, Volume 4, Issue 3, pp 225-246

Motion from point matches: Multiplicity of solutions

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Abstract

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.

    This work was partially supported under ESPRIT contract P940.