= 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.<Epipolar Geometry in the OpenCV-Python tutorials>[Basic Concepts, diagram of the baseline, scene point and epipolar 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>.
Back to article page
