Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.

Person tracking using motion detection and optical flow

Person tracking systems to date have either relied on motion detection or optical flow as a basis for person detection and tracking. As yet, systems have not been developed that utilise both these techniques. We propose a person tracking system that uses both, made possible by a novel hybrid optical flow-motion detection technique that we have developed. This provides the system with two methods of person detection, helping to avoid missed detections and the need to predict position, which can lead to errors in tracking and mistakes when handling occlusion situations. Our results show that our system is able to track people accurately, with an average error less than four pixels, and that our system outperforms the current CAVIAR benchmark system.

Adaptive optical flow for person tracking

Person tracking systems are dependent on being able to locate a person accurately across a series of frames. Optical flow can be used to segment a moving object from a scene, provided the expected velocity of the moving object is known; but successful detection also relies on being able segment the background. A problem with existing optical flow techniques is that they don’t discriminate the foreground from the background, and so often detect motion (and thus the object) in the background. To overcome this problem, we propose a new optical flow technique, that is based upon an adaptive background segmentation technique, which only determines optical flow in regions of motion. This technique has been developed with a view to being used in surveillance systems, and our testing shows that for this application it is more effective than other standard optical flow techniques.