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Memristor with memory properties can be applied to connection points (synapses) between cells in a cellular neural network (CNN). This paper highlights memristor crossbar-based multilayer CNN (MCM-CNN) and its application to edge detection. An MCM-CNN is designed by adopting a memristor crossbar composed of a pair of memristors. MCM-CNN based on the memristor crossbar with changeable weight is suitable for edge detection of a binary image and a color image considering its characteristics of programmablization and compactation. Figure of merit (FOM) is introduced to evaluate the proposed structure and several traditional edge detection operators for edge detection results. Experiment results show that the FOM of MCM-CNN is three times more than that of the traditional edge detection operators.