Uncalibrated Reconstruction of
Curved Surfaces

Jun Sato and Roberto Cipolla
Department of Engineering
University of Cambridge
Cambridge CB2 1PZ, UK.
js2@eng.cam.ac.uk, cipolla@eng.cam.ac.uk

Abstract:

In this paper, we show that even if the camera is uncalibrated, and its translational motion is unknown, curved surfaces can be reconstructed from their apparent contours up to a 3D affine ambiguity. Furthermore, we show that even if the reconstruction is non-metric (non-Euclidean), we can still extract useful information from the reconstruction for many computer vision applications, such as distinguishing curved surfaces from fixed features and computing the time-to-contact to the curved surfaces.

• Introduction
• Camera Model
• Epipolar Geometry under Pure Translation
• Affine Reconstruction of Curved Surfaces
  • Epipolar Parameterisation
  • 3D Motion and Image Velocity and Acceleration
  • Camera Motion from Frontier Points
  • Recovery of Surface Depth
  • Recovery of Curved surfaces
  • Distinction of Apparent Contours
  • Time-to-contact to curved surfaces
• Experiments
  • Reconstruction of curved surfaces
  • Distinction of Apparent Contours
  • Computation of time-to-contact
• Discussion and Conclusions
• Acknowledgements
• References
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