The Minimum Barrier Distance: A Summary of Recent Advances

In this paper we present an overview and summary of recent results of the minimum barrier distance (MBD), a distance operator that is a promising tool in several image processing applications. The theory constitutes of the continuous MBD in R, its discrete formulation in Z (in two different natural formulations), and of the discussion of convergence of discrete MBDs to their continuous counterpart. We describe two algorithms that compute MBD, one very fast but returning only approximate MBD, the other a bit slower, but returning the exact MBD. Finally, some image processing applications of MBD are presented and the directions of potential future research in this area are indicated.