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196 8. Computer Vision in VR
Figure 8.10. Perspective distortion using points in a different plane results in a differ-
ent correction.
of them, say h
22
= 1. Thus for points (X
i
, Y
i
); 0 ≤ i ≤ 3 and their matches
(X
mi
, Y
mi
); 0 ≤ i ≤ 3, we get the linear equations
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
X
0
Y
0
10 00−X
0
X
m0
−Y
0
X
m0
000X
0
Y
0
1 −Y
m0
X
0
−Y
m0
Y
0
X
1
Y
1
10 00−X
1
X
m1
−Y
1
X
m
000X
1
Y
1
1 −Y
m1
X
1
−Y
m1
Y
1
X
2
Y
2
10 00−X
2
X
m2
−Y
2
X
m2
000X
2
Y
2
1 −Y
m2
x
2
−Y
m2
Y
2
X
3
Y
3
10 00−X
3
X
m3
−Y
3
X
m3
000X
3
Y
3
1 −Y
m3
X
3
−Y
m3
Y
3
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
h
00
h
01
h
02
h
10
h
11
h
12
h
20
h
21
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
=
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
X
m0
Y
m0
X
m1
Y
m1
X
m2
Y
m2
X
m3
Y
m3
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
.
(8.4)
This simple-looking (and first-guess) method to determine H, and with
it the ability to correct ...