Abstract: This paper presents a fast and parsimonious parsing method to accurately and robustly detect a vectorized wireframe in an input image with a single forward pass. The proposed method is end-to-end trainable, consisting of three components: (i) line segment and junction proposal generation, (ii) line segment and junction matching, and (iii) line segment and junction verification. For computing line segment proposals, a novel exact dual representation is proposed which exploits a parsimonious geometric reparameterization for line segments and forms a holistic 4-dimensional attraction field map for an input image. Junctions can be treated as the basins in the attraction field. The proposed method is thus called Holistically-Attracted Wireframe Parser (HAWP). In experiments, the proposed method is tested on two benchmarks, the Wireframe dataset [14] and the YorkUrban dataset [8]. On both benchmarks, it obtains state-of-the-art performance in terms of accuracy and efficiency. For example, on the Wireframe dataset, compared to the previous state-of-the-art method L-CNN [36], it improves the challenging mean structural average precision (msAP) by a large margin (2.8% absolute improvements), and achieves 29.5 FPS on a single GPU (89% relative improvement). A systematic ablation study is performed to further justify the proposed method.