Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

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.