Self-calibration of a General Radially Symmetric Distortion Model

  • Jean-Philippe Tardif
  • Peter Sturm
  • Sébastien Roy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3954)


We present a new approach for self-calibrating the distortion function and the distortion center of cameras with general radially symmetric distortion. In contrast to most current models, we propose a model encompassing fisheye lenses as well as catadioptric cameras with a view angle larger than 180°.

Rather than representing distortion as an image displacement, we model it as a varying focal length, which is a function of the distance to the distortion center. This function can be discretized, acting as a general model, or represented with e.g. a polynomial expression.

We present two flexible approaches for calibrating the distortion function. The first one is a plumbline-type method; images of line patterns are used to formulate linear constraints on the distortion function parameters. This linear system can be solved up to an unknown scale factor (a global focal length), which is sufficient for image rectification. The second approach is based on the first one and performs self-calibration from images of a textured planar object of unknown structure. We also show that by restricting the camera motion, self-calibration is possible from images of a completely unknown, non-planar scene.

The analysis of rectified images, obtained using the computed distortion functions, shows very good results compared to other approaches and models, even those relying on non-linear optimization.


Interest Point Optical Center View Angle Camera Model Distortion Function 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jean-Philippe Tardif
    • 1
  • Peter Sturm
    • 2
  • Sébastien Roy
    • 1
  1. 1.DIROUniversité de MontréalCanada
  2. 2.INRIA Rhône-AlpesMontbonnot St MartinFrance

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