Stabilization of parametric active contours using a tangential redistribution term

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.