Motion from point matches: Multiplicity of solutions
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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.
• 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.
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- Motion from point matches: Multiplicity of solutions
International Journal of Computer Vision
Volume 4, Issue 3 , pp 225-246
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