Image Processing Reference
In-Depth Information
Therefore,
¼ p
00
þ tp
01
p
00
y
1
y
2
ð
Þ þ up
10
p
00
ð
Þ þ tu p
11
p
01
p
10
p
00
ð
Þ
þ
2
1
3
2
4
2
5
4
3
þ
2
3
:
6
¼
0
:
6
þ
0
:
5
þ
0
:
6
0
:
5
¼
4
1
2
1
5
2
4
þ
1
3
:
3
We next consider a trilinear interpolation of 3-D LUTs.
6.2.2 T
RILINEAR
I
NTERPOLATION
In the 3-D case, the underlying function is a function of three variables, f(x, y, z), and
the LUT is uniformly spaced in a 3-D lattice of N
M
L points. An example of
such a lattice for N
¼
M
¼
L
¼
4 is shown in Figure 6.6. As can be seen, there are a
total of 64 grid points uniformly spaced in the 3-D space.
Nowassumethatwehavea3-DLUTofsizeN
M
L grid points uniformly
spaced in the xyz 3-D space and would like to interpolate the grid point (x, y, z).
Let the surrounding eight points in the xyz plane be n
000
½
n
001
n
010
n
011
n
100
n
101
n
110
n
111
and the corresponding points in the f plane be p
000
½
p
001
p
010
, as shown in Figure 6.7. Let t, u,andv be the relative
distances from the plane and the axes, as shown in Figure 6.7.
p
011
p
100
p
101
p
110
p
111
z
y
x
FIGURE 6.6
Uniformly sampled lattice in 3-D space.
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