Memristor Cellular Nonlinear Networks (M-CNNs) have been recently introduced as a functional upgrade of standard CNNs, empowered by the potential of memristors to perform storage and computing functionalities in the same area. This paper exploits the diverse features of M-CNNs, which are equipped with threshold-based binary resistance switching devices, introducing two state-of-the-art image processing M-CNNs: a) the multi-tasking CORNER-EDGE M-CNN, which performs corner or edge detection depending on the initial states of the memristors within the network; b) the memcomputing STORE-EDGE M-CNN, which outputs the edges of a binary input image, that is simultaneously stored in the memristors of the cellular array.