Image Processing Reference
In-Depth Information
Therefore,
D
1
¼ X
1
X
3
X
4
f
X
5
g D
2
¼
{X
2
}
The total average distortion is
0
þ
0
þ
4
:
123
þ
2
þ
3
:
605
D ¼
¼
1
:
9456
5
The new reconstruction vectors are computed as
2
4
3
5
2
4
3
5
0
1
2
X
1
þ
X
3
þ
X
4
þ
X
5
4
r
1
¼
¼
0
:
5
r
2
¼ X
2
¼
1
:
5
2
Classifying the training vectors with new centroid results in
kX
1
r
1
k¼
1
:
8708,
kX
1
r
2
k¼
5
:
656
! X
1
2 D
1
kX
2
r
1
k¼
4
:
415,
kX
2
r
2
k¼
0
! X
2
2 D
2
kX
3
r
1
k¼
2
:
549,
kX
3
r
2
k¼
4
:
123
! X
3
2 D
1
kX
4
r
1
k¼
1
:
2247,
kX
4
r
2
k¼
4
:
472
! X
4
2 D
1
kX
5
r
1
k¼
2
:
915,
kX
5
r
2
k¼
5
:
385
! X
5
2 D
1
Therefore,
D
1
¼ X
1
X
3
X
4
f
X
5
g D
2
¼
{X
2
}
The total average distortion is
1
:
8708
þ
0
þ
2
:
549
þ
1
:
2247
þ
2
:
915
D ¼
¼
1
:
7119
5
The new reconstruction vectors are
2
4
3
5
2
4
3
5
0
1
2
X
1
þ
X
3
þ
X
4
þ
X
5
4
r
1
¼
¼
0
:
5
r
2
¼ X
2
¼
1
:
5
2
Carrying out one more iteration does not change the overall average distortion.
The K-means algorithm is locally optimal and there is no guarantee that it will
converge to the global optimal solution. It is also very slow because for every
iteration, all the vectors in the data base are compared with each codeword vector.
There are other algorithms, such as pairwise nearest neighbor and simulated anneal-
ing for VQ design, that are faster than K-means algorithm.
An important application of VQ is image data compression. Image data com-
pression using VQ is a lossy compression technique. Once the codebook has been
designed, the uncompressed image is divided into blocks and each block is converted
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