Reference-free calibration method for asynchronous rotation in robotic CT

Abstract

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.

Keywords

Robotic CT reference-free geometry calibration

1 Introduction

With the development of X-ray imaging technology, numerous innovative computed tomography devices with unique geometries have been developed to meet the diverse requirements of various imaging situations. Such as the C-arm equipment used during surgery [2 , 18]. Robotic CT is a novel imaging platform based on two manipulators. The high flexibility of manipulators enables robotic CT to scan various samples along arbitrary trajectories. However, poor mechanical precision of manipulators can lead to deviations from the scheduled trajectory during data acquisition. Therefore, performing geometry calibration to obtain accurate geometry information is crucial for producing high-quality images.

Researchers have developed various calibration methods for estimating CT geometry. The calibration methods for robotic CT are based on calibration methods of traditional CT and can be roughly divided into two types according to whether a reference object is used in the calibration, which are reference-relied and reference-free calibration methods. The first method is based on well-designed calibration phantoms [15] or objects with specific markers [5, 21]. The coordinates of precise markers and their corresponding projection points are utilized to estimate geometry information [12]. It can be used for both offline and online calibration processes. Some studies [23] are based on the simultaneous calibration of phantom and reconstruction images, or implement a self-calibration [6] first to obtain precise coordinates of the phantom. The reference-free calibration method [4] typically utilizes information from the projections of scanned objects to alternately optimize the reconstructed image and the geometry definition. Therefore, it’s basically an online calibration method.

The geometry deviation that occurs in a typical CT system is usually constant within different scanning tasks. In the calibration of such a stable system, an offline calibration can be performed first to obtain correct the geometry definition, and the reconstruction can be performed under the geometry estimated by the reference object. However, the deviation in different scanning tasks varies for robotic CT systems, making offline calibration impractical. Furthermore, online calibration using a reference object occupies part of the projection area to gather sufficient information for geometry estimation, thereby reducing the reconstruction volume. Therefore, reference-free methods are practical for estimating the geometry of robotic CT. There are already some reference-free calibration methods [10, 16] in the typical CT system. Kyriakou et al. [11] defined the structure of the circular cone-beam CT using eight parameters and simultaneously calibrated them. Panetta et al. [19] developed a cost function using projection data depending on the misalignment parameters.

However, the deviation of robotic CT within different projection angles is unique, and this characteristic will result in a significantly increased number of parameters needed to express the complete geometry compared with a typical CT system. Due to the large number of parameters involved in defining the scanning geometry, reference-free calibration for robotic CT is quite challenging to solve [3]. Li et al. [13] proposed an LLE-based reference-free calibration for the robot-based CT system defined on nine degrees of freedom within each projection angle. They achieved good results in practice. But performing calibration on all geometry parameters will increase computation. It’s obvious that not all types of deviation occurring in the robotic CT system have the same impact on image quality. These various types of deviation can be primarily categorized as position deviation and asynchronous rotation, based on the causes of the deviation. Inspired by the simplified number of parameters used in calibrating a typical CT system [25], we believe that a comparison should be performed first to evaluate the impact of different types of deviations on image quality. This will help in selecting the parameter with greater influence for a simplified model, which can reduce the complexity and stabilize the solution process.

In this work, we first analyzed the impact of different deviation types existed in robotic CT equipment on reconstruction images. Then, we proposed a novel reference-free calibration method aimed at the asynchronous rotation of a robotic CT system. Last, we tested the proposed calibration with two sets of simulation phantoms as well as an experiment on a real phantom.

