International Journal of Computer Vision

, Volume 4, Issue 3, pp 225–246

Motion from point matches: Multiplicity of solutions

  • Olivier D. Faugeras
  • Steve Maybank

DOI: 10.1007/BF00054997

Cite this article as:
Faugeras, O.D. & Maybank, S. Int J Comput Vision (1990) 4: 225. doi:10.1007/BF00054997


In this paper, we study the multiplicity of solutions of the motion problem. Given n point matches between two frames, how many solutions are there to the motion problem? We show that the maximum number of solutions is 10 when 5 point matches are available. This settles a question that has been around in the computer vision community for a while. We follow two tracks.
  • • The first one attempts to recover the motion parameters by studying the essential matrix and has been followed by a number of researchers in the field. A natural extension of this is to use algebraic geometry to characterize the set of possible essential matrixes. We present some new results based on this approach.

  • • The second question, based on projective geometry, dates from the previous century.

We show that the two approaches are compatible and yield the same result.

We then describe a computer implementation of the second approach that uses MAPLE, a language for symbolic computation. The program allows us to compute exactly the solutions for any configuration of 5 points. Some experiments are described.

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Olivier D. Faugeras
    • 1
  • Steve Maybank
    • 2
  1. 1.INRIAValbonne CedexFrance
  2. 2.Hirst Research CenterWembleyEngland