Visual resolution of gratings by the compound eye of the bee Apis mellifera
Research School of Biological Sciences, Australian National University, Box 475, Canberra, ACT 2601, Australia
e-mail: horridge{at}rsbs.anu.edu.au
Accepted 19 March 2003
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Summary |
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Key words: bee, Apis mellifera, vision, grating resolution
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Introduction |
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At about the same time, Baumgärtner
(1928) studied the relatively
poor discrimination between two rectangular patches of different colours. A
rectangle 2 cm wide x 1 cm high could be detected from a maximum
distance of 12 cm, whereas one 1 cm wide x 2 cm high could be detected
from a maximum distance of 40 cm. This difference was attributed to the
difference in the interommatidial angle in the two directions.
Baumgärtner's result is sometimes quoted as evidence that the resolution
of pattern perception is limited by the interommatidial angle.
There was nothing further until Srinivasan and Lehrer
(1988) trained bees to
discriminate from a distance between a vertical and a horizontal black and
white grating presented on a vertical surface. They found a limiting period
near 2.5°. The trained bees were tested with targets of grey separately
against vertical or, in different experiments, against horizontal gratings,
and there was no difference in the resolution in the two directions. Based on
this single result, they proposed that the resolution is limited by the field
size of the individual receptors and not by the interommatidial angle, which
is approximately 1° in the vertical and 2° in the horizontal direction
at the front of the eye.
Srinivasan and Lehrer
(1988) also used vertical and
horizontal gratings composed of coloured papers that present negligible (2%)
green contrast, or alternatively negligible blue contrast, at the edges where
the colours meet, and found similar responses over a range of smaller periods.
The blue receptors alone (with patterns with no green contrast) had a limiting
period near 3.5° (see Fig.
4A). This is an interesting result because later Giger and
Srinivasan (1996
) trained with
shuffled positions of the bars and found that the orientation cue is detected
by green receptors only, and therefore requires green contrast. The earlier
result was not explained, and the nature of the cue for the blue receptors was
unknown.
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This is all that is available concerning the resolution of grating patterns
and their relation to the receptor array of the bee. A few studies of the
resolution of coloured patches of different sizes
(Lehrer and Bischof, 1995;
Giurfa et al., 1996
), which is
quite a different task, produced conflicting results, but it is now clear that
the resolution of coloured patches depends strongly on the stabilisation of
the target on the eye, which in turn depends on green contrast
(Horridge, 1999
).
The limits of resolution of grating patterns can be explained if the cue is a difference in non-directional modulation detected by blue or green receptors, which both respond to black and white gratings. This hypothesis, that there is a difference in flicker, explains the discrimination between vertical and horizontal gratings with no green contrast and also why resolution is the same in the two directions. Near the resolution limit the orientations of the edges are not necessarily discriminated at all, but only the difference in the modulation as the eye scans first one target and then the other.
The purpose of the following work is to test this hypothesis, but the apparatus differs from that used previously, so it is necessary to repeat the earlier measurements and then make entirely new measurements with improved controls all on the same apparatus. In order to discover the actual cues used by the bees in each training situation, it is essential to test trained bees with a variety of patterns, including some that they cannot discriminate, giving an opportunity to exclude each possible cue.
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Materials and methods |
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The targets carry the patterns on white cards, which can be rotated. During training the target that displays the rewarded pattern and its reward are interchanged with the non-rewarded target every 5 min to prevent the bees from learning which arm of the apparatus to choose. In the figures the rewarded pattern is always shown on the left (labelled + at the top).
With the baffle at a distance of 27 cm, the square targets subtend an angle of approximately 55° at the point of choice. The bees required 20 or so visits to build up a discrimination After an initial training period of 23 h, each first choice in each 5 min period was recorded while training continued. These results are labelled `train'. In other experiments, labelled `test', a different pair of patterns was substituted for those in the training, and the bees' first choices towards these were recorded in each period of 5 min. In the tests it was essential to give a reward, otherwise the bees continued to search in the Y-maze, and would not go away. All tests were done with one target rewarded and then repeated with the other target rewarded. Tests with gratings of different periods were interleaved during continued periods of training, so the trained bees did not become familiar with any of the tests. The same test pattern did not return for at least an hour. In some of the tests the bees failed to discriminate, so they learned nothing from the tests.
Calibrations
The grey and black patterns were made by a Hewlett Packard Laserjet 4M
printer. The coloured papers, Nos 384 fawn and 595 light blue, were supplied
by Canson Australia Pty, 17 Metropolitan Ave, Nunawading, Victoria, Australia.
The reflectance spectra of the papers were measured as photon flux with a PC
1000 Fiber Optic Spectrometer (Ocean Optics Inc., Dunedin, FL, USA), near noon
and again in the mid-afternoon. The detector, which has a spot field, was
placed at the choice point of the bees and the papers at their usual place in
the training and tests. The measurements covered a range from 290 to 830 nm
with a mean resolution of 0.52 nm. In the conditions of the experiments, in
indirect light, there was negligible reflection of ultraviolet from these
papers.
