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Camera Models16-385 Computer Vision (Kris Kitani)
Carnegie Mellon University
What’s the difference between these two images?
What’s the difference between these two images?
Different imaging conditions induce different projections
Camera is close to object
small focal length
Camera is far from object
large focal length
There are many types of camera models (projections)
CCD camera
P =
2
4↵x
0 px
0 ↵y
py
0 0 1
3
5
2
41 0 0 00 1 0 00 0 1 0
3
5
How many degrees of freedom?
(assuming that axes are aligned)
CCD camera
10 DOF
P =
2
4↵x
0 px
0 ↵y
py
0 0 1
3
5
2
41 0 0 00 1 0 00 0 1 0
3
5
How many degrees of freedom?
(assuming that axes are aligned)
Finite projective camera
P =
2
4↵x
s px
0 ↵y
py
0 0 1
3
5
2
41 0 0 00 1 0 00 0 1 0
3
5
(assuming that axes are aligned)
How many degrees of freedom?
Finite projective camera
11 DOF
P =
2
4↵x
s px
0 ↵y
py
0 0 1
3
5
2
41 0 0 00 1 0 00 0 1 0
3
5
(assuming that axes are aligned)
How many degrees of freedom?
Orthographic camera (parallel projection)
Image World
(assuming that axes are aligned)
P = K
2
41 0 0 00 1 0 00 0 0 1
3
5
Orthographic camera (parallel projection)
Image World
(assuming that axes are aligned)
P = K
2
41 0 0 00 1 0 00 0 0 1
3
5Affine camera
Weak Perspective Camera
(assuming that axes are aligned)
P = K
2
41 0 0 00 1 0 00 0 0 Z̄
3
5
When can you assume a weak perspective camera model?
When can you assume a weak perspective camera model?
all the mountains are roughly ‘far away’
Weak Perspective Camera
(assuming that axes are aligned)
P = K
2
41 0 0 00 1 0 00 0 0 Z̄
3
5Affine camera
Perspective vs Weak Perspective Projection
Weak perspective
Perspective
X
�
Z̄fC