Crowd motion analysis, where there is interdependence amongst the constituent elements, is a relatively unexplored application area in computer vision. In this work, we propose a fast method for short-term crowd motion prediction using a sparse set of particles. We study the dynamics of a crowd motion model and linear cyclic pursuit. We show that linear cyclic pursuit naturally captures the repulsive and attractive forces acting on the individual crowd member. The pursuit parameters are estimated from videos in an online manner using a feature tracker. Short term trajectory prediction is done by numerical solution of estimated cyclic pursuit equation. We demonstrate the suitability of the proposed technique through extensive experimentations.

Depending on implementation, active contours have been classified as geometric or parametric active contours. Parametric contours, irrespective of representation, are known to suffer from the problem of irregular bunching and spacing out of curve points during the curve evolution. In a spline-based implementation of active contours, this leads to occasional formation of loops locally, and subsequently the curve blows up due to instabilities. In this paper, we analyze the reason for this problem and propose a solution to alleviate the same. We propose an ordinary differential equation (ODE) for controlling the curve parametrization during evolution by including a tangential force. We show that the solution of the proposed ODE is bounded. We demonstrate the effectiveness of the proposed method for segmentation and tracking tasks on closed as well as open contours.

Parametric active contours have been used extensively in computer vision for different tasks like segmentation and tracking. However, all parametric contours are known to suffer from the problem of frequent bunching and spacing out of curve points locally during the curve evolution. In a spline based implementation of active contours, this leads to occasional formation of loops locally, and subsequently the curve blows up due to instabilities. It has been shown earlier that in addition to usual evolution along the normal direction, the curve should also be evolved in the tangential direction for stability purposes. In this paper, we provide a mathematical basis for selecting such a suitable tangential component for stabilisation. We prove the boundedness of the evolved curve in this paper, and provide the physical significance. We demonstrate the usefulness of the proposed method with a number of experiments.