Fast Methods for Implicit Active Contour Models

Abstract

Implicit active contour models belong to the most popular level set methods in computer vision. Typical implementations, however, suffer from poor efficiency. In this chapter we survey an efficient algorithm that is based on an additive operator splitting (AOS). It is suitable for geometric and geodesic active contour models as well as for mean curvature motion. It uses harmonic averaging and does not require to compute the distance function in each iteration step. We prove that the scheme satisfies a discrete maximumminimum principle which implies unconditional stability if no balloon forces are present. Moreover, it possesses all typical advantages of AOS schemes: simple implementation, equal treatment of all axes, suitability for parallel computing, and straightforward generalization to higher dimensions. Experiments show that one can gain a speed up by one order of magnitude compared to the widely used explicit time discretization.