Page 145 - Introduction to Statistical Pattern Recognition

4 Parametric Classifiers 127

(0) (b)
Fig. 4-2 Relation between mi@) and gj(t).

Observed
at t=T
Filter No 1
g,(t) - 1 - X(t)€W,

C

Fig. 4-3 Block diagram of a matched filter classifier.

performs the same function as the correlation classifier, is shown in Fig. 4-3.
Again, the matched filter becomes the Bayes classifier with a proper threshold,
when the distributions are normal with the equal covariance I.

Distance Classifier

The correlation and matched filter classifiers are directly related to
another popular classifier called a distance cfuss$er as follows.
Suppose we multiply (4.3) by 2, and then add and subtract XTX from the
left-hand side. The resulting decision rule is

(XTX - 2MTX + M:M ) - (XTX - 2M:X + M;M2)

(4.9)

or