On the exhaustive generation of discrete figures with connectivity constraints

This paper deals with a generalization of polyominoes called ( a, b ) -connected discrete figures , where a and b respectively denotes the connectivity of the foreground (i.e. black pixels ) and background (i.e. white pixels ). Formally, a finite set of pixels P is ( a, b )-connected if P is a -connected and P̄ is b -connected. By adapting a combinatorial structure enumeration algorithm due to Martin, we successfully generate ( a, b )-connected discrete figures up to size n = 18.