Abstract
In this article, 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 five point matches are available. This settles a question which has been around in the Computer Vision community for a while. We present two approaches:
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the first one is based on algebraic geometry has been developed by Demazure [Dem88]. We show that it provides a very simple answer to the multiplicity of solutions when more than 5 point matches are available, namely not more than 3.
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the second one is based on projective geometry and is based on the work of Kruppa [Kru13]. We correct Kruppa's result and show that it is compatible with Demazure's.
We then describe a computer implementation of the second approach that uses MAPLE, a language for symbolic computation. The program allows us to exactly compute the solutions for any configurations of 5 points. Some preliminary experiments are described.
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© 1989 Springer-Verlag Berlin Heidelberg
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Faugeras, O.D., Maybank, S. (1989). Motion from point matches: multiplicity of solutions. In: Boissonnat, J.D., Laumond, J.P. (eds) Geometry and Robotics. GeoRob 1988. Lecture Notes in Computer Science, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51683-2_30
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DOI: https://doi.org/10.1007/3-540-51683-2_30
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