Suppose we have a dataset $D = \{p_1, \dots, p_N\}$. Each $p_i$ is an ordered pair. Our objective is to fit a line with parameters $\theta = (m, b)$. For a homography, our parameters are $\theta = H, \|h\| = 1$. This is a least squares problem of the form $\|y - (mx+ b)\|^2$.
If the two cameras are on the same $x$-axis, then we can simplify our model.
Special case: cameras are parallel to each other. Both cameras have the same $Y$ coordinates, but different $X$ coordinates. Without loss of generality, suppose the origin is at the pinhole of the first camera.
$$ x_1 = \frac{X}{Z}, x_2 = \frac{X + t_x}{Z}\\ y_1 = \frac{Y}{Z}, y_2 = \frac{Y}Z{} $$
Notice that the $X$ coordinates differ by $t_x / Z$, which is proportional to the depth of the object. We call $t_x$ the baseline, and $t_x / Z$ the disparity.
Our correspondence problem is also much easier because we only have to search along a particular row. This approach is called plane sweep stereo.
Computing NCC volume
Now suppose we have two cameras that are not parallel. How do we align the images form the cameras? Then we can relate the images as