Page 389 - Introduction to Information Optics

374 7. Pattern Recognition with Optics

calculated by multiplying the preceding w(i) with the normalized correlation
peak intensity p ;/p max, where p { is the correlation peak intensity for r,-(.x, y)
together with the target 0(x, y), and p max = max{p f-, i = 1, . . . , N] is the highest
peak intensity among them. By properly choosing a certain nonlinear function
to the JTPS, the monostable convergence of this iteration can be achieved.
The proposed filtered iteration not only suggests that the weight coefficients
w(i) be fed back to the reference patterns but also implies that the teed back
coefficients can be used to weight the composite filter. Since the feature of a
reference pattern can be enhanced with an intensity compensation filter (ICF);
i.e., the reciprocal of the reference power spectrum, the composite filter can be
obtained by linearly combining all the ICFs contributed by each reference
pattern; that is,

A' is
J-f( n n\ _
(p q}
' ~
where T denotes the thresholding operation with t t as the threshold value, and
K t is the iterative feedback weight coefficient for the filter.
To determine r £ , we assume that only one reference pattern [assuming
r,-(x, y)"] is present and the target 0(x, y) is equal to r {(x, y). f, can then be
adjusted until the sharpness of the output autocorrelation profile meets a
certain requirement; e.g., the optimum sharpness under noisy constraint.
Another way of determining t t is to solve the following equation:

2
2
<r (t i)/n (t l) = C (7.15)
where C is a user-provided parameter, f,i(t {) and a(t^ are the mean and the
2
standard deviation of \R t(p, q^/T^R^p, q)\ } t.\ i.e., the cross-power spectrum
of the reference and the object (now equal to the reference function) compen-
2 2
sated with the ICF. a (t-)/ii (t^ is inversely proportional to the ratio of peak
intensity to the average background intensity, whereas the range for parameter
C is usually chosen from 0.01 to 1. K i is initialized such that all the ICF have
the same average intensity. The new weight coefficient K' t is equal to the
preceding coefficient K t times the normalized correlation peak intensity /?,-/P max-
The iteration process can be summarized as follows:
1. Compute all the ICF.
2. Initialize the reference and filter weight coefficients.
3. Compute the composite filter (combine all the weighted ICF).
4. Forward the Fourier transform of the target and reference functions.
5. Capture the JTPS and multiply it by the composite filter.
6. Inverse the Fourier transform of the filtered JTPS.
7. Analyze the correlation output for decision making.