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    Algebraic Error Based Triangulation and Metric of Lines

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    Issue Date
    2015-07-28
    Author
    Wu, Fuchao
    Zhang, Ming
    Wang, Guanghui
    Hu, Zhanyi
    Publisher
    Public Library of Science
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Rights
    This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.
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    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.
    URI
    http://hdl.handle.net/1808/19890
    DOI
    https://doi.org/10.1371/journal.pone.0132354
    Collections
    • Electrical Engineering and Computer Science Scholarly Works [289]
    Citation
    Wu, Fuchao, Ming Zhang, Guanghui Wang, and Zhanyi Hu. "Algebraic Error Based Triangulation and Metric of Lines." PLOS ONE PLoS ONE 10.7 (2015): n. pag. http://dx.doi.org/10.1371/journal.pone.0132354.

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    KU Libraries
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    785-864-8983

    KU Libraries
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    Lawrence, KS 66045
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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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