## 1 Introduction  
Hand detection and tracking are crucial front-end procedures for many human hand-gesture tasks and remain challenging topics for researchers. They play a vital role in various computer vision applications, including hand pose estimation, human-computer interaction (HCI) systems, virtual reality (VR), augmented reality (AR), and more. These tasks are essential in numerous human-machine applications, such as providing navigational assistance for the visually impaired [1], enabling contactless navigation for surgeons to minimize contamination during surgery [2], recognizing and interpreting sign language through hand gestures [3], and facilitating interactive remote control for VR video games [4]. Hand gestures can be classified into two categories: static gestures and dynamic gestures. Static hand gestures refer to hand postures where the position remains unchanged for a certain period of time, while dynamic hand gestures involve hand postures where the hand position changes over time. Static gestures are characterized by factors such as orientations, shape, and contextual environment, whereas dynamic gestures, also known as trajectory-based gestures, are characterized by factors such as trajectory and motion speed [5]. In the context of trajectory-based gestures, the accurate detection and tracking of the hand play a vital role. Recognizing and interpreting dynamic hand gestures requirescapturing the hand's motion trajectory and accurately tracking its movement. Detection ensures that the hand is identified and localized within the frame, while tracking enables the continuous monitoring of the hand's position, orientation, and motion throughout a sequence of frames. The detection and tracking of the hand are critical for trajectory-based gesture recognition. By extracting the trajectory pattern from landmarks such as the center of the palm, user can analyze the hand's motion and obtain meaningful features for gesture recognition algorithms. The integration of detection and tracking techniques allows the user to capture and analyze the temporal dynamics of hand gestures, providing more accurate and reliable recognition results. In general, two main approaches can be implemented for hand detection and tracking: marker-aided and vision-based marker-less methods. The former approach requires the user to wear a glove-like device, which provides more accurate results. However, wearing such a device inconveniences the user and restricts the naturalness of HCI [6]. The latter technique is undoubtedly a better approach as it allows for natural HCI interaction without the need for wearable devices. However, its accuracy may vary when the vision system is exposed to external factors such as extreme lighting conditions and cluttered backgrounds. In addition to accurate hand detection, tracking hand movement is essential for many hand-based computer vision applications. The hand tracking must be smooth, fast, and accurate to extract and decode information correctly. However, reliably detecting hands from cluttered scenes remains a challenging task. This is due to the complex appearance diversities of dexterous human hands in color images, including variations in hand shapes, skin colors, illuminations, orientations, scales, etc. [7]. Human hands are dynamic and tend to move quickly, making tracking difficult (e.g., clenching and releasing a fist, scratching the nose, waving hands). Furthermore, occlusion is a common issue encountered in hand detection systems [8]. Occlusion occurs when the hand is obstructed by other objects during real-time detection, such as covering the left hand with the right hand or placing the hand in front of the face. This introduces higher complexity to the system as the extracted information is limited for achieving the goal of hand detection. Apart from the occlusion with external objects, the human hand can also be self-occluded; for example, when clenching a fist, the fingertips are occluded by the palm.