Page 399 - Introduction to Information Optics

384 7. Pattern Recognition with Optics
a
(-<5x2, -<5yfc ~ )- Tne rest °f tne terms OT.'k-i and Kgi" for m ^ ") represent
the cross-correlation functions between target m and target n. In this multiple-
target tracking problem, we have assumed that the targets in any single input
frame do not look alike, so the cross-correlation functions Rk$-i and R™£
generate much weaker correlation signals than that generated by the function
R^k- i- Furthermore, the size and the gray level of the targets are also assumed
to be relatively congruous with each other, so the intensities of the autocor-
relation peaks generated from jRJf;?- 1, n = 1 to N, are not significantly different.
By translating the coordinate origin from the optical axis to (0, a), the
correlation peaks that are generated from the same target in the k — 1 and the
k frames are then located at (dx" k, dy^) in the new coordinate system. If these
correlation peaks are associated with the proper target motions, the locations
of the targets in the k frame are given by

n
x" k = xj|_ ! + <$*£, y k = tf_ i + dyl n=ltoN. (7.28)

The preceding equation shows that the new locations of the targets in the k
frame can be updated based on their locations in the previous frame and the
position measurements of the correlation peaks. It is apparent that the k and
k + 1 frames can be sent to the input plane in the next tracking cycle, so that
multiple targets can be tracked simultaneously on a near real-time basis.
Note that the position of the correlation peak in the new coordinate system
represents the average velocity of a target during the sampling interval <5f; i.e.,

i- = Sx/fa, J = dy/dt. (1.29)

Therefore, with a constant sampling interval and assuming that the sensor is
not skewing or panning, the new coordinate system represents the plane of
average velocity. For example, targets moving with constant velocity produce
stationary correlation peaks, targets moving with constant acceleration gener-
ate correlation peaks that are located at equally separated intervals on a
straight line, and correlation peaks located at the origin of the new coordinate
plane correspond to stationary objects or background scene. In our demonstra-
tion, multiple targets are traveling at different velocities and in different
directions; thus, the correlation peaks generated are located at different
positions at the velocity plane.
In general, the motion of the targets can be represented by dynamic models,
which are governed by well-known laws of physics. Unpredictable changes in
target motions, commonly called maneuvers, can also be treated as gradual
changes of motion parameters, if the sampling interval is sufficiently short
compared with the maneuver time. Therefore, it is not difficult to associate the
measurements in the velocity plane with the targets, based on the past history