Abstract This paper presents a region-partition based attraction fifield dual representation for line segment maps, and thus poses the problem of line segment detection (LSD) as the region coloring problem. The latter is then addressed by learning deep convolutional neural networks (ConvNets) for accuracy, robustness and effificiency. For a 2D line segment map, our dual representation consists of three components: (i) A region-partition map in which every pixel is assigned to one and only one line segment; (ii) An attraction fifield map in which every pixel in a partition region is encoded by its 2D projection vector w.r.t. the associated line segment; and (iii) A squeeze module which squashes the attraction fifield to a line segment map that almost perfectly recovers the input one. By leveraging the duality, we learn ConvNets to compute the attraction fifield maps for raw input images, followed by the squeeze module for LSD, in an end-to-end manner. Our method rigorously addresses several challenges in LSD such as local ambiguity and class imbalance. Our method also harnesses the best practices developed in ConvNets based semantic segmentation methods such as the encoder-decoder architecture and the a-trous convolution. In experiments, our method is tested on the WireFrame dataset [12] and the YorkUrban dataset [6] with state-of-the-art performance obtained. Especially, we advance the performance by 4.5 percents on the WireFrame dataset. Our method is also fast with 6.6 ∼ 10.4 FPS, outperforming most of the existing line segment detectors. The source code of this paper is available at https: //github.com/cherubicXN/afm_cvpr2019.