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Inferring Bias and Uncertainty in Camera Calibration

Abstract

Accurate camera calibration is a precondition for many computer vision applications. Calibration errors, such as wrong model assumptions or imprecise parameter estimation, can deteriorate a system’s overall performance, making the reliable detection and quantification of these errors critical. In this work, we introduce an evaluation scheme to capture the fundamental error sources in camera calibration: systematic errors (biases) and uncertainty (variance). The proposed bias detection method uncovers smallest systematic errors and thereby reveals imperfections of the calibration setup and provides the basis for camera model selection. A novel resampling-based uncertainty estimator enables uncertainty estimation under non-ideal conditions and thereby extends the classical covariance estimator. Furthermore, we derive a simple uncertainty metric that is independent of the camera model. In combination, the proposed methods can be used to assess the accuracy of individual calibrations, but also to benchmark new calibration algorithms, camera models, or calibration setups. We evaluate the proposed methods with simulations and real cameras.

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Notes

  1. 1.

    Note, that the normalization of \(\epsilon _{\mathrm {bias}}\) is different to Hagemann et al. (2020), to clarify its relation to the estimated accuracy \({\hat{s}}_d^2\). The definition of the bias ratio, however, remains unaffected.

  2. 2.

    Here, we assume the underlying distribution is Gaussian but might be subject to sporadic outliers. The MAD multiplied by a factor of 1.4826 gives a robust estimate for the standard deviation (Rousseeuw and Croux 1993).

  3. 3.

    The decomposition of the target must lead to an overdetermined estimation problem.

  4. 4.

    As reference, we used the average of ten calibrations with 50 random images each.

  5. 5.

    Mapping error compared to the simulated ground-truth camera model.

  6. 6.

    Mapping error compared to the reference calibration.

  7. 7.

    The calibrations shown in Fig. 4 already take into account the board non-planarity.

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Acknowledgements

We thank Paul-Sebastian Lauer (Robert Bosch GmbH) for supporting the experimental setup and the data acquisition. We also thank the reviewers for the valuable comments.

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Correspondence to Annika Hagemann.

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Communicated by Zeynep Akata.

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Hagemann, A., Knorr, M., Janssen, H. et al. Inferring Bias and Uncertainty in Camera Calibration. Int J Comput Vis (2021). https://doi.org/10.1007/s11263-021-01528-x

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Keywords

  • Camera calibration
  • Uncertainty
  • Systematic errors
  • Bias
  • Computer vision