8-point algorithm for computing the fundamental matrix with more than 8 matches

Question

Does the 8 point algorithm have to be computed with only 8 matches?

Say I have n > 8 matches. When trying to solve the equations system in order to compute the fundamental matrix F, do I have to select a subset of 8 points for building A or could I create the matrix A of n rows and then solve the SVD with the bigger A.

Would decomposing the SVD of the bigger A be even any better? Or would it be even worse?

Thanks

I checked the Multiple View Geometry book chapter 11. And while they do a brief discussion about the fact that the rank of the A matrix corresponds to a unique solution when it is 8, but I can't seem to find whether they discuss this exact point.

Thanks

Answer 1

The more matches the better, as the solution will be more robust against outliers (bad matches) and noise in the estimated locations.

With more than 8 matches you simply have an over-determined system of equations, which can be solved using the least squares solution.

The SVD for the matrix representing this system of equations will give you the least squares solution, so you don’t even need to change your code…