Digital and cellular convexity

Abstract We introduce a new definition of cellular convexity on square mosaics. We also define digital convexity for 4-connected sets of points on a square lattice. Using these definitions we show that a cellular complex is cellularly convex if and only if the digital region determined by the complex is digitally convex. We also show that a digital region is digitally convex if and only if the minimum-perimeter polygon (MPP) enclosing the digital region contains only the digital region. This result is related to a property of the MPP of the half-cell expansion of the complex determined by the digital region.