2 Material and methods

Typically, the reconstruction of CT images in robotic CT can be expressed as: $\begin{matrix} X = argmin ∥ AX - P_{devia} ∥_{2}^{2} \end{matrix}$ (1) where X, A, and P_devia are reconstruction images, system matrix, and projections under deviated geometry, respectively. The reference-free calibration can be expressed as:

$\begin{matrix} [X, A] = argmin ∥ AX - P_{devia} ∥_{2}^{2} \end{matrix}$ (2) where X and A are both variables to be solved. This problem can be solved using the idea of alternatively optimizing the system matrix and reconstruction images. Previous research has shown the visibility of alternative optimization. The geometry definition within each projection angle is independent, and the system matrix A in each projection angle can be defined with nine parameters in each projection angle, which is: $\begin{matrix} A = [S, D, R] \end{matrix}$ (3) where S, D, R are three vectors which stand for the coordinates of source, coordinates of detector center, and the three rotation angles of the detector. Considering independence between projection angles, the number of parameters to be solved will be very large. Under this situation, Equation 2 will become a highly underdetermined equations, which makes it hard to find the solution.

Actually, the deviation existed in robotic CT systems is mainly brought by limited mechanical accuracy as well as the delay in the movement of manipulators, which stand for the deviated motion as well as deviated rotation. Considering the feature of manipulators, the deviated system matrix A is simplified as a combination of the default circular trajectory A_cir and deviation brought by errors of manipulators, which is: $\begin{matrix} A = A_{cir} + Δ A (Δ α, Δ C) \end{matrix}$ (4) where ΔA (Δα, ΔC) stands for the deviation in system matrix brought by deviated rotation angle Δα and deviated motion ΔC. Inspired by the idea of local linear embedding, a grid of unsolved parameters is introduced in each iteration process. A series of new geometry based on default geometry is established, using geometry parameters provided by grid point. Re-projection images are generated using new geometry definitions, and difference between re-projection and original projection guides the direction of optimization of parameters. The optimization of the k^th iteration can be expressedas: $\begin{matrix} k \to k + 1 : X_{k + 1} = argmin ∥ \sum_{m = 1}^{η} W (A_{km} X_{k} - P_{devia}) \cdot A_{km} X - P_{devia} ∥_{2}^{2} \end{matrix}$ (5) where k represents the number of iterations, and m represents the index of grid point. A_km is the re-projection system matrix under the m^th grid point of the k^th iteration, which consists of the system matrix of the k^th iteration A_k and the adjustment of system matrix ΔA_km defined by the m^th grid point. $\begin{matrix} A_{km} = A_{k} + Δ A_{km} \end{matrix}$ (6)

In Equation 5, η is the hyperparameter that controls the step length. W (A_kmX_k - P_devia) is a weighting function based on the difference between re-projection images A_kmX_k and gathered deviated projection P_devia. The weights function offers weights for each grid points. In this paper, we choose the weight of the nearest point as 1 and weights of other as 0. In the iteration, geometry and reconstruction images are optimized alternatively. The range of estimated geometry is adjusted as the number of iterations increases, according to the step range hyperparameter, which is expressed as: $\begin{matrix} Δ A_{k + 1} = δ_{k} \cdot A_{k} (δ_{k} \in (0, 1)) \end{matrix}$ (7) where δ_k is a hyperparameter which controls the step range in each iteration, and ΔA_k, ΔA_k+1 represent the range of estimated geometry in the k^th and (k + 1) ^th iteration. In this work, a reference-free calibration focused on the deviation of rotation angle is proposed. Flowchart of the algorithm is shown in Fig. 1.

Fig. 1

Flowchart of proposed reference-free calibration method.

3 Results

3.1 3.A Comparison of motion-asynchronism and angle-asynchronism

We first compare the impact of motion asynchronism and asynchronous rotation on image quality. Detail deviation values are shown in Table 1. Detail projection parameters are shown in Table 2. Two types of deviations are simulated under the same geometry. A digital chicken phantom is used in the simulation. As expressed in Equation 4, deviation in rotation angle Δα and motion ΔC are separately simulated to observe the degradation of image quality. The default geometry definition is a typical circular geometry defined using parameters shown in Table 2. Deviation in motion is simulated by adding random jitter into the three coordinated axes of the position of source and detector. As shown in Table 1, a gaussian random deviation is added into each coordination of the source and detector. The generation of rotation deviation is simulated referring to measure data from actual equipment. The deviation of the rotation angle consists of accumulated error as well as random error in each projection angle, which is:

