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An Approach to the Vanishing Line Identification Based on Normalized Barycentric Coordinates

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Abstract

The vanishing line is useful information for recovering affine properties of the plane in computer vision. This paper describes how to determine analytically the vanishing line from a single perspective view of a plane containing the four points of known normalized barycentric coordinates in a general position, and further how to compute the vanishing line via the eigenvector representation. We also propose that the projectivity may be expressed directly and analytically from the vanishing line and three 3D–2D point correspondences. It is shown that plane affine properties may be computed and the metric may be recovered from known metric information, which includes an angle, two equal but unknown angles, and a length ratio of two non-parallel line segments, without using the image of the circular points as an intermediate step. The correctness and performance of the novel results are demonstrated by thorough testing on both synthetic and real data.

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Acknowledgments

The author thanks the anonymous referees for valuable suggestions. This work was supported by the Fundamental Research Funds for the Central Universities under Grant No. 100405012.

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  1. Department of Mathematics, Northeastern University, Shenyang , 110004, P. R. China

    Yang Guo

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  1. Yang Guo
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Correspondence to Yang Guo.

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Guo, Y. An Approach to the Vanishing Line Identification Based on Normalized Barycentric Coordinates. J Math Imaging Vis 50, 286–299 (2014). https://doi.org/10.1007/s10851-014-0499-y

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  • DOI: https://doi.org/10.1007/s10851-014-0499-y

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