  This paper presents a region-partition based attraction field 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 efficiency. 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 field 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 field to a line segment map that
almost perfectly recovers the input one. By leveraging the duality, we learn
ConvNets to compute the attraction field maps for raw in-put 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 and the YorkUrban dataset 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 existing line segment detectors.
