Dimensional operators for mathematical morphology on simplicial complexes

Specifically, we explore properties of the dimensional operators, small, versatile operators that can be used to define new operators on simplicial complexes, while maintaining properties from mathematical morphology. These operators can also be used to recover many morphological operators from the literature. Matlab code and additional material, including the proofs of the original properties, are freely available at http://code.google.com/p/math-morpho-simplicial-complexes.