Structure From Motion
If we have two cameras whose parameters we don’t know, can we recover camera location and orientation without a calibration object in order to recover the 3D world?
Recall that $\mathbf{q}^TF\mathbf{p} = 0$. In order to find $F$, we can use an 8-point algorithm.
Suppose $\mathbf{p} = \begin{bmatrix}x_1 \\ y_1 \\ 1\end{bmatrix}$ and $\mathbf{q} = \begin{bmatrix}x_2 \\ y_2 \\ 1\end{bmatrix}$ correspond to the same 3D point. Then, we have a linear system of equations with the entries of $F$ as coefficients.
Since this gives us one equation, we can find eight points which give us eight equations represented as $A\mathbf{f} = \mathbf{0}$. To solve this we want to find $\mathbf{f}$ that minizes $|A\mathbf{f}|$. Additionally, we need $F$ to have rank less than $3$ (not full rank). In order to do this, we can just do singular value decomposition.
Correspondence Outliers
Sometimes, with correspondence, there were matches which were wrong. They were not a few pixels off but completely wrong.
One way of finding a line of best fit is RANSAC. The algorithm consists of randomly sampling two points, fitting a line and counting how many points lie close to the line. This is repeated, and the line with the most inliers is chosen.