Databases Reference
In-Depth Information
T A B L E 10 . 5
Progression of codebooks
using splitting.
Codebook
Height
Weight
One-level
62
127
Initial two-level
62
127
72
137
Final two-level
58
98
69
168
Initial four-level
58
98
68
108
69
168
79
178
Final four-level
52
73
62
116
65
156
71
176
Example10.4.2:
Let's revisit Example
10.4.1
. This time, instead of using the initial codewords used in Example
10.4.1
, we will use the splitting technique. For the perturbations, we will use a fixed vector
=
(
. The perturbation vector is usually selected randomly; however, for purposes of
explanation it is more useful to use a fixed perturbation vector.
We begin with a single-level codebook. The codeword is simply the average value of the
training set. The progression of codebooks is shown in Table
10.5
.
The perturbed vectors are used to initialize the LBG design of a two-level vector quantizer.
The resulting two-level vector quantizer is shown in Figure
10.11
. The resulting distortion
is 468.58. These two vectors are perturbed to get the initial output points for the four-level
design. Using the LBG algorithm, the final quantizer obtained is shown in Figure
10.12
.
The distortion is 156.17. The average distortion for the training set for this quantizer using
the splitting algorithm is higher than the average distortion obtained previously. However,
because the sample size used in this example is rather small, this is no indication of relative
merit.
10
,
10
)
If the desired number of levels is not a power of two, then in the last step, instead of
generating two initial points from each of the output points of the vector quantizer designed
previously, we can perturb as many vectors as necessary to obtain the desired number of
vectors. For example, if we needed an eleven-level vector quantizer, we would generate a
one-level vector quantizer first, then a two-level, then a four-level, and then an eight-level
vector quantizer. At this stage, we would perturb only three of the eight vectors to get the
eleven initial output points of the eleven-level vector quantizer. The three points should be
those with the largest number of training set vectors, or the largest distortion.
