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The geometry of a pinhole camera. Note: the x 1 x 2 x 3 coordinate system in the figure is left-handed, that is the direction of the OZ axis is in reverse to the system the reader may be used to. The geometry related to the mapping of a pinhole camera is illustrated in the figure. The figure contains the following basic objects:
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Epipolar constraints can also be described by the fundamental matrix, [1] or in the case of noramlized image coordatinates, the essential matrix [2] between the two cameras. If the points x L and x R are known, their projection lines are also known. If the two image points correspond to the same 3D point X the projection lines must intersect ...
A light ray enters a component crossing its input plane at a distance x 1 from the optical axis, traveling in a direction that makes an angle θ 1 with the optical axis. After propagation to the output plane that ray is found at a distance x 2 from the optical axis and at an angle θ 2 with respect to it.
A 3D point x is projected onto two camera images through lines (green) which intersect with each camera's focal point, O 1 and O 2. The resulting image points are y 1 and y 2. The green lines intersect at x. In practice, the image points y 1 and y 2 cannot be measured with arbitrary accuracy. Instead points y' 1 and y' 2 are detected and used ...
The camera matrix derived in the previous section has a null space which is spanned by the vector = This is also the homogeneous representation of the 3D point which has coordinates (0,0,0), that is, the "camera center" (aka the entrance pupil; the position of the pinhole of a pinhole camera) is at O.