MOTION FROM POINT MATCHES - MULTIPLICITY OF SOLUTIONS

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. © 1990 Kluwer Academic Publishers.