Direct Passive Navigation

Shahriar Negahdaripour, Berthold K. Horn

Research output: Contribution to journalArticlepeer-review

154 Scopus citations


The authors show how to recover the motion of an observer relative to a planar surface from image brightness derivatives. They compute the spatial and temporal brightness gradients (at a minimum of eight points). Two iterative schemes for solving nine nonlinear equations in terms of the motion and surface parameters that are derived from a least-squares formulation are presented. An initial pass over the relevant image region is used to accumulate a number of moments of the image brightness derivatives. All of the quantities used in the iteration are efficiently computed from these totals without the need to refer back to the image. 10 refs.

Original languageEnglish (US)
Pages (from-to)168-176
Number of pages9
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number1
StatePublished - Jan 1987
Externally publishedYes


  • Eigenvalue decomposition
  • least-squares
  • optical flow
  • planar surfaces
  • structure and motion

ASJC Scopus subject areas

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


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