Table 1
Deviation in simulation experiment

Deviation types Value

Motion-asynchronism N(0, 0.5) (mm)

Angle-asynchronism $\frac{0 . 5^{\circ} \cdot (p - 1)}{projnum} + N (0, \frac{0 . 5^{\circ}}{projnum})$

Deviation types	Value
Motion-asynchronism	N(0, 0.5) (mm)
Angle-asynchronism	$\frac{0 . 5^{\circ} \cdot (p - 1)}{projnum} + N (0, \frac{0 . 5^{\circ}}{projnum})$

Table 2

Geometry definition in simulation and experiment

Parameters	Value
Geometry	SDD: 810 mm
	SOD: 540 mm
	Projnum: 660
	RotationAngle: 220°
Detector	Size: 536
	Pixel size: 0.8 mm
Image	Size: 536
	Voxel size: 0.3 mm

$\begin{matrix} Δ α_{p} = (p - 1) \cdot Δ β + Δ γ \end{matrix}$ (8) where Δβ and Δγ stand for the accumulated error and random error, respectively. And Δα_p is the deviation of rotation angle in the p^th projection.

Figure 2 illustrates the comparison of the impact of different deviations on images. It could be seen that both types of deviation would degrade the image quality. However, the artifacts brought by motion deviation were more like image blur artifacts. While observing Fig. 2(a), asynchronous rotation during scanning will result in incorrect image structures, as shown in the top left corner of the figure. Besides, when considering the image evaluation index, we could find that the evaluation index of (a) reduces by 9.4% compared to images with default uncalibrated geometry, while the index of (b) reduces by 3.8%. Besides, we conducted multiple simulations with a specific number of repetitions to compare the influence of different types of deviations on the reconstruction images in multiple simulation experiments. Results were shown in Table 3. We found that degradation caused by asynchronous rotation is server than the degradation caused by motion deviation. Therefore, we tested the proposed reference-free calibration method on asynchronous rotation.

Fig. 2

Comparison of image degradation under different deviation types. (a) is the digital phantom. (b), (c) and (d) are reconstruction images under angle, motion geometry error and no geometry error.

Table 3

Image evaluation indexes in simulation experiment

Types	PSNR	SSIM	Reduction_P	Reduction_S
Motion	34.37±5.1e-3	0.7772±4.3e-6	3.85%	7.29%
Angle	29.62 ± 2.1e-7	0.7620 ± 1.4e-10	9.32%	9.57%
No Error	36.36±2.2e-8	0.8502±6.6e-12	—	—

3.2 3.B Simulation of asynchronous rotation in single rotation angle

The projection geometry parameters were the same with Table 2. We first tested the performance of the proposed method under the calibration of single-angle rotation asynchrony. The deviation in rotation angle was generated using the parameters shown in Table 1. Images of the proposed method and reconstruction with default geometry are shown in Fig. 3(c) and 3(b). We found that most artifacts brought by deviations in the rotation angle could be calibrated by the proposed method. The evaluation indexes after calibration was obviously improved. However, when we looked at the regions as the enlarged image on the coronal view showed, we could find certain distortion. Compared to uncalibrated images, these regions showed obvious improved image quality. While compared with standard digital phantom, these regions still didn’t have the same quality as standard images. This showed limited calibration ability for complex object. Besides, when looking at the deviation images, we could find that the reconstruction center of the proposed calibration method was not consistent with the originalcenter.

Fig. 3

Simulation results of chicken digital phantom under deviation in single rotation angle. (a) is the digital phantom. (b), (c) are reconstruction results with default geometry parameters and results after proposed calibration method. (images are shown in [0,1]).

3.3 3.C Simulation of asynchronous rotation in single rotation angle with large deviation of orbits

In a real situation, there may exist large deviation of orbits. In order to verify the visibility of the proposed method under large deviation of orbits, a simulation on digital chicken phantom was conducted.

