8 point algorithm for estimating Fundamental Matrix

Question

I'm watching a lecture about estimating the fundamental matrix for use in stereo vision using the 8 point algorithm. I understand that once we recover the fundamental matrix between two cameras we can compute the epipolar line on one camera given a point on the other. To my understanding this epipolar line (after it's been rectified) makes it easy to find feature correspondences, because we are simply matching features along a 1D line.

The confusion comes from the fact that 8-point algorithm itself requires at least 8 feature correspondences to estimate the Fundamental Matrix.

So, we are finding point correspondences to recover a matrix that is used to find point correspondences?

This seems like a chicken-egg paradox so I guess I'm misunderstanding something.

Answer 1

The fundamental matrix can be precomputed. This leads to two advantages:

1. You can use a nice environment in which features can be matched easily (like using a chessboard) to compute the fundamental matrix.
2. You can use more computationally expensive operations like a sequence of SIFT, FLANN and RANSAC across the entire image since you only need to do that once.

After getting the fundamental matrix, you can find correspondences in a noisy environment more efficiently than using the same method when you compute the fundamental matrix.