1. sports
2. billiards

1
What does an insect see? A short review.
Adrian Horridge
Research School of Biological Sciences, Australian National University,
Box 475, Canberra, ACT 2601, Australia.
[email protected]
(a)
target at 1
m
9c
target at 2
27
cm
position 1
2
baffle
hole in
baffle
choice chamber
bees fly
in here
(b)
9 cm
27 cm
reward
box
choice
chamber
25
cm
100
target at 2
50
target at 1
Introduction
Some would say that we may
never know what insects actually see.
Indeed, little can be said about most of
them, but the honeybee is a special case
because bees can be trained. Early
workers trained bees with a number of
patterns, and the bees learned to land on
the one that rewarded them with odourless
sugar solution. Later, individually marked
bees learned to fly into an experimental
choice chamber and select one of two
patterns displayed vertically on the back
walls (Fig. 1). At the centre of each
pattern was a hole, but only one of these
holes led to a small chamber behind,
where the bees found the reward. The two
patterns (and the reward) changed sides
every 5 min to make the bees look at
them, rather than simply choose the
rewarded side. The trained bees were then
tested with a large variety of test patterns
that were intercalated so that the bees
could not learn them in the tests.
air
baffle
Summary:- The units of vision are small
motion detectors and feature detectors
3 ommatidia wide. The latter respond to
passing edges and their orientation. The
responses of the edge and area detectors
are summed by type and position in
each local region of the eye, to form
cues. The coincidence of cues in a local
region is remembered as a label on a
landmark in that retinotopic direction.
Bees learn landmark labels to identify a
place and find the reward; they are not
interested in patterns.
position 2
Email:
Figure 1. (a) The apparatus for training
bees with the target at a controlled range
from the point of the bees’ decision. The
bees fly in the front, then have to choose
between the two targets and enter the
hole in a transparent baffle. The targets,
with the reward box behind one, are
interchanged every 5 min. (b) The angles
subtended by the targets at two different
positions 1 and 2. (after Horridge, 2006b)
2
A century of training and then
testing the trained bees at first revealed
that the bees measured a few parameters of
patterns, namely, the total length of edges
in the pattern, the area and colour, as if
they had feature detectors for edges and
also for brightness of areas, region by
region. They also detected certain
properties of the whole pattern, namely
whether it was circular or had radial
spokes or sectors, and whether it was
smooth or highly disrupted (Hertz, 1933).
In very large patterns, subtending >100º,
bees learned the positions of areas of black
in the periphery of the rewarded pattern
and just below the reward hole, and then
selected ‘the best fit’ when tested against
other patterns (Wehner, 1969).
In all the work until recently, noone considered that ‘the best fit’ for the
bees was a place rather than a pattern. The
size and other properties of the units in the
visual system which detected and
measured the contrast, orientation of
edges, or the radial and tangential
contours were unknown.
The feature detectors
In each ommatidium of the
compound eye, bees have three colour
types of ordinary photoreceptors, with
their spectral sensitivity peaking in the
UV, blue and green. These feed into an
array of feature detectors with balanced
excitatory and inhibitory inputs that are so
arranged that they detect contrast at edges
but are insensitive to changes in
brightness (Fig. 2).
The total modulation in a local
region, effectively the total length of edge,
is the preferred cue. The feature detectors
for modulation were measured in the
following way. Bees were trained to
discriminate between a horizontal and a
vertical black grating, or between a
grating of any orientation and a grey paper
of matched brightness. The minimum
period that was resolved was 2º,
irrespective of the orientation of the
rewarded grating.
The orientations of the edges are
known to be discriminated only by the
input channel from the green receptors
(Giger and Srinivasan, 1996). The limit
was little more when the bars were
coloured to remove contrast to the green
receptors (Srinivasan and Lehrer, 1988;
Horridge 2003e). Therefore the difference
between the finest gratings was detected,
not by orientation detectors, but by
radially-symmetrical modulation detectors
that resolve a 2º grating irrespective of the
colour contrast (Fig. 2b).
