Globally minimal path method using dynamic speed functions based on progressive wave propagation

Abstract

In this paper, we propose a novel framework which extends the classical minimal path methods. Usually, minimal path methods can be interpreted as the simulation of the outward propagation of a wavefront emanating from a specific start point at a certain speed derived from an image. In previous methods, either a static speed is computed before the wavefront starts to propagate, or the normal of the wavefront is used to update the speed dynamically. We generalize the latter methods by introducing more general dynamic speed functions: During the outward propagation of the wavefront, features of the region already visited by the wavefront are used to update the speed dynamically. Our framework can incorporate both the fast marching method and Dijkstra's algorithm. We prove that the global optimum can be found using our approach and demonstrate its advantage experimentally by applying it for segmentation of tubular structures in synthetic and real images. © 2013 Springer-Verlag.