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Optimal Camera Calibration with Statistical Model Selection

Utilizing the Information Theoretic Criterion (AIC) for camera calibration to select the best model while minimizing parameters. Avoid over-parameterization for reliable estimates, with a focus on distortion complexities. Statistical inference based on Fisher's distribution aids in model selection. Three hypotheses are tested for distortion types. Various models are evaluated using AIC and model selection. Real wide-angle data is examined, implementing AIC for different criteria.

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Optimal Camera Calibration with Statistical Model Selection

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  1. Information Thoretic Criterion (AIC) and Camera Calibration

  2. G. Wei, K. Arbter, G. Hirzinger, “Active self-calibration of robotic eyes and hand-eye relationships with model identification,” IEEE Transaction Robotics and Automation, vol. 14(1), pp. 158-166, Feb. 1998. • Statistical inference based on Fisher’s distribution. • Select the best model to describe a problem while minimizing the number of parameters. Increase the reliability of the estimated parameters. • Avoid over-parameterization which can increase variance. • Three hypotheses are tested based on distortion parameters complexity (total of two tangential coefficients and one radial coefficient): • Without radial and tangential distortion. • Without tangential distortion but with radial distortion. • With both radial and tangential distortion.

  3. M. T. El-Melegy and A. A. Farag, “Nonmetric lens distortion calibration: closed-form solutions, robust estimation and model selection,” in Ninth IEEE Int. Conf. on Computer Vision, 2003. vol. 1, pp. 554-559, 13-16 Oct. 2003. • Geometric inference. • Criterion defined in terms of the fitness of the data to the model and the complexity of the model. • Complexity of the model is dependent on the number of lines used for distortion calibration and the number of points used. • Three models are tested with AIC and MDL on synthetic data: • Without distortion. • One radial distortion coefficient. • Two radial distortion coefficients.

  4. M, Ahmed and A. Farag, “Nonmetric Calibration of Camera Lens Distortion: Differential Methods and Robust Estimation,” in IEEE Transactions on Image Processing, vol. 14, Iss. 8, pp. 1215-1230, August 2005. • In the conclusion the authors plans are to incorporate statistical model selection.

  5. [Broaddus05] C. Broaddus, “Universal Geometric Camera Calibration with Statistical Model Selection,” Masters Thesis, Department of Electrical Engineering, The University of Tennessee, Knoxville, TN 2005. • Show results on real wide angle data and not just synthetic data. • Implement AIC for five model selection criterions (AIC MDL BIC SSD CAIC) others show it for only AIC and MDL. • AIC model is penalized only for the number of distortion coefficients. AIC model is not penalized for features found in the image (number of images and number of points).

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