Multiple Interpretations of the Shape and Motion of Objects from Two Perspective Images

Shahriar Negahdaripour

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The following problem is investigated: given the position coordinates in two images of all points on an object obtained from two different camera positions, under what conditions can there be more than one interpretation for the shape of the object and the transformation between the coordinate systems at the two camera positions? It is shown that only certain hyperboloids of one sheet and their degeneracies, such as hyperbolic paraboloids, circular cylinders, and intersecting planes, that are viewed from a point on their surface can give rise to an ambiguity. In the case of hyperboloids of one sheet and hyperbolic paraboloids, there can be three possible solutions. In the case of circular cylinders and intersecting planes, there are at most two solutions. The author gives the relationship among the multiple interpretations and determines them all in closed form in terms of the true solution.

Original languageEnglish (US)
Pages (from-to)1025-1039
Number of pages15
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number11
StatePublished - Nov 1990
Externally publishedYes


  • Absolute and relative orientation
  • conjugate pairs
  • correspondences
  • eigenvalue/eigenvector decomposition
  • motion field
  • motion vision
  • photogrammetry
  • quadrics

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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