- An image point
back projects to a ray defined by
and the camera center.
**Calibration relates the image point to the ray's direction**. - Suppose points on the ray are written as
in the camera Euclidean frame. Then these points map to the point
- Thus,
is the (affine) transformation between
and the ray's direction
measured
in the cameras Euclidean frame.
- The angle between two rays
and
corresponding
to image points
and
may be obtained as
(by the cosine formula)
- The above shows that if
is known (
*camera is calibrated*), then the angle between rays can be computed from their corresponding image points.*A calibrated camera is like a 2D protractor*. - An image line
defines a plane through the camera center
with normal direction
.
*Proof*. Points on back projects to directions which are orthogonal to the plane normal. Hence, . Since points on satisfy we have that .

Subhashis Banerjee 2008-01-20