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Recent studies have shown that slight perturbations in the input data can significantly affect the robustness of Deep Neural Networks (DNNs), leading to misclassification and confidence reduction. In this paper, we introduce a novel technique based on the Selective Sobel Convolution (SSC) operation in the training loop, that increases the robustness of a given DNN by allowing it to learn important edges in the input in a controlled fashion. This is achieved by introducing a trainable parameter, which acts as a threshold for eliminating the weaker edges. We validate our technique against the attacks of Cleverhans library on Convolutional DNNs against adversarial attacks. Our experimental results on the MNIST and CIFAR10 datasets illustrate that this controlled learning considerably increases the accuracy of the DNNs by 1.53% even when subjected to adversarial attacks.