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Using Geometric Interval Algebra Modeling for Improved Three-Dimensional Camera Calibration

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Abstract

This paper addresses the problem of estimating camera calibration parameters by using a novel method based on interval algebra. Unlike existing solutions, which usually apply real algebra, our method is capable of obtaining highly accurate parameters even in scenarios where the input data for camera calibration are severely corrupted by noise or no artificial calibration target can be introduced on the scene. We introduce some key concepts regarding the usage of interval algebra on projective space, which might be used by other computer vision methods. To demonstrate the robustness and effectiveness of our method, we present results for camera calibration with varying levels of noise on the input data of a world coordinate frame (standard deviation of up to 0.5 m) and their corresponding projections onto an image plane (standard deviation of up to 10 pixels), which are significantly larger than noise levels considered by state-of-the-art methods.

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Notes

  1. Available: http://www.vision.caltech.edu/bouguetj/calib_doc/index.html.

  2. Available at: https://www.blender.org/.

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Acknowledgements

The authors would like to thank the support of CNPq under Procs. 307510/2017-4 and 313163/2014-6, FAPEMIG under Proc. PPM-00542-15, CEFET-MG and CAPES.

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Authors and Affiliations

  1. Federal University of Ouro Preto, João Monlevade, MG, 35931-008, Brazil

    Darlan N. Brito

  2. Federal Center of Technological Education of Minas Gerais, Belo Horizonte, MG, 30510-000, Brazil

    Flávio L. C. Pádua

  3. Federal University of Itajubá, Itabira, MG, 35903-087, Brazil

    Aldo P. C. Lopes

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Brito, D.N., Pádua, F.L.C. & Lopes, A.P.C. Using Geometric Interval Algebra Modeling for Improved Three-Dimensional Camera Calibration. J Math Imaging Vis 61, 1342–1369 (2019). https://doi.org/10.1007/s10851-019-00907-x

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