## 1 Introduction  
Tracking lung tumors accurately in real time in a three-dimensional (3D) space is particularly important for image-guided radiation therapy for lung cancer patients. Unless accurate tumor tracking is achieved, not only is it challenging to provide a sufficient dose escalation to the tumor, complications arise by emitting excessive doses to healthy tissue surrounding the tumor [1; 2; 3; 4]. The main cause of uncertainties in tumor tracking is movement of the internal organs due to the patient's respiration [5; 6]. A number of techniques have been explored to reduce such tumor-tracking uncertainty. External respiratory surrogates are actively being used to indirectly track the tumor location, which include reflective landmarks placed on the abdominal surface of the patient [7; 8; 9], a strain gauge-based pressure-sensing belt [10; 11], and optical abdominal surface imaging [12; 13; 14]. These surrogates are advantageous in that they are non-invasive and require no additional radiation dose to the patients. However, these external signals may not accurately reflect the movement of the tumor within the human body [15], and the signals may differ depending on how the external signal equipment is installed, thereby degrading the repeatability of the signals [16]. On the other hand, a method for tracking a fiducial marker [17; 18], or using an electromagnetic transponder [19; 20] implanted in or around the tumor, has been developed, which has excellent tracking accuracy owing to its direct tumor tracking. However, patients may feel uncomfortable during such an invasive surgical procedure for implant placement. Several fiducial-less methods also have been proposed and track tumor or respiratory motion successfully; however, the techniques can be applied using a separate dedicated tracking system (e.g., multiple X-ray cameras [21], Xsight lung tracking system [22], 4D ultrasound imaging [23]). For non-invasive and direct tumor tracking, studies using an on-board kV fluoroscopy system have been reported [6; 24; 25; 26; 27]. When the tumors shown through the fluoroscopy have an adequately high contrast, such methods can yield good results. However, because it is difficult to obtain high-contrast tumors through fluoroscopic means, these methods have been tested on images acquired from the anterior-posterior direction, where there is relatively little overlap with other organs. These methods, which only work in a specific direction of rotation, are not suitable for rotational cone-beam systems. In addition, because the tumor location is tracked by relying on 2D fluoroscopy, there is no resolution information in the direction of the radiation direction, i.e., the depth direction, making it impossible to trace the full 3D tumor location [6]. To track the complete six degrees-of-freedom (DOF) tumor movement, 2D/3D registration using megavoltage (MV) fluoroscopy [5] or templates containing tumor movements according to the respiratory phase [28] have been used. An MV fluoroscopy technique has a disadvantage in that separate MV images have to be acquired and synchronized with kV images. In addition, this method has been tested only at certain angles of the gantry, and it does not guarantee a good level of performance with kV images obtained in the left-right direction where the tumor overlaps with other organs. A template-based method should approximate the tumor location at the gantry angles where the tumor is not visible owing to an overlap with other objects using the surrounding gantry angle data where the tumor is visible, which results in a degraded performance at certain gantry angles. To avoid excessive radiation uptake of healthy tissue, the radiotherapy system should accurately irradiate the tumor to the treatment beam at various angles while rotating around the freely breathing patient. In response to this need, in this study we propose a method for tracking the respiratory phase and 3D tumor position in real time during treatment using a kV image mounted on the treatment system.