Convergence analysis of active contours in image segmentation

Active contours effectiveness in image segmentation is well known. As any adaptive system, the iterations required by the contour to delineate the target is of importance. In this process, some nodes reach their position before than others and due to the internal forces, the neighboring nodes evolve towards a final shape constrained to the external forces. This paper presents a signal-processing perspective of that scenario by deriving a novel frequency-based formulation. The main result of the analysis is the speed of convergence, which depends analytically on the stiffness properties and especially on the second-order parameters and the length of the snake segments. This initial attempt to characterize the snake dynamics is supported with simulation results.