Image plane
Image plane
Centre of
projection
f
(a) Perspective
(b) Affine
Figure 10.6 Perspective and affine camera models
10.4.1 Affine camera model
In the affine camera model, Equation 10.21 is changed to
⎡
⎣
x
i
y
i
1
⎤
⎦
=
⎡
⎣
p
11
p
12
p
13
p
14
p
21
p
22
p
23
p
24
0001
⎤
⎦
⎡
⎢
⎢
⎣
x
p
y
p
z
p
1
⎤
⎥
⎥
⎦
(10.38)
This equation can be written in short form as
x
i
=P
A
x
p
(10.39)
Here, we use the subindex A to indicate that the affine camera transformation is given by a
special form of the projection P. The last row in Equation 10.39 can be omitted. It is shown in
the notation to emphasize that it is a special case of the perspective model. However, unlike the
case for perspective camera, points in the image plane are in Euclidean coordinates. That is, the
affine camera maps points from the projective space to the Euclidean plane.
Appendix 2: Camera geometry fundamentals 365
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