsets. We categorize two types of ordered subsets of sources and detectors: source subsets and detector subsets. Each source subset includes a group of sources that illuminate the same detectors, along with the illuminated detectors. Similarly, each detector subset includes a group of detectors illuminated by the same sources, along with the sources that illuminate them. The calibration of the sources in source subsets and the detectors in detector subsets is performed alternately until convergence, ensuring that the calibrated geometry to accurately describe all the illumination relationships. These calibration steps are detailed in a workflow. During each step, the estimations for different ordered subsets are independent and parallelizable to significantly improving computational efficiency. A calibration phantom is involved in our method. During the calibration, we iteratively estimate the parameters by minimizing the average re-projection error (aRPE) of the balls in the calibration phantom. We evaluated the proposed method by simulation and actual experiments. The aRPE was reduced to 0.0087 mm and the reconstructed images were clear without obvious misalignment in simulation. Compared to estimating all parameters together, our method improved computational efficiency by a factor of 2.20. The targeted spatial resolution (2.5 lp·mm−1) of an actual MS-staticCT system was obtained. These results verified the efficiency and accuracy of the proposed method.

BACKGROUND: Geometric calibration is essential in developing a reliable computed tomography (CT) system. It involves estimating the geometry under which the angular projections are acquired. Geometric calibration of cone beam CTs employing small area detectors, such as currently available photon counting detectors (PCDs), is challenging when using traditional-based methods due to detectors’ limited areas. OBJECTIVE: This study presented an empirical method for the geometric calibration of small area PCD-based cone beam CT systems. METHODS: Unlike the traditional methods, we developed an iterative optimization procedure to determine geometric parameters using the reconstructed images of small metal ball bearings (BBs) embedded in a custom-built phantom. An objective function incorporating the sphericities and symmetries of the embedded BBs was defined to assess performance of the reconstruction algorithm with the given initial estimated set of geometric parameters. The optimal parameter values were those which minimized the objective function. The TIGRE toolbox was employed for fast tomographic reconstruction. To evaluate the proposed method, computer simulations were carried out using various numbers of spheres placed in various locations. Furthermore, efficacy of the method was experimentally assessed using a custom-made benchtop PCD-based cone beam CT. RESULTS: Computer simulations validated the accuracy and reproducibility of the proposed method. The precise estimation of the geometric parameters of the benchtop revealed high-quality imaging in CT reconstruction of a breast phantom. Within the phantom, the cylindrical holes, fibers, and speck groups were imaged in high fidelity. The CNR analysis further revealed the quantitative improvements of the reconstruction performed with the estimated parameters using the proposed method. CONCLUSION: Apart from the computational cost, we concluded that the method was easy to implement and robust.

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The C-arm biplane imaging system, designed for cerebral angiography, detects pathologies like aneurysms using dual rotating detectors for high-precision, real-time vascular imaging. However, accuracy can be affected by source-detector trajectory deviations caused by gravitational artifacts and mechanical instabilities. This study addresses calibration challenges and suggests leveraging interventional devices with radio-opaque markers to optimize C-arm geometry. We propose an online calibration method using image-specific features derived from interventional devices like guidewires and catheters (In the remainder of this paper, the term”catheter” will refer to both catheter and guidewire). The process begins with gantry-recorded data, refined through iterative nonlinear optimization. A machine learning approach detects and segments elongated devices by identifying candidates via thresholding on a weighted sum of curvature, derivative, and high-frequency indicators. An ensemble classifier segments these regions, followed by post-processing to remove false positives, integrating vessel maps, manual correction and identification markers. An interpolation step filling gaps along the catheter. Among the optimized ensemble classifiers, the one trained on the first frames achieved the best performance, with a specificity of 99.43% and precision of 86.41%. The calibration method was evaluated on three clinical datasets and four phantom angiogram pairs, reducing the mean backprojection error from 4.11 ± 2.61 to 0.15 ± 0.01 mm. Additionally, 3D accuracy analysis showed an average root mean square error of 3.47% relative to the true marker distance. This study explores using interventional tools with radio-opaque markers for C-arm self-calibration. The proposed method significantly reduces 2D backprojection error and 3D RMSE, enabling accurate 3D vascular reconstruction.

Industrial measurements increasingly employ a redundant robotic system with an external turntable due to its efficiency, flexibility, and automation advantages. However, the actual viewpoint pose reached by the robotic system deviates from its simulated design pose due to orientation errors, resulting in poor measurement quality of complex surfaces. Geometry calibration is necessary for reducing robot orientation errors. However, most calibration methods ignore the factors of multiple error coupling and robotic absolute positioning error propagation, ultimately affecting calibration accuracy. In order to resolve this problem, this article proposes a robust self-calibration method for the simultaneous identification of geometric pose parameters. First, considering the overall synchronized control of orientation errors, a comprehensive error transfer model is derived as the theoretical basis. Then, the error model receives the system orientation errors as input, which are detected from a multiview visual measurement process on a calibration panel. Finally, the error model is solved using a self-adaptive Levenberg–Marquardt (SALM) algorithm, and the identified error vectors are used for online compensation of the kinematic model, improving the orientation accuracy of the robotic system. Simulations and experiments verify the accuracy and robustness of the proposed method. The experiment results show that the root mean square error (RMSE) detection deviation of the measuring point cloud compensated by self-calibration is reduced by 96.9% from 2.215 to 0.068 mm compared with before calibration. This self-calibration method is simple, economical, and general and can be further extended to other multiaxis automation systems.