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Relative Pose from SIFT Features

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Computer Vision – ECCV 2022 (ECCV 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13692))

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Abstract

This paper derives the geometric relationship of epipolar geometry and orientation- and scale-covariant, e.g., SIFT, features. We derive a new linear constraint relating the unknown elements of the fundamental matrix and the orientation and scale. This equation can be used together with the well-known epipolar constraint to, e.g., estimate the fundamental matrix from four SIFT correspondences, essential matrix from three, and to solve the semi-calibrated case from three correspondences. Requiring fewer correspondences than the well-known point-based approaches (e.g., 5PT, 6PT and 7PT solvers) for epipolar geometry estimation makes RANSAC-like randomized robust estimation significantly faster. The proposed constraint is tested on a number of problems in a synthetic environment and on publicly available real-world datasets on more than 800 00 image pairs. It is superior to the state-of-the-art in terms of processing time while often leading more accurate results. The solvers are included in GC-RANSAC at https://github.com/danini/graph-cut-ransac.

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Notes

  1. 1.

    Precisely, fundamental matrix \(\textbf{F}\) can be estimated from two affine and a point correspondence.

  2. 2.

    Note that the constraint  (14) derived in [10] is a linear combination of constraints (16) and (17) and can be obtained by eliminating q from these two equations.

  3. 3.

    This solver corresponds to the well-known eight-point solver [18].

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Acknowledgments

This work was supported by the ETH Zurich Postdoctoral Fellowship, by the OP VVV funded project CZ.02.1.01/0.0/0.0/16_019/0000765 “Research Center for Informatics”, and the ERC-CZ grant MSMT LL1901.

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Authors and Affiliations

  1. ETH Zurich, Computer Vision and Geometry Group, Zürich, Switzerland

    Daniel Barath

  2. Visual Recognition Group, Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czechia

    Zuzana Kukelova

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  1. Daniel Barath
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  2. Zuzana Kukelova
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Correspondence to Daniel Barath .

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Editors and Affiliations

  1. Tel Aviv University, Tel Aviv, Israel

    Shai Avidan

  2. University College London, London, UK

    Gabriel Brostow

  3. Google AI, Accra, Ghana

    Moustapha Cissé

  4. University of Catania, Catania, Italy

    Giovanni Maria Farinella

  5. Facebook (United States), Menlo Park, CA, USA

    Tal Hassner

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Barath, D., Kukelova, Z. (2022). Relative Pose from SIFT Features. In: Avidan, S., Brostow, G., Cissé, M., Farinella, G.M., Hassner, T. (eds) Computer Vision – ECCV 2022. ECCV 2022. Lecture Notes in Computer Science, vol 13692. Springer, Cham. https://doi.org/10.1007/978-3-031-19824-3_27

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  • DOI: https://doi.org/10.1007/978-3-031-19824-3_27

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