Clustering, triangulation, and evaluation of 3D lines in multiple images

Three-dimensional (3D) lines require further enhancement in both clustering and triangulation. Line clustering assigns multiple image lines to a single 3D line to eliminate redundant 3D lines. Currently, it depends on the fixed and empirical parameter. However, a loose parameter could lead to over-clustering, while a strict one may cause redundant 3D lines. Due to the absence of the ground truth, the assessment of line clustering remains unexplored. Additionally, 3D line triangulation, which determines the 3D line segment in object space, is prone to failure due to its sensitivity to positional and camera errors.

This paper aims to improve the clustering and triangulation of 3D lines and to offer a reliable evaluation method. (1) To achieve accurate clustering, we introduce a probability model, which uses the prior error of the structure from the motion, to determine adaptive thresholds; thus controlling false clustering caused by the fixed hyperparameter. (2) For robust triangulation, we employ a universal framework that refines the 3D line with various forms of geometric consistency. (3) For a reliable evaluation, we investigate consistent patterns in urban environments to evaluate the clustering and triangulation, eliminating the need to manually draw the ground truth.

To evaluate our method, we utilized datasets of Internet image, totaling over ten thousand images, alongside aerial images with dimensions exceeding ten thousand pixels. We compared our approach to state-of-the-art methods, including Line3D++, Limap, and ELSR. In these datasets, our method demonstrated improvements in clustering and triangulation accuracy by at least 20% and 3%, respectively. Additionally, our method ranked second in execution speed, surpassed only by ELSR, the current fastest algorithm. The C++ source code for the proposed algorithm, along with the dataset used in this paper, is available at https://github.com/weidong-whu/3DLineResconstruction.