
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
denes the constant for DCT. Formally, the
forward DCT is dened as
Cuvuvfxy
N
yv
N
uv N
xy
N
xy
N
(,)()()(,)cos
(2 1)
2
cos
(2 1)
2
;0
,0
1
,0
1
∑∑
=α α
×
+π
≤≤−
=
−
=
−
(3.28)
Similarly, the inverse DCT is dened as
fxyuvCuv
N
yv
N
uv N
uv
uv
(,)()()(,)cos
(2 1)
2
cos
(2 1)
2
;0
,,0
,0
∑∑
=αα
×
+π
≤≤−
=
−
=
−
(3.29)
where
u
u()
1
α= =
and
v
N
()
2
;1,2,, 1α= =…−
The forward and ...