Fu-Dong Wang

Nan Xue, Tianfu Wu, Song Bai et al.

This article presents Holistically-Attracted Wireframe Parsing (HAWP), a method for geometric analysis of 2D images containing wireframes formed by line segments and junctions. HAWP utilizes a parsimonious Holistic Attraction (HAT) field representation that encodes line segments using a closed-form 4D geometric vector field. The proposed HAWP consists of three sequential components empowered by end-to-end and HAT-driven designs: (1) generating a dense set of line segments from HAT fields and endpoint proposals from heatmaps, (2) binding the dense line segments to sparse endpoint proposals to produce initial wireframes, and (3) filtering false positive proposals through a novel endpoint-decoupled line-of-interest aligning (EPD LOIAlign) module that captures the co-occurrence between endpoint proposals and HAT fields for better verification. Thanks to our novel designs, HAWPv2 shows strong performance in fully supervised learning, while HAWPv3 excels in self-supervised learning, achieving superior repeatability scores and efficient training (24 GPU hours on a single GPU). Furthermore, HAWPv3 exhibits a promising potential for wireframe parsing in out-of-distribution images without providing ground truth labels of wireframes.

Nan Xue, Tianfu Wu, Song Bai et al.

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, and the YorkUrban dataset. 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, it improves the challenging mean structural average precision (msAP) by a large margin ($2.8\%$ absolute improvements) and achieves 29.5 FPS on single GPU ($89\%$ relative improvement). A systematic ablation study is performed to further justify the proposed method.

Nan Xue, Song Bai, Fu-Dong Wang et al.

This paper presents regional attraction of line segment maps, and hereby poses the problem of line segment detection (LSD) as a problem of region coloring. Given a line segment map, the proposed regional attraction first establishes the relationship between line segments and regions in the image lattice. Based on this, the line segment map is equivalently transformed to an attraction field map (AFM), which can be remapped to a set of line segments without loss of information. Accordingly, we develop an end-to-end framework to learn attraction field maps for raw input images, followed by a squeeze module to detect line segments. Apart from existing works, the proposed detector properly handles the local ambiguity and does not rely on the accurate identification of edge pixels. Comprehensive experiments on the Wireframe dataset and the YorkUrban dataset demonstrate the superiority of our method. In particular, we achieve an F-measure of 0.831 on the Wireframe dataset, advancing the state-of-the-art performance by 10.3 percent.

Fu-Dong Wang, Gui-Song Xia, Nan Xue et al.

Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise constraints can be formulated as a quadratic assignment problem (QAP), which is NP-complete and results in intrinsic computational difficulties. In this paper, we present a functional representation for graph matching (FRGM) that aims to provide more geometric insights on the problem and reduce the space and time complexities of corresponding algorithms. To achieve these goals, we represent a graph endowed with edge attributes by a linear function space equipped with a functional such as inner product or metric, that has an explicit geometric meaning. Consequently, the correspondence between graphs can be represented as a linear representation map of that functional. Specifically, we reformulate the linear functional representation map as a new parameterization for Euclidean graph matching, which is associative with geometric parameters for graphs under rigid or nonrigid deformations. This allows us to estimate the correspondence and geometric deformations simultaneously. The use of the representation of edge attributes rather than the affinity matrix enables us to reduce the space complexity by two orders of magnitudes. Furthermore, we propose an efficient optimization strategy with low time complexity to optimize the objective function. The experimental results on both synthetic and real-world datasets demonstrate that the proposed FRGM can achieve state-of-the-art performance.