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2014/01/29(…) 19:22:25.87 ID:6HhTafK0o
2.3.3. Separability
The DCT transform equation (4) can be expressed as,
( ) () ()‡” ‡” ( ) |
=
|
=




+




+ =
1
0
1
0 2
(2 1) , cos 2
(2 1) , cos
N
x
N
y N
y v f x y N
x u C u v u v ƒÎ ƒÎ
ƒ¿ ƒ¿ , (6)
for uv N , 0,1,2, , 1 = c | .
This property, known as separability, has the principle advantage that C(u, v) can be computed in
two steps by successive 1-D operations on rows and columns of an image. This idea is
graphically illustrated in Figure 8. The arguments presented can be identically applied for the
inverse DCT computation (5).


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