Multigrid Geometric Active Contour Models

Geometric active contour models are very popular partial differential equation-based tools in image analysis and computer vision. We present a new multigrid algorithm for the fast evolution of level-set-based geometric active contours and compare it with other established numerical schemes. We overcome the main bottleneck associated with most numerical implementations of geometric active contours, namely the need for very small time steps to avoid instability, by employing a very stable fully 2-D implicit-explicit time integration numerical scheme. The proposed scheme is more accurate and has improved rotational invariance properties compared with alternative split schemes, particularly when big time steps are utilized. We then apply properly designed multigrid methods to efficiently solve the occurring sparse linear system. The combined algorithm allows for the rapid evolution of the contour and convergence to its final configuration after very few iterations. Image segmentation experiments demonstrate the efficiency and accuracy of the method.