Five-point motion estimation made easy

Estimating relative camera motion from two calibrated views is a classical problem in computer vision. The minimal case for such problem is the so-called five-point problem, for which the state-of-the-art solution is Nistér's algorithm [1][2]. However, due to the heuristic nature of the procedures it applies, to implement it needs much effort for non-expert user. This paper provides a simpler algorithm based on the hidden variable resultant technique. Instead of eliminating the unknown variables one by one (i.e, sequentially) using the Gauss-Elimination as in [1], our algorithm eliminates many unknowns at once. Moreover, in the equation solving stage, instead of back-substituting and solve all the unknowns sequentially, we compute the minimal singular vector of the coefficient matrix, by which all the unknown parameters can be estimated simultaneously. Experiments on both simulation and real images have validated the new algorithm.