# Calibration Method of Projectional Geometry for X-ray C-arm Fluoroscopy Using Sinogram Data
## 1 Introduction  
Radiation-based imaging has played an important role in the development of medical technology. After [PERSON] discovered X-rays in the 19 th century, researchers were given insight into the internal structure of the human body. The development of two-dimensional (2D) radiographic imaging has provided clues about the unique structures of the human body, and three-dimensional (3D) computed tomography (CT) has provided tools for non-invasively observing the interior of the human body in 3D form. This development has significantly contributed to the advancement of medical diagnostic skills. Image-guided surgery uses medical imaging technology to develop diagnostic and interventional technologies [1]. Radiographic imaging is one of the most commonly used imaging modalities for image-guided surgery, providing physicians with live positional information. As such, it plays an important role in the accuracy and safety of the operation [2]. Importantly, image data distortion must be minimized to ensure the accuracy of image-guided surgery, which necessitates accurate knowledge of the geometric information corresponding to the imaged volume and the development of an image-guided surgical system. Vascular intervention using angiographic imaging represents one of the clinical applications of the image-guided approach. In this procedure, a catheter is inserted into the patient's body and fed in the desired direction [3]. When the catheter reaches its destination, it can be maneuvered to remove sediment from the vessel or insert a mesh-type structure to widen the narrowed vessel, or even inject therapeutic drugs. The medical staff can track the catheter's location during these procedures using 2D radiographic imaging, and 3D Cone-Beam CT (CBCT) is only used as an auxiliary means of helping determine andguide the catheter location. This necessitates the development of techniques for intuitively determining the 3D location of the catheter using the spatial relationship between 3D CBCT data and 2D radiographs taken repeatedly during the procedures. There are some existing approaches to estimating the 3D position of the catheter by utilizing the image registration techniques of 2D radiographic imaging and 3D CBCT data. Calculating the precise location of the catheter necessitates precise calibration of the projectional geometry of the radiographic imaging device, which is essential for the implementation of 2D and 3D image registration techniques. Therefore, previous studies have been conducted to accurately calculate the geometric information of the imaging device and improves the accuracy of the registration between the 2D and 3D CT images based on this information. Consequently, the findings of this study contribute to the advancement of this work by improving the accuracy and stability of image-guided surgery. The accuracy of the geometric parameters of the imaging device that acquires the image data influences the accuracy of registration between the 2D radiographic image and the 3D CT data. Image registration with inaccurate geometric parameters cannot guarantee high accuracy, which negatively impacts the accuracy and stability of image-guided surgery. Therefore, several groups are also interested in improving the calibration accuracy of the projectional geometry of the imaging device to improve the accuracy of the registration and ultimately guarantee the safety of the image-guided surgical system. Calibration techniques for radiographic systems have been studied as methods for calculating the geometric information of radiographic images using a calibration phantom [4; 5; 6; 7]. The phantom-based calibration method requires several radiographic images of a phantom that employs ball bearings to establish accurate locations at multiple angles. The geometric parameters of the system are then calculated using the spatial relationship between the 2D images acquired by the imaging device and the known 3D spatial fiducial markers of the phantom calibration model. [PERSON] et al.