Efficient algorithm for finding the exact minimum barrier distance

Abstract

The minimum barrier distance, MBD, introduced recently in [1], is a pseudo-metric defined on a compact subset D of the Euclidean space Rn and whose values depend on a fixed map (an image) f from D into R. The MBD is defined as the minimal value of the barrier strength of a path between the points, which constitutes the length of the smallest interval containing all values of f along the path.In this paper we present a polynomial time algorithm, that provably calculates the exact values of MBD for the digital images. We compare this new algorithm, theoretically and experimentally, with the algorithm presented in [1], which computes the approximate values of the MBD. Moreover, we notice that every generalized distance function can be naturally translated to an image segmentation algorithm. The algorithms that fall under such category include: Relative Fuzzy Connectedness, and those associated with the minimum barrier, fuzzy distance, and geodesic distance functions. In particular, we compare experimentally these four algorithms on the 2D and 3D natural and medical images with known ground truth and at varying level of noise, blur, and inhomogeneity.