Motion from point matches: multiplicity of solutions

The authors study the multiplicity of solutions of the motion problems. Given n point matches between two frames, an effort is made to determine the number of solution to the motion problem. It is shown that the maximum number of solutions is ten when five-point matches are available. Two approaches are used. The first attempts to recover the motion parameters by studying the essential matrix. A natural extension of this is to use algebraic geometry to characterize the set of possible essential matrixes. The authors present some results based on this approach. The second one, based on projective geometry, dates from the previous century. The authors show that the two approaches are compatible and yield the same result. They then describe a computer implementation of the second approach that uses MAPLE, a language for symbolic computation. The program allows the exact computation of the solutions for any configuration of five points