Instrumentation & Measurement Magazine 25-9 - 17

object size and position while differentiating those features according
to their suitability for measurements with a stationary
or moving sensor. Another key point is the use of a highly simplified,
analytical description of the measurement situation in
order to be able to set up particularly time-efficient simulations
with which the described effects can be demonstrated. To determine
the position of an object in space, the vertical distance,
lateral displacement and size of the object from a reference
point (e.g., center of the fish body) must be estimated. For these
different object parameters (distance, size, electrical properties,
etc.) significant features are necessary for this in each case.
Numerous works, both based on theoretical models as
well as biological experiments, have dealt with object localization
in weakly electric fish. A few directly related works to
this study are mentioned. An approach that uses a measurement
domain comparable to the voltage profile in this work
was proposed by Babineau et al. [9]. Another localization
method based on contourrings of rotated and linearly shifted
ensembles of electrosensory viewpoints was proposed by
Wolf-Homeyer et al. [17].
In an early modeling study [13], Rasnow suggested that:
first, the peak of the measured voltage indicates the rostrocaudal
position (between head and tail of the fish) of the object;
and second, that the amplitude of the voltage depends on its
distance. The first statement of Rasnow, that the localization
of the peak indicates the rostrocaudal position of the object, is
verified for a static sensor line in this work and for a moving
sensor line in [14].
The second statement alone is not true, since a small object
can generate the same amplitude as a larger object located further
away (Fig. 5a). The change in amplitude depends on the
object size and distance. The closer an object is located to the sensor
surface, the greater the change in amplitude and waveform.
The size of an object has also a significant effect: large objects
cause larger field distortions as well as larger amplitude changes.
Based on a keystone work [6], von der Emde et al. investigated
whether a weakly electric fish is able to classify objects at
different distances. They established the ratio of the maximum
slope and the amplitude as a measure to determine object-distance
unambiguously.
The same results for distance estimation based on the ratio
of maximum slope and amplitude were verified in simulation
by Sicardi et al. [18]. These results have also been confirmed
in this work by introducing a simplified analytical simulation
model of the weakly electric fish with a static and moving sensor
line. The S/A ratio can be used for object localization with
static and moving sensor line as long as the measured voltage
profile over the sensor line is symmetrical.
In three-dimensional space, the weakly electric fish can
identify the location of an object initially in the rostrocaudal-dorsoventral
axis [10]. The lateral distance as a further
dimension in the three-dimensional space is estimated by the
ratio of slope and amplitude [6] as well as by motion parallax
with the feature peak trace [14] for a moving sensor line or by
the combination of amplitude and slope as shown in Fig. 6b for
object localization with a static sensor line.
December 2022
Rasnow proposed a relative width for electrolocation,
which indicates the width of the electric image on the skin
surface at certain amplitudes in relation to the peak [13]. Similarly,
Chen et al. defined the full-width at half-maximum
(FWHM) as the width of the electric image at the point where
the amplitude is half the maximum value [15]. This feature was
developed for a temporal sensor measurement when an object
moves along the rostocaudal axis.
Hofmann et al. investigated another distance feature from
behavioral characterizations and computational reconstruction
of the sensory inputs of a weakly electric fish [11]. Their
distance feature allows a continuous estimation of distance
and is based on the electrosensory flow generated by the fish.
The electrosensory flow contains behaviorally relevant information
that are only accessible through active behavior.
Sensory behaviors are a common feature of (active) sensory
systems [11].
A feature for size estimation with a static sensor line is
shown in this work (Fig. 6b), but to determine the shape of an
object in three-dimensional space, some additional parameters
are necessary. These parameters result from the scanning behavior
of the weakly electric fish (swimming around an object
and changing body posture, i.e., sensor shape) [11], [12], [14].
One next step will include real world measurements to get
access to environmental parameters of the fluid like salinity
and conductivity and use artificial objects of known material
properties in these experiments. Another next step will be a
generation of a more complex simulation model of the weakly
electric fish (i.e., using a two-dimensional sensor line) to understand
the natural scanning behavior, as investigated in [11].
Acknowledgment
This work has been supported by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation)-Reference
No. SCHN 1339/4-1, EN 826/8-1.
References
[1] J. Mogdans and H. Bleckmann, " Coping with flow: behavior,
neurophysiology and modeling of the fish lateral line system, "
Biological Cybernetics, vol. 106, no. 11, pp. 627-642, 2012.
[2] W. G. Crampton, " Electroreception, electrogenesis and electric
signal evolution, " J. Fish Biology, vol. 95, no. 1, pp. 92-134, 2019.
[3] H. W. Lissmann and K. E. Machin, " The mechanism of object
location in gymnarchus niloticus and similar fish, " J. Experimental
Biology, vol. 35, no. 2, pp. 451-486, 1958.
[4] C. D. Hopkins, " Design features for electric communication, " J.
Experimental Biology, vol. 202, no. 10, pp. 1217-1228, 1999.
[5] G. von der Emde, " Active electrolocation of objects in weakly
electric fish, " J. Experimental Biology, vol. 202, no. 10, pp.
1205-1215, 1999.
[6] G. von der Emde, S. Schwarz, L. Gomez, R. Budelli, and K. Grant,
" Electric fish measure distance in the dark, " Nature, vol. 395, no.
6705, pp. 890-894, 1998.
[7] A. A. Caputi and R. Budelli, " Peripheral electrosensory imaging
by weakly electric fish, " J. Comparative Physiology A, vol. 192, no.
6, pp. 587-600, 2006.
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