Epipolar Geometry

Consider the general case in which we do not have parallel optical axes. Given a point $p$ in the left image, where can the corresponding point $p'$ be in the right image?

Stereo correspondence constraints

In perspective projection, lines project into lines.

So the line containing the center of projection and the point $p$ in the left image must project to a line in the right image.

Epipolar Constraint

Geometry of two views constraints where the corresponding pixel for some image point in the first view must occur in the second view.

Epipolar geometry: Terms

• Baseline: lien joining the camera centers
• Epiploar plane: plane containing baseline and world point
• Epipolar line: intersection of epipolar plane with the image plane - come in pairs
• Epipole: point of intersection of baseline with image plane.

The epipolar constraint reduces the "correspoindence problem" into a 1D search across an epipolar line