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

Published

Journal Article

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. © 1992 Kluwer Academic Publishers.

Full Text

Duke Authors

Cited Authors

  • Tomasi, C; Kanade, T

Published Date

  • January 1, 1992

Published In

Volume / Issue

  • 9 / 2

Start / End Page

  • 137 - 154

Electronic International Standard Serial Number (EISSN)

  • 1573-1405

International Standard Serial Number (ISSN)

  • 0920-5691

Digital Object Identifier (DOI)

  • 10.1007/BF00129684

Citation Source

  • Scopus