Page 407 - Introduction to Information Optics

392 7. Pattern Recognition with Optics

be actually implemented in a commercially available SLM. One important
aspect of pattern recognition is detectability, which can be defined as the
correlation peak intensity- to -sidelobe ratio, as given by

detectability ^ ^L- . (7,34)
* sidelobe

The other aspect of pattern recognition is accuracy of detection, which can
be determined by the sharpness of the correlation profile, such as

accuracy = -E2i_ s (7.35)
M)
where
rr
2
/ 0 = |R(x,j;)| rfx4', (7.36)
«/ «/
and jR(x, y) is the output correlation distribution. The major objective of using
a SA composite filter is to improve discriminability against similar targets. By
using the conventional Fisher ratio (FR),

FR A )} ~ E{I 2(0)}\ 2
' { " / j

discriminability among similar targets can be differentiated, where ^ and I 2
are the correlation and the cross-correlation peak intensities, respectively. In
other words, the higher the FR would be, the higher the target discriminability.
Another major objective for design of an SA filter is reliability of the target
detection, which can be defined by the following discrimination ratio:

reliability = DR 4 Zi , (7.38)

where I t and 7 ; denote the correlation and the cross-correlation peak inten-
sities, n l and n 2 represent the target and the antitarget sets, respectively, and
min and max are the minimum and the maximum values that belong to the
corresponding set. In other words, the higher the DR, the higher the reliability
of target detection.
One of the advantages of using SAQCF is that the filters are positive real
function filters, unlike the bipolar filter, which can be directly implemented in
an amplitude-modulated SLM. By using the same training sets as shown in
Fig. 7.29, several QCFs, for N — 3, 5, . . . , 17 quantized levels, have been syn-