Centers of sets of pixels

The center of a connected graph G is the set of nodes of G for which the ma ximum distance to any other node of G is as small as possible. If G is a si mply connected set of lattice points (" pixels") with graph structure defin ed by 4-neighbor adjacency, we show that the center of G is either a 2 x 2 square block, a diagonal staircase, or a (dotted) diagonal line with no gap s. (C) 2000 Elsevier Science B.V. All rights reserved.