Convergence analysis of active contours

Active contours are very useful tools in image segmentation and object tracking in video sequences. The practical implementations are built with an iterative algorithm based on a second order system defined in the spatial domain, where the elasticity and rigidity are the static parameters for its characterization and mass and damping are the dynamic parameters. In the process, the contour is influenced by external and internal forces varying its shape adaptively. The number of iterations required by the contour to delineate the objects is determined by these forces, by its initialization and by the coefficients of the second order system. This paper analyzes the convergence of active contours using the frequency based formulation and shows that the convergence depends on the dynamic parameters of the second order system and the distance between nodes of the contour attracted by the external forces.