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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