Minimal Solvers for Rectifying from Radially-Distorted Scales and Change of Scales


This paper introduces the first minimal solvers that jointly estimate lens distortion and affine rectification from the image of rigidly-transformed coplanar features. The solvers work on scenes without straight lines and, in general, relax strong assumptions about scene content made by the state of the art. The proposed solvers use the affine invariant that coplanar repeats have the same scale in rectified space. The solvers are separated into two groups that differ by how the equal scale invariant of rectified space is used to place constraints on the lens undistortion and rectification parameters. We demonstrate a principled approach for generating stable minimal solvers by the Gröbner basis method, which is accomplished by sampling feasible monomial bases to maximize numerical stability. Synthetic and real-image experiments confirm that the proposed solvers demonstrate superior robustness to noise compared to the state of the art. Accurate rectifications on imagery taken with narrow to fisheye field-of-view lenses demonstrate the wide applicability of the proposed method. The method is fully automatic.

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James Pritts acknowledges the European Regional Development Fund under the project Robotics for Industry 4.0 (Reg. No. CZ.02.1.01/0.0/0.0/15_003/0000470) and Grant SGS17/185/OHK3/3T/13; Zuzana Kukelova the ESI Fund, OP RDE programme under the project International Mobility of Researchers MSCA-IF at CTU No. CZ.02.2.69/0.0/0.0/17_050/0008025; and Ondřej Chum Grant OP VVV funded project CZ.02.1.01/0.0/0.0/16_019/0000765 “Research Center for Informatics”. Viktor Larsson received funding from the ETH Zurich Postdoctoral Fellowship program and the Marie Sklodowska-Curie Actions COFUND program. Yaroslava Lochman was also supported by Robotics for Industry 4.0 as well as ELEKS Ltd.

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Communicated by C.V. Jawahar, Hongdong Li, Greg Mori, Konrad Schindler.

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Pritts, J., Kukelova, Z., Larsson, V. et al. Minimal Solvers for Rectifying from Radially-Distorted Scales and Change of Scales. Int J Comput Vis 128, 950–968 (2020).

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  • Rectification
  • Radial lens distortion
  • Minimal solvers
  • Repeated patterns
  • Symmetry
  • Local features