Page 398 - Introduction to Information Optics

7,4. Target Tracking 383

The adaptive property of this system enables the tracking of targets under
change in orientation, scale, and perspective during the course of their
movement.
Let /"(.\, >'), n = \ to IV, be the targets in an image sequence, each of which
are moving independently. Two sequential scenes are displayed on the input
plane of a JTC such that the previous frame (k — 1) and the current frame (k)
are positioned in the upper and lower halves of the SLM, respectively. The
corresponding image function is given by

(7.26)

where 2« is the height of the active aperture of the SLM, (Xfc-i,}i- 1) are the
locations of the targets in the k — 1 frame, and (c>x k, dy*) are the relative
translation of the targets from the k — I frame to the k frame. The correspond-
ing JTPS is then introduced as modulation at the input plane SLM for the
correlation detection cycle. The output complex light distribution is given by

N N
v ,,\— V V' J}m,n t v i vm n .. , ..m ..n \
a A ' 3'' ~" 2_ 2^ K >< - 1 -fc - " + k - 1 "~ fc - 1 ' ^ + >fe ~ 1 ~ ^fc ~ 1 )
X
X
X
n = 1 m = 1
A< JV
+ E I
m v" _1_ ^Sv" i' J_ ii m
k- i ~ •Xk- 1 + ox k, y + y k

(7.27)

where

!
RW(x - a, }.' - jS) = ./H-X, ^) (8) / fc'( rx, y) * <5(x - a, y - /?)
m
is the correlation function between / fc and / k" located at (a, /?).
Note that the autocorrelation functions R%'$ and K^'" lik _ j are located at the
origin of the output plane. The correlation between the same target in the k
and the k — 1 frames, given as R k; k _ l, is diffracted around (5x1,5x1 + ®) and