We present simulation results of a deep cellular neural network leveraging memristive dynamics to classify and segment images from commonly examined datasets. We have investigated the use of both volatile (NbO_x-Mott) and non-volatile (TaO_x) memristive devices in memristive cellular neural networks. We simulated deep neural networks using these devices and compared their image classification and segmentation accuracies on commonly investigated datasets to traditional convolutional and cellular architectures of similar complexity. Our results reveal that the exploitation of memristive dynamics in cellular structures can increase classification accuracy by more than 2.5 percent as compared to the traditional convolutional implementations while concurrently improving the mean intersection over union in semantic segmentation on the Cityscapes dataset by 8 percent.