In reconstruction images, similar results with the one under usual mentioned deviation of orbits were found. Reconstruction images were shown in the Fig. 4. Golden standard of digital phantom, reconstructions under default geometry, and images with the proposed calibration method were shown in (a), (b), and (c), respectively. For image evaluation indexes, a mean value of the whole reconstructed volume was shown in the results. Proposed results also showed good performance under unusual deviation of orbits.

Fig. 4

Simulation results of chicken digital phantom under large deviation in single rotation angle. (a) is the digital phantom. (b), (c) are reconstruction results with default uncalibrated geometry and results after proposed calibration method. (images are shown in [0,1]).

In Fig. 5, the real deviation of rotation angle used in simulation as well as the difference between real deviation and the deviation after calibrated was plotted. As the blue line showed, large deviation of rotation angle in the 100th, 200th, 300th, 400th, and 500th projection number was added to evaluate the effect of large deviation of orbit on proposed reference-free method. The gray line represented the difference between real deviated geometry and calibrated geometry, which was obtained by subtracting the true geometry from the calibrated geometry. As it was shown in Fig. 5, the value of difference deviation within all projection angles stays constant, which indicates that proposed reference-free calibration was not affected by large deviation in orbits.

Fig. 5

Deviation in rotation angle. Blue line shows the deviation used in simulation. Gray line indicates difference between calibrated deviation and real deviation.

3.4 3.D Simulation of asynchronous rotation in double rotation angle

Besides, it was hard to find a similar model with a deviation in a single rotation angle during real scanning. Therefore, we tested the calibration with a deviation of two rotation angles. The deviation of the rotation angle was generated using the same pattern as introduced in section C. The accumulated errors of the detector and the source were set to be 0.5° and 1°, respectively. We tested the performance with a single cylinder phantom. The phantom was made of several standard hollow cylinders within a larger cylinder. Reconstruction images and the difference images in the simulation were shown in Fig. 5(a). We could observe significant geometric artifacts around the edges of the hollow cylinders in the original reconstruction images. The reconstruction images of the proposed calibration method showed sharp edges. Besides, we could find obvious deviation of the reconstruction center both in the original reconstruction images and the calibrated images, and the deviation of reconstruction center within the original images and calibrated images stays constant. We also plotted the details of the images in Fig. 6(b). Images of the proposed method showed sharper edges compared to uncalibrated images. Same issues were also observed in the plot details as the arrow showed. Although the reconstruction of the proposed method didn’t show obvious artifacts, the difference images showed any different reconstruction center with digital phantom, which means the calibrated geometry is not consistent with real deviated geometry.

Fig. 6

Simulation results of cylinder digital phantom under deviation in double rotation angles. (a) shows reconstruction images and the difference images. (b) shows the plot details. (images are shown in [0,1], difference images are shown in [–1,1]).

Furthermore, the proposed method selected the RMS between re-projection images and original projections to determine the direction of optimization. Therefore, it was necessary to evaluate the performance of the proposed method on different objects. We conducted an additional calibration simulation test using a more complicated chicken phantom. Results were depicted inFig. 7.

Fig. 7

Simulation results of chicken digital phantom under deviation in double rotation angle. (a) is the digital phantom. (b), (c) are reconstruction results with default uncalibrated geometry and results after proposed calibration method. (images are shown in [0,1]).

The image of the proposed calibration method was shown in Fig. 7(c). We found that the artifacts in Fig. 7(b) were more pronounced than that under deviation in a single rotation angle. In addition, the proposed calibration method demonstrated superior image recovery capability compared to the original images.

3.5 3.E Performance on real phantom scan data

We also tested the performance of the proposed method on real data. The geometry of the real data was the same as the parameters shown in Table 2, except for the number of projections, which was 550 over 220°. The results were shown in Fig. 8. We found artifacts around the edge of the hollow cylinder in the original images, where the arrow pointed at. After calibration, the mentioned artifacts were obviously removed. However, geometric distortion was observed in the images of proposed method, where the tomography of the hollow cylinder was obviously not round.

