The introduction of memcomputing memristors into the design of Cellular Nonlinear Networks (CNNs) allows to reduce the integrated circuit area typically allocated to each processing element in hardware realizations. Furthermore, the highly nonlinear dynamics of memristors enriches the multivariate signal processing capabilities of these cellular memprocessing structures. This is demonstrated in this paper, where the standard and generalized Dynamic Route Map analysis tools are employed to elucidate the mechanisms by which a Memristor CNN with bistable-like and analog dynamic nonvolatile memristors executes fundamental image processing operations, respectively.