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Image and Video Compression
book

Image and Video Compression

by Madhuri A. Joshi, Mehul S. Raval, Yogesh H. Dandawate, Kalyani R. Joshi, Shilpa P. Metkar
November 2014
Intermediate to advanced content levelIntermediate to advanced
236 pages
7h 4m
English
CRC Press
Content preview from Image and Video Compression
33Image Transforms
Now,
=
=
=
π
=
π
N
Fuve fuy
N
fuye
v
N
j
N
vy
u
N
j
N
ux
1
(,)(,)(Intermediateresult)
1
(,)(Finalresult)
0
1
2
0
1
2
3.4.2 Translation
A 2D image f(x,y) is translated by (x
0
,y
0
) to form the translated version f(x x
0
,
y y
0
). Let the Fourier transform of this version be
F
uv
tran
s
,
:
F
N
fx xyye
N
fx xyye e
uv
trans
x
N
y
N
j
N
ux xvyy
x
N
y
N
j
N
ux vy j
N
ux vy
1
(,)
1
(,)
,
0
1
0
1
00
2
[( )( )]
0
1
0
1
00
2
()
2
()
00
00
∑∑
∑∑
=−
=−
=
=
π
−+
=
=
π
+−
π
+
FFuve
uv
trans
j
N
ux vy
(,)
,
2
()
00
=
π
+
fx xyyFuve
j
N
ux vy
(,)(,)
00
2
()
00
∴− −→
π
+
(3.18)
For the inverse Fourier transform,
Fu uv vfxye
j
N
ux vy
()(,)
0,0
2
()
00
−−
π
+
(3.19)
It can be seen from Equations (3.18) and (3.19) that translating the origin i ...
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Publisher Resources

ISBN: 9781482228229