Fig. 8

Reconstruction of real cylinder phantom. (a) and (b) are reconstruction under default geometry and calibrated geometry with proposed method. (images are shown in [0, 0.022]).

This could reveal the intricate deviation in a real situation, and simply calibrate the deviation within the rotation angle without considering deviations brought by other types of deviation would introduce artifacts into reconstruction images as well as the calibration process. Besides, the most obvious artifacts that existed in the original reconstruction images were consistent with the artifacts that appeared in the simulation. And this kind of artifacts brought by the deviation of asynchronous rotation can be calibrated by proposed method.

Besides, direct evaluation of image quality alone was not sufficient for illustrating the feasibility of the proposed method, an MTF analysis based on a line-pair phantom was conducted. The geometry definition was the same as the one shown in Table 2, except for the number of projections as 660. Reconstruction images of the line-pair phantom are shown on the left side of Fig. 9(A) and (B) stand for the reconstruction under default geometry and calibrated geometry. Four line-pairs with different sizes were selected to define the MTF curve. Bicubic spline interpolation was used to get the smooth curve. The MTF result was shown in the right side. As we can see, the proposed geometry calibration improved the performance of the system. However, the precision of the proposed calibration method was limited, small artifacts could also be observed in the reconstruction images, which was the same with the phenomenon within Fig. 7.

Fig. 9

Results of MTF analysis. (a) and (b) are reconstruction under default geometry and calibrated geometry with proposed method. Red and blue lines represent images using default geometry and calibrated geometry. (images are shown in[0, 0.04]).

4 Discussions and conclusions

This study first compared the impact of two different types of deviations on reconstruction images by simulating reconstructions under different types of deviated geometry. The asynchronous rotation showed heavier image degradation compared with jitter during the motion of manipulators. Considering the geometry defined in the calibration of a typical CT system [9, 24], it’s evident that focusing on a few parameters will simplify the requirements for the calibration process as well as make the solving easier. For the calibration of a robotic CT system, it’s basically an underdetermined problem. Expressing the scanning geometry of robotic CT, nine independent parameters within every projection angle need to be calibrated, which is obviously unsolvable without enough reference information. Reducing the number of parameters could focus on a major problem existed in the scanningsystem.

The proposed calibration has showed obvious improvement in image quality for both calibration of single rotation angle dual rotation angles, which indicates that the gradient of projection images stands for the gradient of geometry parameters to a certain extent. As we know, the function between geometry parameters and projection images is basically a non-convex function, so it’s hard to optimize the function directly. Referring to the idea of local linear embedding [20, 27], we think sampling enough points in the parameter space of this function can provide estimation of projection images and estimate the direction to adjust the parameters.

Besides, the performance of the proposed calibration method under objects with different complexity are also evaluated. For objects with rich detail information as well as complex structures, the function between projection and geometry parameters is more complex and harder to be estimated. For complex objects, although the overall structure can be corrected, there are still be some small artifacts in the detail structures, and the projection information of complex objects is more complex. The same problem was also reported in some reference-free calibration methods of a typical CT system. Von et al. [22] used single point object to calculate the reprojection error in 2004. Ouadah et al. [17] adopted a bearings phantom to perform nine-freedom calibration.

In this study, the mean square error of the difference between re-projection images and real projection images is selected as the objective function, so change in the objective function is more complex for structurally rich objects. The direction of gradient between the objective function and geometry parameters may not be exactly the same, so we can opt for a denser grid of points for parameters sampling, so as to obtain more accurate results. For simpler objects, we find that the image can be easily corrected, and there are no obvious artifacts in the final corrected image. Therefore, we should consider adding other parameters to the objective function to jointly monitor the gradient change direction of the corrected parameters. The gradient direction of the geometric parameters determined when the two objectives are subtracted at the same time may be more accurate than the gradient direction obtained by using only projection.

