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Motion And Structure from Motion in a Piecewise Planar Environment

Author: Faugeras

Year: 1988

Notes:

  • camera is moving in a static environment
  • for points in a same plane, the transformation is a homography
  • We can get plane equation and motion from homography
  • theorem: $$ H_{12} = \alpha R + t n^T $$
  • 8 solutions to this equation according to the multiplicity of the singular values of H:
    • if 3 distinct values : 8 solutions
    • if 2 distinct values : 4 solutions
    • else it is undefined
  • Degenerate cases:
    • No translation
    • translation orthogonal to plane