Algebraic Error Based Triangulation and Metric of Lines

Fuchao Wu, Ming Zhang, Guanghui Wang and Zhanyi Hu

PLOS ONE, 2015, vol. 10, issue 7, 1-27

Abstract: Line triangulation, a classical geometric problem in computer vision, is to determine the 3D coordinates of a line based on its 2D image projections from more than two views of cameras with known projection matrices. Compared to point features, line segments are more robust to matching errors, occlusions, and image uncertainties. In addition to line triangulation, a better metric is needed to evaluate 3D errors of line triangulation. In this paper, the line triangulation problem is investigated by using the Lagrange multipliers theory. The main contributions include: (i) Based on the Lagrange multipliers theory, a formula to compute the Plücker correction is provided, and from the formula, a new linear algorithm, LINa, is proposed for line triangulation; (ii) two optimal algorithms, OPTa-I and OPTa-II, are proposed by minimizing the algebraic error; and (iii) two metrics on 3D line space, the orthogonal metric and the quasi-Riemannian metric, are introduced for the evaluation of line triangulations. Extensive experiments on synthetic data and real images are carried out to validate and demonstrate the effectiveness of the proposed algorithms.

Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0132354 (text/html)
https://journals.plos.org/plosone/article/file?id= ... 32354&type=printable (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0132354

DOI: 10.1371/journal.pone.0132354

Access Statistics for this article

More articles in PLOS ONE from Public Library of Science
Bibliographic data for series maintained by plosone ().