Recently, computational color constancy via convolutional neural networks (CNNs) has received much attention. In this paper, we propose a color constancy algorithm called the Dense Color Constancy (DCC), which employs a self-attention DenseNet to estimate the illuminant based on the $2$D $\log$-chrominance histograms of input images and their augmented edges. The augmented edges help to tell apart the edge and non-edge pixels in the $\log$-histogram, which largely contribute to the feature extraction and color ambiguity elimination, thereby improving the accuracy of illuminant estimation. Experiments on benchmark datasets show that the DCC algorithm is very effective for illuminant estimation compared to the state-of-the-art methods.