Physical constraints that underly the formation of periodic motions can be effectively used to accurately reconstruct the periodic motion from even single camera views. As shown in our earlier work, this reduces to a problem of geometric inference. In this paper, we focus on periodic motions exhibited by humans, which are generally not perfectly periodic, and explore the suitability of the reconstruction techniques in these scenarios. We examine the degree of periodicity of human gait empirically, including the applicability of our motion model. Importantly, we illustrate the usefulness of these techniques by applying them to the task of clinical gait analysis. A computational tool to analyze periodic human motion can prove to be invaluable in medical applications either in terms of assessing deviations from normal patterns or evaluating changes resulting from therapy or other clinical procedures.

Periodicity has been recognized as an important cue for tasks like activity recognition and gait analysis. However, most existing techniques analyze periodic motions only in image coordinates, making them very dependent on the viewing angle. In this paper we propose a new technique for reconstructing periodic point trajectories in 3D given only their apparent trajectories in image coordinates from a single stationary camera. We show that this reconstruction is possible without performing a costly gradient descent-type optimization, and is based only on a single SVD. This new algorithm is shown to accurately reconstruct natural human motions, allowing them to be compared in 3D world coordinates, independent of the angle from which they were originally viewed.

In this paper, we consider the problem of localizing a projectile in 3D based on its apparent motion in a stationary monocular view. A thorough theoretical analysis is developed, from which we establish the minimum conditions for the existence of a unique solution. The theoretical results obtained have important implications for applications involving projectile motion. A robust, nonlinear optimization-based formulation is proposed, and the use of a local optimization method is justified by detailed examination of the local convexity structure of the cost function. The potential of this approach is validated by experimental results.

We present a novel technique for the detection of thrown objects and other free-flying bodies in video sequences. Our method runs in real-time and was designed to be used as a component in a deployed surveillance system. We detect regions of interesting motion that fit certain size, compactness and speed criteria, and use the expectation maximization algorithm to detect objects on parabolic trajectories over a short time window. The system was shown to successfully detect thrown objects of various sizes in a large test set of indoor and outdoor videos.

This paper presents a novel technique for camera tampering detection. It is implemented in real-time and was developed for use in surveillance and security applications. This method identifies camera tampering by detecting large differences between older frames of video and more recent frames. A buffer of incoming video frames is kept and three different measures of image dissimilarity are used to compare the frames. After normalization, a set of conditions is tested to decide if camera tampering has occurred. The effects of adjusting the internal parameters of the algorithm are examined. The performance of this method is shown to be extremely favorable in real-world settings.