Determining maximum k-width-connectivity on meshes

Let I be a n×n binary image stored in a n×n mesh of processors with one pixel per processor. Image I is k-width-connected if, informally, between any pair of pixels of value `I´ there exists a path of width k (composed of 1-pixels only). The authors consider the problem of determining the largest integer k such that I is k-width-connected, and present an optimal O (n) time algorithm for the mesh architecture