November 2014
Intermediate to advanced
236 pages
7h 4m
English
book
Image and Video Compression
by Madhuri A. Joshi, Mehul S. Raval, Yogesh H. Dandawate, Kalyani R. Joshi, Shilpa P. Metkar
Content preview from Image and Video Compression
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38 Image and Video Compression
where g(:) and h(:) represent the forward and the reverse kernel in the trans-
formation. In the case of the DCT,
gxyuvuv
xu
N
yv
N
hxyuv(,,,)()()cos
21
2
cos
21
2
(,,,)
()
()
=α α
+π
+π
=
Therefore, forward and reverse kernels are identical. They are also symmet-
ric and separable. Then
uv()()αα
denes the constant for DCT. Formally, the
forward DCT is dened as
Cuvuvfxy
xu
N
yv
N
uv N
xy
N
xy
N
(,)()()(,)cos
(2 1)
2
cos
(2 1)
2
;0
,1
,0
1
,0
1
∑∑
=α α
+π
×
+π
≤≤−
=
−
=
−
(3.28)
Similarly, the inverse DCT is dened as
fxyuvCuv
xu
N
yv
N
uv N
uv
N
uv
N
(,)()()(,)cos
(2 1)
2
cos
(2 1)
2
;0
,1
,,0
1
,0
1
∑∑
=αα
+π
×
+π
≤≤−
=
−
=
−
(3.29)
where
u
N
u()
1
;0
α= =
and
v
N
uN
()
2
;1,2,, 1α= =…−
The forward and ...
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