International Journal of Computer Vision

, Volume 9, Issue 2, pp 137–154

Shape and motion from image streams under orthography: a factorization method

  • Carlo Tomasi
  • Takeo Kanade

DOI: 10.1007/BF00129684

Cite this article as:
Tomasi, C. & Kanade, T. Int J Comput Vision (1992) 9: 137. doi:10.1007/BF00129684


Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step.

An image stream can be represented by the 2F×P measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3.

Based on this observation, the factorization method uses the singular-value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a partially filled-in measurement matrix that may result from occlusions or tracking failures.

The method gives accurate results, and does not introduce smoothing in either shape or motion. We demonstrate this with a series of experiments on laboratory and outdoor image streams, with and without occlusions.

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Carlo Tomasi
    • 1
  • Takeo Kanade
    • 2
  1. 1.Department of Computer ScienceCornell UniversityIthaca
  2. 2.School of Computer ScienceCarnegie Mellon UniversityPittsburgh

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