Add to ORKGMathematical morphology is a discipline that provides a formal framework for the analysis and manipulation of images. Its theoretical foundations have been well-established in the last forty years and it has shown to be a powerful tool in the development of a large number of image processing applications. This paper shows that a lot of knowledge that is developed in the field of mathematical morphology can be applied to Discrete-Time Cellular Neural Networks (DTCNNs). DTCNN equivalences of the elementary morphological operators, which are the basic building blocks for complex image operations, are introduced and the correctness of these templates is formally proved.</p