The calibration equipment generated digitized values, which were multiplied
at 10 nm intervals, over the range from 380620 nm, with the known
spectral sensitivity curves of the bee receptor types, exactly as done by
Giger and Srinivasan (1996).
The products were summed to give the relative receptor excitation of the blue
and green receptors, for each paper. The Canson 384 fawn/595 light blue
combination gave negligible contrast to the green receptors. The emission
curves of the papers, the relative excitation they generate at the receptors,
and the contrasts have been recently published
(Horridge, 1999
).
Before each training or test that involved a plain grey target, a range of grey papers were compared with the target pattern to obtain one of the same luminance. This was done first by human eye with the targets placed side by side far away so that the gratings were not resolved.
Scoring and statistics
Each bee was identified by colours painted on the thorax and on the
abdomen, and the criterion for the score was when the bee passed through the
hole in a baffle. Unmarked recruits were removed. A record was kept of the
first choice made by each bee in each period of 5 min, not the first choice of
each arrival. Two statistical calculations were made. In the first, the
fraction of correct choices was counted in each block of 20 choices. The
standard deviation (S.C.) between 1020 of these blocks was
calculated as a percentage and placed after each score.
In the second method (van Hateren et
al., 1990), S.D. was estimated from the value of
[p(1p)/n], where p is the
fraction of correct choices and n is the total number of choices.
This method assumes that there are no trends, that the individual choices are
independent and they have a binomial distribution about the mean. The
S.D. estimated from this formula is given in parentheses after each
score. By this method a score of 57% correct based on 200 choices is twice the
estimated S.D. away from the null (random) hypothesis of 50%.
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Results |
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To test whether the cue is related to size or spatial frequency, the trained bees were tested with a pattern of 10 sectors versus a pattern of 36 sectors, both made in alternate sectors with the blue and fawn papers that gave no green contrast (Fig. 2B). The result was 72.0% in favour of the larger sectors. Clearly, in a forced choice, the bees discriminated something related to size or modulation.
The trained bees were also tested with a horizontal versus a vertical black and white grating of period 4° with a result of 60.5% correct choice, n=200 (not illustrated), in favour of the vertical (previously unrewarded) grating. They had obviously not learned the edge orientations, and in the forced choice they probably reverted to their spontaneous preference. When tested with a black and white checkerboard of period 8° versus a grey target (45% black), the result was 52% in favour of the check (not illustrated), showing that the bees had not relied upon a simple difference in modulation. The horizontal bars in the training pattern were larger in the horizontal direction than the vertical bars, and the results suggest that when trained on a period of 14° without green contrast, something coloured and related to size is detected with the help of horizontal scanning movements in flight. This is an unexpected interpretation that could apply to earlier work. This cue was avoided in the next experiment.
Training with no green contrast, oblique gratings
In this experiment, the patterns presented no difference in modulation as
the bees scan in the horizontal direction. A new group of bees was trained to
discriminate between two orthogonal gratings of period 14° with no
contrast to the green receptors. The rewarded grating was oriented at 45°,
the other at 135° to the vertical (Fig.
2C). The patterns were asymmetrical about the central reward hole
and were turned through 180° every 5 min to prevent the bees learning the
bar location. Although training continued all day, the final result was 47.7%
correct choice, n=300.
In this case, there was no orientation cue, no modulation difference, no difference in size of areas that can be detected by scanning motion, no average colour difference, and no fixed positions of areas of different colour. Of course, the bees saw the targets and the colour but they did not discriminate the patterns.
Horizontal versus vertical, black and white gratings
To confirm the earlier finding
(Srinivasan and Lehrer, 1988)
with a different procedure, a new group of bees was trained to discriminate
between a horizontal (rewarded) and a vertical (unrewarded) black and white
grating of period 5°, with the patterns rotated by 180° every 5 min to
prevent the bees learning the bar positions
(Fig. 3A). In the earlier work
the patterns were fixed and there were no baffles to make the bees pause in
flight. After 2 h training the result was 70.5±3.4% (3.2%) correct over
the next 200 choices. The trained bees were tested with black and white
horizontal gratings of various periods versus plain matched grey
targets (45% black). There was no discrimination with a period of 2.0°,
poor at 2.5°, but with larger periods the performance improved rapidly
(Fig. 4B).
Similarly, new bees were trained with the vertical (rewarded) versus the horizontal grating of period 5° and tested with black and white vertical gratings of various periods versus plain grey targets (45% black). The results with horizontal gratings were similar to those with vertical gratings, both tested against grey targets (Fig. 4B). When trained on a period of 5° the resolution was independent of direction, as previously found with different apparatus. Whether the cue in this case was edge orientation or modulation, or something else, remains to be determined.
Oblique black and white gratings
The next experiment measured the resolution when there is green contrast
but no difference in modulation caused by scanning. A group of bees was
trained to discriminate between two black and white gratings of period
18°, one at +45° to the vertical, the other at -45°
(Fig. 3B). The targets were
rotated by 180° every 5 or 10 min so that the bees did not use the
locations of the bars as cues. After 3 h training the result was
79.0±4.3% (2.4%) correct choice, n=300. The trained bees were
tested with equally spaced black and white gratings of various smaller periods
in interleaved tests. The performance dropped to 57.5% correct at a period of
4°, 53.0% at 3°, and 51.5% at 2.5°
(Fig. 4B). Significantly, the
resolution with oblique gratings was not as good as that with horizontal or
vertical black and white gratings versus grey.
