Page 223 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

212 FEATURE EXTRACTION AND SELECTION

Example 6.4 License plate recognition (continued)
In the license plate application, discussed in Example 6.2, the
measurement space (consisting of 15 11 bitmaps) is too large with
respect to the size of the training set. Linear feature extraction based
on maximization of the inter/intra distance reduces this space to at
most D max ¼ K 1 ¼ 35 features. Figure 6.10(a) shows how the
inter/intra distance depends on D. It can be seen that at about
D ¼ 24 the distance has almost reached its maximum. Therefore, a
reduction to 24 features is possible without losing much information.
Figure 6.10(b) is a graphical representation of the transformation
matrix W. The matrix is 24 165. Each row of the matrix serves as a
vector on which the measurement vector is projected. Therefore, each
row can be depicted as a 15 11 image. The figure is obtained by
means of MATLAB code that is similar to Listing 6.3.

Listing 6.3
PRTools code for creating a linear feature extractor based on maximiza-
tion of the inter/intra distance. The function for calculating the mapping
is fisherm. The result is an affine mapping, i.e. a mapping of the
type Wz þ b. The additive term b shifts the overall mean of the features
to the origin. In this example, the measurement vectors come directly
from bitmaps. Therefore, the mapping can be visualized by images. The
listing also shows how fisherm can be used to get a cumulative plot of
J INTER/INTRA , as depicted in Figure 6.10(a). The precise call to fisherm
is discussed in more detail in Exercise 5.

(a) (b)

250 50
200 J INTER/INTRA 40
150 30
100 20
γ
50 D 10
0 0
0 10 20 30 40 50
D

Figure 6.10 Feature extraction in the license plate application. (a) The inter/intra
distance as a function of D. (b) First 24 eigenvectors in W depicted as 15 11 pixel
images