Medians of discrete sets according to a linear distance

In this paper we present some results concerning the median points of a dis crete set according to a distance defined by means of two directions p and q. We describe a local characterization of the median points and show how t hese points can be determined from the projections of the discrete set alon g directions p and q. We prove that the discrete sets having some connectiv ity properties have at most four median points according to a linear distan ce, and if there are four median points they form a parallelogram. Finally, we show that the 4-connected sets which are convex along the diagonal dire ctions contain their median points along these directions.