# Calibration Method of Projectional Geometry for X-ray C-arm Fluoroscopy Using Sinogram Data
## 1 Introduction
proposed an algorithm for estimating the geometric parameters of the system by attaching calibration markers to the X-ray source housing [4]. When the X-ray images are acquired, the calibration markers are always presented with the objects. However, such markers can introduce noise and scattering effects and can act as physical obstacles that prevent the accurate diagnosis of a patient. [PERSON] et al. proposed an algorithm to improve and verify the accuracy of CBCT geometric parameter estimation by performing additional calibration with the results of the initial calibration [5]. Calibration errors caused by phantom tolerance were corrected during the calibration procedures in their study. [PERSON] et al. also proposed a calibration method that uses a Computer-Aided Design (CAD) model to estimate the initial projective model of the X-ray device and then compute the real projective parameters by comparing the projective model from X-ray images with the CAD-based projective mode [8]. There have also been efforts to improve calibration accuracy with a new calibration phantom design. [PERSON] et al. devised a low-cost method for creating a calibration phantom [7]. The goal of their research was to devise a method for creating a phantom using lightweight and inexpensive LEGO blocks. Consequently, the calibration phantom could be easily and cheaply designed and built for clinical applications. [PERSON] et al. proposed a paddle-wheel type phantom for cone-beam CT geometric calibration [9], and [PERSON] reported geometrical calibration results using a new phantom with a cylindrical shape and then embedding fiducial markers on the body. The calibration using the new phantom improved the accuracy compared to traditional designs. In addition, [PERSON] et al. used Singular Value Decomposition (SVD) to calculate the geometric parameters of the radiographic system [6]. Although their study proposed an approach similar to that in this study that applies SVD [10; 11] to the calibration of the radiographic imaging device, their work had a limitation in the degree of freedom of the geometric parameters. Furthermore, the approach proposed herein can be applied to the same device when provided with known geometric parameters. Previous research presented efforts to improve the geometric calibration of the X-ray imaging device using a calibration pattern fixed to the X-ray source and providing an algorithm to calibrate the geometric parameters. Furthermore, some studies proposed a low-cost, easily manufactured calibration phantom. These studies, however, had several limitations. When a calibration pattern is attached for calibration, the markers on the calibration pattern can sometimes occlude the patient's lesion. This usually makes diagnosis of the patient's disorder difficult. In addition, for calibration, the calibration algorithms typically acquired a single or several projectional images of the phantom. Although they showed promising calibration accuracy, it was challenging to maintain calibration accuracy along the various orientations of the C-arm X-ray gantry. This study was designed and conducted to overcome such limitations and improve the calibration accuracy along various orientations of the C-arm X-ray gantry. This study aims to develop a projectional geometry calibration method for radiographic use, which is essential for performing registration between 2D radiographic images and CBCT data acquired intraoperatively during an image-guided angiographic intervention. The clinical target of this study is a C-arm angiographic imaging device that has been used in vascular intervention procedures and is equipped with CBCT imaging capabilities. While operating the CBCT, this device can provide sinogram data and radiographic image data with multi-directional projection images at various angles, which are then used to reconstruct 3D CT volume data.