However, we can still find that in the difference image, there is a certain deviation between the reconstruction center of the image corrected by the proposed method and that of the standard image, which indicates that the corrected geometry is not exactly the same as the real deviation geometry. However, the projected gap between the two geometries is small, or the gap between the reconstructed images is small. This shows that the reconstructed image differences obtained under several conditions of geometric deviation are relatively close. The calibrated geometric obtained by the proposed method may not be consistent with the real scanning geometry. Same problem was also reported by other reference-free calibration methods [1, 14].

In our actual experiment, we found that ignoring other parameters in the actual device will cause the correction process to be affected to a certain extent, but the major artifacts in the original image can be effectively corrected.

In general, we compared different types of deviation in robotic CT and found that asynchronous rotation appears to have a greater impact on the reconstruction images. We proposed a reference-free calibration method based on an alternative calibration of the reconstruction images and the geometry definition, which focused on the calibration of asynchronous rotation. The proposed method had got good results in both simulation and experiment data. But the calibrated geometry could not be granted to be the same with actual deviated geometry, although the geometry artifacts inside images were eliminated. Besides, proposed method used deviation information between projection images and real projection images to get the direction of optimization, which was not practical for complex objects. Adding other constrains in image region [8] or using deep neural networks to get novel guide information [26] may help to get more robust results.

Footnotes

Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No. 11975250 and 12175267.

References

Berger

, Müller

, Aichert

, Unberath

, Thies

, Choi

, Fahrig

and Maier

, Marker-free motion correction in weight-bearing cone-beam CT of the knee joint, Medical Physics 43 (2016), 1235–1248.

Bracken

, Kim

, Messenger

, Cleveland

, Fullerton

, Eshuis

, Grass

and Carroll

, TCT-666 Short-roll C-arm computed tomography (C-arm CT) scans to guide transcatheter aortic valve replacements, Journal of the American College of Cardiology 64 (2014), B194.

Chen

, He

, Feng

, Liu

, Yang

, Wei

and Wang

General rigid motion correction for computed tomography imaging based on locally linear embedding, Optical Engineering 57 (2018), 023102.

Chen

, Xi

, Cong

, Liu

, Wei

and Wang

X-ray CT geometrical calibration via locally linear embedding, J Xray Sci Technol 24 (2016), 142–256.

Cho

, Moseley

, Siewerdsen

and Jaffray

Accurate technique for complete geometric calibration of cone-beam computed tomography systems, Medical Physics 32 (2005), 968–983.

Duan

, Cai

, Ling

, Huang

, Qi

, Chen

, Zhou

and Xu

, Knowledge-based self-calibration method of calibration phantom by and for accurate robot-based CT imaging systems, Knowledge-Based Systems 229 (2021).

Girard

, AI-Ahmad

, Rosenberg

, Luong

, Moore

, Lauritsch

, Boese

and Fahrig

, Contrast-enhanced C-Arm CT evaluation of radiofrequency ablation lesions in the left ventricle, JACC: Cardiovascular Imaging 4 (2011), 259–268.

Gong

, Zeng

and Wang

, Image reconstruction model for limited-angle CT based on prior image induced relative total variation, Applied Mathematical Modelling 74 (2019), 586–605.

Gross

, Heil

, Schulze

, Schoemer

and Schwanecke

, Auto calibration of a cone-beam-CT, Medical Physics 39 (2012), 5959–5970.

10.

Kingston

, Sakellariou

, Varslot

, Myers

and Sheppard

, Reliable automatic alignment of tomographic projection data by passive auto-focus, Medical Physics 38 (2011), 4934–4945.

11.

Kyriakou

, Lapp

, Hillebrand

, Ertel

and Kalender

, Simultaneous misalignment correction for approximate circular cone-beam computed tomography, Physics in Medicine and Biology 53 (2008), 6267–6289.

12.

, Luo

, You

, Getzin

, Zheng

, Wang

and Gu

, An nonlinear optimization using circular rotation trajectory for CBCT systems, the object function is the backprojection devia of points between the many backprojections and their mean value, Medical Physics 46 (2018), 152–164.

13.

