Center of rotation automatic measurement for fan-beam CT system based on sinogram image features
Introduction
Projection center of rotation (COR) is one of the important parameters for fan-beam CT system to guarantee the accuracy of the image reconstruction. And it should be strictly controlled with high precision, because the fan-beam reconstruction algorithms are derived on the basis of the assumption that the projection center of rotation is collinear with the midline of the fan-beam [1], [2]. However, during the testing process, whether the usage of laboratory-built industrial CT systems or those commercially available CT systems, the tested object between the X-ray focus and the detector must be frequently moved to obtain the optimal imaging position and magnification, even sometimes the tested object is moved along the direction perpendicular to the midline of the fan-beam according to large field of view (LFOV) reconstruction algorithm [3], [4]. The COR is obliged to be calibrated before every CT scan, otherwise, serious artifacts would be introduced. Previous studies indicated that the reconstructed images were very sensitive to the errors of COR, for example, a small deviation of 0.4 pixels from COR would cause severe artifacts in the reconstructed images [5].
In previous researches, several kinds of methods for determining COR have been extensively used, such as the center-of-sinogram method, the geometrical method, the iterative method and the opposite-angle method [6], [7], [8], [9], [10]. In the center-of-sinogram method, two projections which are 180° opposite to each other are used, and the midpoint of the two projected feature locations on the detector is an estimate of the COR. This method is based on the assumption that the line connecting the X-ray focus and the COR is perpendicular to the detector. But the assumption is not always true, and during the calibration a specific straight metal wire is always required. The geometry method is the improvement of the center-of-sinogram method, which permits the line connecting the X-ray focus and the COR not to be perpendicular to the detector, while, the projected location of the central ray and the distance from X-ray focus to the detector need to be exactly calculated. The iterative reconstruction algorithm starting from the reconstructed image with errors of COR is employed in the iterative method. And the iterating times is controlled by the optimal criterion until getting the best image quality. Due to time-consuming of this method, it is seldom adopted in practice. The opposite-angle method is based on the fact that among all the 180° opposite angle projection pairs, only the ray passing the COR projects the same location on the detector in 0° and 180°. Recently, LI proposed a method to seek the projected location of the ray passing the COR by using the opposite angle projection pairs [11]. But his algorithm will introduce large error when the sample is a circular shape.
In this paper, we propose a novel method to determine the COR for fan-beam CT system based on image cross correlation. Only the sinogram of the scanned slice is used for locating COR based on the image cross correlation without the calibration phantom in our developed method. Due to the image cross correlation operation and the unique coordinate of the peak value, it can be implemented with a good ability of anti-noise. In the following sections, the theory of the novel method based on image cross correlation is outlined and our experimental results are presented. In Section 3, anti-noise ability and accuracy analysis by computer simulation is studied to investigate the detailed information of COR effectively. In Section 4, to verify the feasibility and accuracy of the proposed method, the experiments are performed in a 2D CT system and then some experimental results are shown. Section 5 is devoted to conclusion.
Section snippets
Method based on image cross correlation
The scanning principle of fan-beam 2D CT system with linear detector array (LDA) is shown in Fig. 1. The X-ray focus is point F, the coordinate system of the scanned slice is XOY and the point O is the COR. Midline of the fan-beam(SO) passes COR and is perpendicular to the LDA. is the coordinate system of LDA where the coordinate of COR is . The X-ray source and the detector remain stationary with respect to each other while the object rotates around the fixed center (point O) within
Anti-noise ability and accuracy analysis by computer simulation
According to the characteristic of cross correlation function, all the data in and are used to calculate the position of the peak value, so the errors caused by the noise in the projection data can be neglected in most cases. In addition, from Step 2, is obtained by averaging the original sonogram along the direction of column, which further decreases the affection of the random noise. To support the ratiocination, the noised sinogram of Shepp–Logan phantom is
Experimental results
To verify the feasibility and accuracy of the proposed method, we performed experiments in a 2D CT system. The experimental conditions were set as
X-ray energy: 220 kV, 5 mA
LDA unit size: 0.4 mm
Total detector units: 1600
Distance from X-ray focus to LDA: 1200 mm
Total number of the projections: 1800 frames
Under the above situations, the special resolution target was scanned and the original fan-beam sinogram was created as shown in Fig. 3. Fig. 4 is the curve plot of . It is apparent that
Conclusion
In this work, we have successfully developed a novel method to determine the location of COR in 2D CT system. Compared with the conventional calibration methods, only the sinogram of the scanned slice is used for locating COR based on the image cross correlation without the calibration phantom in our proposed method. Because the image cross correlation operation is adopted, and the coordinate of the peak value is unique according to the characteristic of cross correlation function, it is easy
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grants 11275019, 21106158 and 61077011, in part by the National State Key Laboratory of Multiphase Complex Systems under Grant MPCS-2011-D-03, in part by the National Key Technology R&D Program of China under Grant 2011BAI02B02, in part by the Beijing Municipal Commission of Education (BMCE) under the joint-building project. This work was also supported in part by the National Research Foundation of
Min Yang received Ph.D. degree from School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics (BUAA) in 2004. He is currently an associate professor in BUAA. His research interests mainly include multi-dimensional information reconstruction and recognition, X-ray digital radiography, CT theory and application.
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Min Yang received Ph.D. degree from School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics (BUAA) in 2004. He is currently an associate professor in BUAA. His research interests mainly include multi-dimensional information reconstruction and recognition, X-ray digital radiography, CT theory and application.
Jing Pan received the B.S. degree in Mechanical Engineering from the North China Institute of Technology (now North University of China), Taiyuan, China, in 2002, and the M.S. degree in Precision Instrument & Mechanism from University of Science and Technology of China, Hefei, China, in 2007. She is currently a Lecturer with the School of Electronic Engineering, Tianjin University of Technology and Education, Tianjin, China. Her research interests include computer vision and pattern recognition.
Jianhai Zhang is a Ph.D. student in Mechanical Engineering from Sungkyunkwan University, Seoul, Korea. His currently research interests include electromagnetic testing and non-destructive evaluation methods.
Sung-Jin Song received a B.S. degree in Mechanical Engineering from Seoul National University, Seoul, Korea in 1981, a M.S. degree in Mechanical Engineering from Korea Advanced Institute of Science and Technology in 1983, and a Ph.D. in Engineering Mechanics from Iowa State University, Ames, Iowa, USA in 1991. He has worked at Daewoo Heavy Industries, Ltd., Inchoen, Korea for 5 years from 1983, where he has been certified as ASNT Level III in RT, UT, MT and PT. He has worked at Chosun University, Gwangju, Korea as Assistant Professor for 5 years from 1993. Since 1998 he has been at Sungkyunkwan University, Suwon, Korea and is currently Professor of Mechanical Engineering. His research interests include non-destructive testing and evaluation theory and applications.
Fanyong Meng received Ph.D. degree from Institute of Process Engineering, Chinese Academy of Science in 2009. He is currently an assistant research fellow at State Key Laboratory of Multiphase Complex Systems. His technical researches are mainly about CT application in gas–solid flow, X-ray digital radiography, and measurement in particle fluid system.
Xingdong Li is currently a research fellow in National Institute of Metrology. He is the secretary-general of Chinese Society for Stereology. His research interests mainly focus on imaging and measurement in nuclear medicine.
Dongbo Wei is currently a professor in Beijing University of Aeronautics and Astronautics. His research interests mainly focus on CT theory and application, imaging and measurement in nuclear medicine.