Full pinhole model
The composition of transformations
,
and
may be summarized by the equation shown in Figure 3.
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That leads to the equation of the pinhole camera model:
with:
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where
and
represent the focal length of the camera in pixels along directions
and
respectively.
The five parameters
of the matrix
are called intrinsic parameters of the camera.
In the end, the pinhole camera model is described by five intrinsic parameters
and six extrinsic parameters (three for the rotation and three for the translation).
In the case of a neglected “skew factor”, the pinhole camera model, which binds 3D coordinates
of a point written in the world reference frame with 2D coordinates
of its projection in the image-point (image point= pixel), is often described as below:
We sometimes refer to this relation as colinearity relations.