Epipolar

Epipolar refers to a concept in stereo vision and multi-view geometry describing the geometric relationship between two camera views of a scene. For any 3D point in the scene, its projections in the two images lie on corresponding lines called epipolar lines. The intersection of the two imaging planes with the line through the two camera centers defines the epipole in each image. The epipolar constraint means that a point in one image can correspond only to points along its epipolar line in the other image; this reduces the correspondence problem from two dimensions to one.

In matrix form, the correspondence between image points x in the first image and x' in the second satisfies x'^T F x = 0, where F is the fundamental matrix for uncalibrated cameras. If the cameras are calibrated, the essential matrix E relates normalized image points by x'^T E x = 0, with E = [t]_x R, encoding the rotation R and translation t between the cameras. Epipolar geometry also defines the epipolar plane, the plane containing the two camera centers and a 3D point; its intersections with the image planes are the epipolar lines.

Practical uses include stereo rectification to align images so that epipolar lines become parallel, typically horizontal, which simplifies correspondence search. Epipolar geometry underpins depth estimation, 3D reconstruction, camera calibration, and numerous computer vision tasks involving multiple views.