The One-Point-One-Line geometry for robust and efficient line segment correspondence

Abstract

Three-dimensional (3D) lines are common elements in artificial scenes and serve as basic, yet essential features for structural 3D reconstruction. The crucial step of 3D line reconstruction, namely two-view line segment matching, still faces challenges in terms of both accuracy and efficiency improvements. Therefore, robust and efficient constraints are needed to establish valid line candidates. This paper introduces a novel geometry constraint called “one-point-one-line geometry” (OPOL) to enhance the precision of line matching and reduce computational complexity. OPOL offers two remarkable advantages: (1) It takes point orientations as the constraint, which is not only invariant to projective transformations, but also alleviates computational requirements. (2) It needs only one point match to construct the geometry constraint, thus both the grouping and validation are greatly reduced. Additionally, we incorporate the line sweep strategy into OPOL, leveraging depth and space constraints derived from existing 3D points to further enhance efficiency. Extensive experiments conducted on large-coverage and high-resolution images (as large as 10336 × 7788 pixels) demonstrated that OPOL matched lines within a second for an image pair. Both quantitative and qualitative results also demonstrated the superior accuracy and efficiency performance of OPOL. We integrated OPOL into multiple view line reconstruction frameworks, and the promising experimental results reveal the performance of OPOL for robust line reconstruction. The OPOL code is publicly available at https://github.com/JoeAlexxxxx/OPOL.