In recent years, personal computing devices such as laptops, tablets and smartphones have become ubiquitous. Moreover, intelligent sensors are being integrated into many consumer devices such as eyeglasses, wristwatches and smart televisions. With the advent of touchscreen technology, a new human-computer interaction (HCI) paradigm arose that allows users to interface with their device in an intuitive manner. Using simple gestures, such as swipe or pinch movements, a touchscreen can be used to directly interact with a virtual environment. Nevertheless, touchscreens still form a physical barrier between the virtual interface and the real world.An increasingly popular field of research that tries to overcome this limitation, is video based gesture recognition, hand detection and hand tracking. Gesture based interaction allows the user to directly interact with the computer in a natural manner by exploring a virtual reality using nothing but his own body language.In this dissertation, we investigate how robust hand detection and tracking can be accomplished under real-time constraints. In the context of human-computer interaction, real-time is defined as both low latency and low complexity, such that a complete video frame can be processed before the next one becomes available. Furthermore, for practical applications, the algorithms should be robust to illumination changes, camera motion, and cluttered backgrounds in the scene. Finally, the system should be able to initialize automatically, and to detect and recover from tracking failure. We study a wide variety of existing algorithms, and propose significant improvements and novel methods to build a complete detection and tracking system that meets these requirements.Hand detection, hand tracking and hand segmentation are related yet technically different challenges. Whereas detection deals with finding an object in a static image, tracking considers temporal information and is used to track the position of an object over time, throughout a video sequence. Hand segmentation is the task of estimating the hand contour, thereby separating the object from its background.Detection of hands in individual video frames allows us to automatically initialize our tracking algorithm, and to detect and recover from tracking failure. Human hands are highly articulated objects, consisting of finger parts that are connected with joints. As a result, the appearance of a hand can vary greatly, depending on the assumed hand pose. Traditional detection algorithms often assume that the appearance of the object of interest can be described using a rigid model and therefore can not be used to robustly detect human hands. Therefore, we developed an algorithm that detects hands by exploiting their articulated nature. Instead of resorting to a template based approach, we probabilistically model the spatial relations between different hand parts, and the centroid of the hand. Detecting hand parts, such as fingertips, is much easier than detecting a complete hand. Based on our model of the spatial configuration of hand parts, the detected parts can be used to obtain an estimate of the complete hand's position. To comply with the real-time constraints, we developed techniques to speed-up the process by efficiently discarding unimportant information in the image. Experimental results show that our method is competitive with the state-of-the-art in object detection while providing a reduction in computational complexity with a factor 1 000. Furthermore, we showed that our algorithm can also be used to detect other articulated objects such as persons or animals and is therefore not restricted to the task of hand detection.Once a hand has been detected, a tracking algorithm can be used to continuously track its position in time. We developed a probabilistic tracking method that can cope with uncertainty caused by image noise, incorrect detections, changing illumination, and camera motion. Furthermore, our tracking system automatically determines the number of hands in the scene, and can cope with hands entering or leaving the video canvas. We introduced several novel techniques that greatly increase tracking robustness, and that can also be applied in other domains than hand tracking. To achieve real-time processing, we investigated several techniques to reduce the search space of the problem, and deliberately employ methods that are easily parallelized on modern hardware. Experimental results indicate that our methods outperform the state-of-the-art in hand tracking, while providing a much lower computational complexity.One of the methods used by our probabilistic tracking algorithm, is optical flow estimation. Optical flow is defined as a 2D vector field describing the apparent velocities of objects in a 3D scene, projected onto the image plane. Optical flow is known to be used by many insects and birds to visually track objects and to estimate their ego-motion. However, most optical flow estimation methods described in literature are either too slow to be used in real-time applications, or are not robust to illumination changes and fast motion. We therefore developed an optical flow algorithm that can cope with large displacements, and that is illumination independent.Furthermore, we introduce a regularization technique that ensures a smooth flow-field. This regularization scheme effectively reduces the number of noisy and incorrect flow-vector estimates, while maintaining the ability to handle motion discontinuities caused by object boundaries in the scene.The above methods are combined into a hand tracking framework which can be used for interactive applications in unconstrained environments. To demonstrate the possibilities of gesture based human-computer interaction, we developed a new type of computer display. This display is completely transparent, allowing multiple users to perform collaborative tasks while maintaining eye contact. Furthermore, our display produces an image that seems to float in thin air, such that users can touch the virtual image with their hands. This floating imaging display has been showcased on several national and international events and tradeshows.The research that is described in this dissertation has been evaluated thoroughly by comparing detection and tracking results with those obtained by state-of-the-art algorithms. These comparisons show that the proposed methods outperform most algorithms in terms of accuracy, while achieving a much lower computational complexity, resulting in a real-time implementation. Results are discussed in depth at the end of each chapter. This research further resulted in an international journal publication; a second journal paper that has been submitted and is under review at the time of writing this dissertation; nine international conference publications; a national conference publication; a commercial license agreement concerning the research results; two hardware prototypes of a new type of computer display; and a software demonstrator.