It is difficult to imagine a difference in the modulation caused by gratings at 45° and those at 135°, so it is probable that the cue is edge orientation, not receptor modulation. This point was tested by presenting the bees trained on black and white oblique gratings (Fig. 3B) with a test checkerboard of period 4° versus a plain grey target (45% black). The result was 51.5% correct, n=200, showing that the bees did not rely on a modulation cue. For the green receptors and oblique black and white gratings the orientation cue in isolation appeared to be visible down to grating periods of 3.5°, which is not as good as the discrimination of modulation.
Alternating horizontal and vertical gratings
The discrimination between horizontal and vertical black and white gratings
(Fig. 3A) could be based on the
difference in orientations of edges or differences in the receptor modulation
caused by the two patterns, but we found indications
(Fig. 4B) that the resolution
is poor when the modulation cue is removed. To test the resolution of black
and white gratings when orientation is eliminated, we required a new regime
that trains the bees to ignore the edge orientations.
A new group of bees was trained with a plain grey target (45% black) versus a black and white grating of period 5° that was alternated between vertical and horizontal every 5 min (Fig. 3D,E). A small period was selected because it was easy to match with a grey level of equal luminance. The task was an easy one; after 3 h training the result was 84.5±3.9% (2.0%) correct choice, n=300. In two separate series of tests, the trained bees were tested with black and white gratings with a range of periods versus the grey target, with the gratings vertical (as in Fig. 3D) or horizontal (as in Fig. 3E). As the period was made smaller, the gratings were less easily discriminated from the grey in the tests (Fig. 4C). The resolution was similar to that after training with two black and white horizontal and vertical gratings (Fig. 4A,B), and similar in vertical and horizontal directions tested separately, but the cue cannot be orientation.
Taken together with the previous experiment, this result shows that orientation and modulation are separate cues, either of which is effective, depending on the training, and that the discrimination of gratings does not rely only upon an orientation cue in oblique rows of facets.
Train and test on checkerboards versus grey
Another training routine that avoided orientation as a cue made use of
checkerboards. A group of bees was trained to discriminate between a
checkerboard of period 5.6° (between diagonal lines of squares)
versus a plain grey target of equal luminance (47% black). This was
an easy task and the performance after only 3 h training was 74.0±4.2%
(3.1%) correct choice, n=200. The trained bees were tested with
checkerboards of smaller periods versus a plain grey target (47%
black), and the results plotted in Fig.
4C. Discrimination was lost when the period between the diagonal
lines of squares approached 2.5°. The cue cannot be orientation, and in
this case the bees were not trained to ignore edge orientation.
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Discussion |
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The cues, and therefore the resolution, depend on the task
The resolution depends on what the bees use for the visual cue. At least
four kinds of cue are already known, with corresponding values of the
resolution. The common statement that the resolution of a compound eye depends
on the interommatidial angle has two sources. The first is the principle that
the facets of the compound eye divide the outside world into an array of
little windows, and, when the rhabdomeres are fused, each detects the photon
flux in its field of view. The spacing between sampling stations must be half
the period of a regular grating that is reconstructed by the visual system.
There is no evidence, however, for reconstruction.
Secondly, if the resolution test depends on the detection of the direction
of motion, as in the optomotor response, the motion is detected from the
modulation at a receptor followed by that at an adjacent visual axis
(Götz, 1965). The angle
between receptor axes is therefore an essential part of the
spatiotemporal filter that detects the direction of motion.
If the cue at the resolution limit is the difference caused by the two targets in the modulation of the individual receptors, there is no need for the edge orientation or the direction of motion to be discriminated, or the pattern to be reconstructed. The discrimination between two gratings then is ultimately limited by the acceptance angle of the receptors, not the angle between their axes. This explains why bees trained without an orientation cue have the same limit near 2.5° when horizontal and vertical gratings are tested separately against grey, although the corresponding interommatidial angles have a ratio of 2:1.
Gratings at 45° versus 135° generate the same modulation from the bees motion in flight, so the only cue then available is the edge orientation, which requires the detection of edge direction from at least two simultaneously modulated ommatidia, and green contrast. The resolution limit for the orientation cue in a grating can only be demonstrated when a modulation difference has been eliminated as a cue, and the grating period is then near 3.5°.
Finally, when the cue is the discrimination between two positions
(Baumgärtner, 1928) or the
detection of a patch of colour versus a blank target
(Lehrer and Bischof, 1995
;
Giurfa et al., 1996
), the limit
of resolution depends on a more complicated processing that requires several
ommatidia. This is quite a different process that is strongly dependent on
green contrast to help stabilize the eye on the target
(Horridge, 1999
).
One lesson from these results is that bees use an extreme abstraction of the pattern, single receptor modulation, as the cue when learning to discriminate between two patterns. They do not remember, and probably do not see, a grating as a pattern of repeated bars.
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Acknowledgments |
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References |
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