Two View Geometry

There are two cases of distinct viewpoint which are often treated separately, but have much in common:

• Stereo: two images acquired simultaneously.
• Motion: two images acquired sequentially.

There are three intertwined goals:

1. Recovery of 3D structure
   Recover the 3D position of scene structure from corresponding points in the two images.

2. Motion Recovery
   Compute the motion (rotation and translation) of the camera between the two views.

3. Correspondence
   Compute points in both images corresponding to the same 3D point.

Here we concentrate on the third point. In particular we will answer the question: given a point in one image, where does the corresponding point in the second image lie? It will be shown that for images of rigid scenes this question can be answered very simply and precisely. There are two cases: first, for images of points on a ``known'' plane, the corresponding point is uniquely determined; second, for any image point the corresponding point is constrained to lie on a line (an epipolar line). In both cases these constraints can be computed from image correspondences directly, without requiring camera calibration.