• Corpus ID: 6428666

On Ullman's theorem in computer vision

@article{Knill2007OnUT,
  title={On Ullman's theorem in computer vision},
  author={Oliver Knill and Jose Ramirez-Herran},
  journal={ArXiv},
  year={2007},
  volume={abs/0708.2438}
}
Both in the plane and in space, we invert the nonlinear Ullman transformation for 3 points and 3 orthographic cameras. While Ullman's theorem assures a unique reconstruction modulo a reflection for 3 cameras and 4 points, we find a locally unique reconstruction for 3 cameras and 3 points. Explicit reconstruction formulas allow to decide whether picture data of three cameras seeing three points can be realized as a point-camera configuration. 
Space and camera path reconstruction for omni-directional vision
TLDR
The structure from motion results give sharp conditions under which the reconstruc-tion is unique, and the reconstruction problem for ori-ented omni-directional cameras, spherical cameras for which the reconstruction is particularly convenient.
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