Instrumentation & Measurement Magazine 25-9 - 14

Fig. 4. Simulation of object localization (left column: different object sizes, right column: different object distances) with a static sensor line.
placed at different vertical distances. The resulting symmetrical
voltage profile and the respective data of the features are
shown in Fig. 4e and Fig. 4f.
As already published by von der Emde et al. [6], the ratio
of maximum slope and amplitude (S/A ratio) is a feature for
distance estimation of objects, presumably also in real fish.
Likewise, the full-width at half-maximum (FWHM) feature,
as published by Chen et al. [15], is a feature for distance estimation
as well. The graphs and data shown in Fig. 4c and
Fig. 4d support both claims. Both features are a measure for
the distance estimation independent of the object size. The according
numerical values of S/A ratio and FWHM features
do not change by varying object size (Fig. 4c, marked in gray).
However, they change for a constant object size at different distances
to the sensor line (Fig. 4f).
By creating a ratio of slope and amplitude, a distance measure
is obtained which is independent of object size. However,
if amplitude and maximum slope are considered individually,
information about the object size can be obtained. This is
shown in the next simulation experiment, in which differently
14
sized objects are placed at varying distances to the sensor line
(Fig. 5).
In Fig. 5a, the object sizes and distances of the respective objects
were chosen in such a way that for each pair of two objects
(blue and black; red and green), the same amplitudes result
in the respective voltage profiles shown in Fig. 5b. The corresponding
numerical values in Fig. 5c are marked in the same
shade of gray. The result of this simulation experiment is that
amplitude alone is not a sufficient foundation for estimating
object size or object distance.
In Fig. 5d, the object sizes and distances of the respective
objects were chosen in such a way that for each pair of two objects
(blue and black; red and green) the same maximum slopes
result in the respective voltage profiles shown in Fig. 5e. The
corresponding numerical values in Fig. 5f are marked in the
same shade of gray. The result of this simulation experiment is
that also the maximum slope alone is not a sufficient foundation
for estimating object size or object distance.
Analog to geometrical optics, e.g., in the human eye, distance
and size of an object cannot be estimated by observing
IEEE Instrumentation & Measurement Magazine
December 2022

Instrumentation & Measurement Magazine 25-9

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