Consider two images of a scene obtained by the same camera from different
position and orientation.
The images of the points at infinity, the vanishing points, are
not affected by the camera translation, but are affected only by the
camera rotation
.
Consider a scene line with vanishing point
in the
first view and
in the second.
The vanishing point
has a direction
in the
first cameras Euclidean frame, and, similarly, the vanishing
point
has a direction
in the second
cameras Euclidean frame. We have
The directions are related by
which represents two independent constraints on
.
Hence, the rotation matrix can be computed from two such corresponding
directions provided we know
.