Abstract: In recent years, the accuracy of edge detection on several benchmarks has been significantly improved by deep learning based methods. However, the prediction of deep neural networks is usually blurry and needs further post-processing including non-maximum suppression and morphological thinning. In this paper, we demonstrate that the blurry effect arises from the binary cross-entropy loss, and crisp edges could be obtained directly from deep convolutional neural networks. We propose to learn edge maps as the representation of local contrast with a novel local contrast loss. The local contrast is optimized in a stochastic way to focus on specific edge directions. Experiments show that the edge detection network trained with local contrast loss achieves a high accuracy comparable to previous methods and dramatically improves the crispness. We also present several applications of the crisp edges, including image completion, image retrieval, sketch generation, and video stylization.