On the Geometry of Visual Correspondence

  • Authors:

  • Cornelia Fermü/ller;Yiannis Aloimonos

  • Affiliations:

  • Computer Vision Laboratory, Center for Automation Research, University of Maryland, College Park, MD 20742-3275/ and Computational Vision and Active Perception Laboratory, Royal Institute of Tech ...;Computer Vision Laboratory, Center for Automation Research, University of Maryland, College Park, MD 20742-3275/ and Computational Vision and Active Perception Laboratory, Royal Institute of Tech ...

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

Image displacement fields—optical flow fields, stereodisparity fields, normal flow fields—due to rigid motion possessa global geometric structure which is independent of the scene inview. Motion vectors of certain lengthsand directions are constrained to lie on the imaging surface atparticular loci whose location and form depends solely on the 3Dmotion parameters. If optical flow fields or stereo disparity fieldsare considered, then equal vectors are shown to lie on conicsections. Similarly, for normal motion fields, equal vectors liewithin regions whose boundaries also constitute conics. By studying various properties of these curves and regions and theirrelationships, a characterization of the structure of rigid motionfields is given. The goal of this paper is to introduce a conceptunderlying the global structure of image displacement fields. This concept gives rise to various constraints that could form thebasis of algorithms for the recovery of visual information frommultiple views.