Biomedical Engineering Reference
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0.6
= 100 msec
τ
0.4
= 50 msec
τ
τ
= 25 msec
0.2
-400
-300
-200
-100
100
200
300
400
pattern velocity [deg/s]
-0.2
-0.4
-0.6
Figure 14.3
Steady-state responses of the minimal correlation model shown in
Figure 14.2
as a
function of pattern velocity for three different low-pass time-constants.
beyond that optimal velocity the response falls off gradually towards zero. Further-
more, the shape of the response curve depends on the time-constant of the detector
low-pass filter: the larger the time-constant, the smaller the velocity at which the
response is maximum.
The time-constant of the detector filter thus becomes a decisive model parameter
that sets the operating range of the motion detection system in the velocity domain.
In particular, it determines the slope of the detector response around velocity zero
and, thus, the gain of the sensor.
14.2.1.2 Pattern dependence
Another peculiar response characteristic of the correlation detector is its dependence
on pattern properties such as its contrast and spatial wavelength. As can be seen
in Equations (14.1) and (14.2), the response depends on the square of the pattern
contrast. This has indeed been experimentally confirmed using low stimulus con-
trasts [57]. For higher contrasts, the experimental data fail to follow a quadratic
contrast dependence. Rather, the response of fly motion sensitive neurons as well as
the strength of the optomotor following behavior saturates for contrasts higher than
about 50% [27]. This might be explained by adaptive changes of internal gain factors
in the detection system [14, 15, 31, 51, 67].
Another feature of correlation detectors, which is obvious in the above formulas,
is that the steady-state response is proportional to the sine of the ratio of the sampling
base and the pattern wavelength. The sampling base of the motion detector, i.e., the
spatial separation of its input lines, limits the spatial resolution of the system. As is
the case for any discrete sampling system, wavelengths can only be resolved up to
a certain limit. The smallest wavelength that can be resolved is given by twice the
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