A morphological cellular automata based on morphological independence

We discuss a definition of Morphological Cellular Neural Networks (MCNN) where the state change operator are Auto-associative Morphological Memories (AMM). The fast convergence properties of AMM and the shape of its fixed point set make the MCNN dynamics trivial. However, segmentation results are poor. We propose a Morphological Cellular Automata (MCA) with assured convergence to a state characterized by morphological dependences and independences between neighbouring cell states. Cell dynamic rules test morphological dependence among neighbouring cell’s states. When neighbouring cell states are morphological dependent in the erosive or dilative sense, the morphologically dominant state colonizes the neighbour with morphological dependent state. The resulting configuration of cell states is composed of homogeneous regions whose boundaries are defined by the morphological independence relation. Results are given on image segmentation, where MCA cells correspond to image pixels.