 Epipolar plane

An epipolar plane contains both camera centers and a scene point. For a scene point away from the camera baseline, these three points determine a unique plane. Its intersection with each image plane is an epipolar line, so corresponding image points lie on the two traces of the same plane.^[ref]

To see the geometry directly, take camera centers $C_L=(0,0,0)$ and $C_R=(B,0,0)$, and a scene point $P=(X,Y,Z)$. The plane they span satisfies $Zy-Yz=0$. For parallel forward-facing image planes at common focal length $f$, its traces have $y=fY/Z$ in both views. This is why an ideal horizontal stereo pair places corresponding image points on the same row.

Moving the scene point within that plane leaves its epipolar lines unchanged. A single trace therefore cannot recover depth. If the scene point lies on the baseline, the three defining points are collinear and no unique epipolar plane is determined. These degeneracies explain both the usefulness and the limits of line-based stereo correspondence.