# Optical Flow-Based Extraction of Breathing Signal from Cone Beam CT Projections
## 1 Introduction  
Lung cancer cases are on the rise globally, with 2.21 million reported cases in the year 2020. It is also a top contributor to cancer-associated mortality as per the statistics provided by World Health Organization [1]. Lung cancer treatment involves radiotherapy in which a radiation pulse is targeted at the tumor site to destroy cancerous cells. The treatment planning process during radiotherapy for cancers of the lung and superior abdominal regions is affected by the breathing motion. Accounting for the breathing motion is necessary through motion management techniques to ensure that the location of the tumor is not misrepresented, allowing the radiation beam to precisely kill the cancerous cells and at the same time minimize the exposure of healthy tissues surrounding the tumor site to a high dose of radiation.  
Several motion management techniques for application in radiotherapy have been developed and tested [2]. Among such techniques commonly used are the application of surface markers that track chest motion as it moves during respiration or the implantation of internal fiducial markers that can help track the tumor motion with better accuracy [3, 4, 5, 6]. It is not evident how well a signal estimated by tracking the movement of a marker block positioned on the skin correlates with a tumor located within the lung. On the other hand, implantation of fiducial markers can pose health risks to the patient. Use of techniquessuch as breath hold and abdominal compression can minimize the effect of motion on the images; however, such techniques can cause discomfort to the patient undergoing the scan.  
Therefore, there is a need to shift towards image-based methods for management of breathing motion that does not rely on marker tracking, and are robust and safe. Image-Guided Radiation Therapy (IGRT) is an emerging technology adopted in clinical practice due to its ability to deliver highly accurate radiation doses to the tumor and reduce the side effects at the same time. Based on a master's thesis [7], this paper presents an image-based method to estimate respiratory motion using Cone Beam Computed Tomography (CBCT) projections. In this work, an optical flow-based approach is first used to produce motion vectors. This process is followed by the application of Principal Component Analysis (PCA) to extract dominant motion patterns from the flow vectors. Moreover, the extracted respiratory signal is used to sort the CBCT projections according to their respiratory phase, which can be used to reconstruct a 4D CBCT image. The reconstructed image is evaluated by comparing it to the image reconstructed considering the ground-truth breathing signal. The contributions of this work lie in building an image-based method that is simple, computationally efficient, and can be used for respiratory phase sorting and 4D CBCT image reconstruction right after the CBCT projections are acquired.  
The subsequent sections of this paper are organized in the following manner. Section 2 includes the literature review. Section 3 discusses the used datasets and methods. Section 4 presents and discusses the experimental results. Section 5 provides a discussion of the results and limitations of this work, and provides future research directions. The paper is concluded in Section 6.