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Homework I
1.
(Camera models) For a camera, the image
x
of a point
X
in
space is given by:
PX
x
, with
x
and
X
homogeneous 3 and 4
vectors respectively.
(a) If
0
PC
, where
C
a homogeneous 4vector, show that
C
is the
camera center.
(b) The camera projection matrix
P
can be written as :
]

[
~
C
I
KR
P
,
where
K
is the calibration matrix,
R
the rotation between the
camera and world coordinate frames, and the camera center C is
expressed as
~
)
1
,
(
C
C
. Show that the calibration matrix can be
obtained from a RQ decomposition of the first 3X3 sub matrix of
the camera matrix P.
(c) In some application we obtained the following camera matrix:
1837
22
.
1
7
.
0
4
.
1
6325250
2
.
919
6
.
46
207
2898920
4
.
555
2
.
679
707
P
.
Find the camera center and the calibration parameters.
2.
(Affine and metric rectification) Consider the image posted in
the class web page. Read the image into matlab and use matlab to
perform the calculations necessary for the following questions:
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 Spring '08
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