, Lowe

, Butler

and Wang

, Motion correction via locally linear embedding for helical photon-counting ct, The 7th Int Conf on Image Formation in X-Ray Computed Tomography, 2022.

14.

, Bohacova

, Uher

, Cong

, Rubinstein

and Wang

, Motion correction for robot-based x-ray photon-counting CT at ultrahigh resolution, SPIE Optical Engineering + Applications 12242 (2022).

15.

, Zhang

and Liu

, A generic geometric calibration method for tomographic imaging systems with flat-panel detectors - A detailed implementation guide, Medical Physics 37 (2010), 3844–3854.

16.

Meng

, Gong

and Yang

, Online geometric calibration of cone-beam computed tomography for arbitrary imaging objects, IEEE Transactions on Medical Imaging 32 (2013), 278–288.

17.

Ouadah

, Stayman

, Gang

, Ehtiati

and Siewerdsen

Self-calibration of cone-beam CT geometry using 3D-2D image registration, Physics in Medical and Biology 61 (2016), 2613–2632.

18.

Park

, Goo

, Lee

and Kim

C-arm cone-beam CT-guided percutaneous transthoracic needle biopsy of small (20mm or Smaller) lung nodules, Chest 138, 237A.

19.

Panetta

, Belcari

, Del

, Moehrs

An optimization-based method for geometrical calibration in cone-beam CT without dedicated phantoms, Physics in Medicine and Biology 53 (2008), 3841.

20.

Roweis

and Saul

, Nonlinear dimensionality reduction by locally linear embedding, Science 290 (2000), 2323–2326.

21.

Sun

, Hou

, Zhao

and Hu

A calibration method for misaligned scanner geometry in cone-beam computed tomography, NDT & E International 39 (2006), 499–513.

22.

Von

, Kachelriess

, Stepina

and Kalender

, Geometric misalignment and calibration in cone-beam tomography, Medical Physics 31 (2004), 3242–3266.

23.

, Yang

, Ma

, Li

, Wu

, Qi

and Zhou

Simultaneous calibration phantom commission and geometry calibration in cone beam CT, Physics in Medicine and Biology 62 (2017), 375–390.

24.

Zechner

, Stock

, Kellner

, Ziegler

, Keuschnigg

, Huber

, Mayer

, Sedlmayer

, Deutschmann

and Steininger

Development and first use of a novel cylindrical ball bearing phantom for 9-DOF geometric calibrations of flat panel imaging devices used in image-guided ion beam therapy, Physics in Medicine and Biology 61 (2016), 592–605.

25.

Zhang

, Du

, Jiang

, Li

, Guang

and Yan

, Iterative geometric calibration in circular cone-beam computed tomography, Optik 125 (2014), 2509–2514.

26.

Zhao

, Pang

, Chen

, Zhu

, Jiang

, Su

and Lu

, Zhou and Q. Feng, SpineRegNet: Spine Registration Network for volumetric MR and CT image by the joint estimation of an affine-elastic deformation field, Medical Image Analysis 86 (2023), 102786.

27.

Zhao

and Zhang

, Supervised locally linear embedding with probability-based distance for classification, Computers & Mathematics with Applications 57 (2009), 919–926.

Reference-free calibration method for asynchronous rotation in robotic CT

Abstract

BACKGROUND:

OBJECTIVE:

METHODS:

RESULTS:

CONCLUSION:

Keywords

1 Introduction

2 Material and methods

3.1 3.A Comparison of motion-asynchronism and angle-asynchronism

Table 1 Deviation in simulation experiment Deviation types Value Motion-asynchronism N(0, 0.5) (mm) Angle-asynchronism 0 . 5 ∘ · ( p - 1 ) projnum + N ( 0 , 0 . 5 ∘ projnum )

Footnotes

Acknowledgments

References

Table 1
Deviation in simulation experiment

Deviation types Value

Motion-asynchronism N(0, 0.5) (mm)

Angle-asynchronism $\frac{0 . 5^{\circ} \cdot (p - 1)}{projnum} + N (0, \frac{0 . 5^{\circ}}{projnum})$