receptors
(a)
four feature detectors
(c) -1
(b)
-1
-1
-1
-1
+6
-1
-1
+1
+2
-1
+1
-1
-1
(e)
(d)
-1
+1
-1
-1
+1
-1
+2
+2
-1
+1
-1
-1
-1
+1
Figure 2. (a) The convergence of
receptors on the four types of feature
detectors for edges, all of which are
insensitive to intensity changes. (b) The
radially
symmetrical
modulation
detector. (c-e) The detectors of edge
orientation with bilateral symmetry are
green sensitive and colour blind. The
numbers show the relative excitation and
inhibition by light. (after Horridge,
2006d)
3
The feature detectors for edge
orientation are symmetrical about their
axis of orientation (Fig. 2c, d, e), as shown
by the inability of the bee to distinguish
which side of an edge is dark and which is
light. To measure their minimum size,
bees that had been trained to discriminate
between orientations of edges at 45º and
135º were tested with a large number of
short parallel edges that were each
reduced in length (with the same total
length of edge) until the orientation was
no longer resolved. The minimum length
for resolution of orientation was 3º
(Horridge, 2003d). The edge detectors
have inputs only from the green receptors
and are therefore colour-blind. When the
bees were trained on a black and white
grating at 45º versus the same grating at
135º, there was no difference in
modulation so the bees were obliged to
use the less preferred difference in edge
orientation, and the limiting period was 3º
(Horridge, 2003e).
The cues related to edges
The cues are formed by the
summation of responses of each kind of
feature detector within the local region on
each side of the target or pattern that the
bee is looking at (Horridge, 1997b). Just
as the receptors count photons, each cue
detector totals the coincident responses of
its own array of feature detectors.
Although simple and sparse, cues are
usually sufficient to identify a place with
certainty. The absence of a cue is itself a
cue (Horridge, 2007). Only one cue of
each type is learned in each local region of
the eye at the range of positions where it
was displayed during the training
(Horridge, 1999, 2003a).
The
summation
of
feature
detectors into cues has some counterintuitive effects on what the bees can
detect. Most significant of these, the layout is lost at this point in the processing
(Fig. 3), but the positions of the centres of
the cues and hubs are preserved and used
as cues (Horridge, 2003a, 2006b).
feature detectors
(a)
vertical
orientation cue
(b)
oblique
orientation cue
(c)
orientation cancelled
(d)
hub
hub
orientation
cancelled
(e)
(f)
hub
one tangential cue
hub
one radial
cue
Figure 3. Summation of feature
detectors for edge orientations in
various ways. Pattern is lost but cues
emerge. (a) Detectors with vertical axes.
(b) A line of detectors with oblique
orientation. (c) Mixed orientations
cancel. (d) The orientation cue is
cancelled in the edges of a square but
weak hubs are detected at the corners.
3) but the positions of the centres (e, f)
A tangential and a radial cue and their
hubs.
4
The bees detect and learn the cues
but they have no information about the
distribution of the feature detectors that
were summed. Consequently, there are
many pairs of different patterns that the
bees cannot distinguish. In tests, the
trained bees detect familiar cues in
unfamiliar patterns but the actual patterns
are of no interest (Horridge, 1996a,
1997a).
To a bee, the orientation cue is a
kind of average of the orientations of
edges in a local region (Fig. 3d). For
example, in a square or a square cross the
orientation cue is cancelled by the edges at
right angles to each other (Srinivasan et
al., 1994). Similarly, the orientation is
destroyed when a bar is broken up into
squares or cut into square steps that are
resolved by the feature detectors for edge
orientation (Horridge, 2003c). The
greatest gap that can be spanned in a row
of small squares is 3º, which is a measure
of the maximum size of the feature
detectors for edge orientation.
The edge detectors also collaborate
together to detect the hubs of radial or
circular patterns (Fig. 3e, f). The type of
pattern, radial or tangential, and the
position of the hub, can be learned, but
again the actual lay-out of the pattern is
lost in the summation (Horridge, 2006b).
There are surprisingly few types of
cues, but more may be discovered. There
is an order of preference for learning the
cues in the training situation, with
modulation the most preferred, then area,
position of centre, a black spot, colour,
radial edges, bilateral symmetry, average
orientation, and finally tangential or
circular edges, which are avoided
(Horridge, 2007). Despite many searches,
no more have been found. This is a small
but obviously adequate collection of cues
for the varied life of a bee.
Most of the natural panorama
exhibits a variety of orientations of edges
with a strong modulation cue for bees, but
within each local region of the eye the
orientation cues cancel out and only the
modulation of green and blue receptors
remains. Here and there, however, the bee
encounters parallel edges, for example in
grass or a branch of a tree, and
occasionally the significant symmetry of a
flower or spider’s web.
Cues related to areas
The unit detectors for areas of
black or colour appear to be single
receptors. The responses of blue and of
green receptors are separately totalled
within the local areas on each side of the
target that the bee is looking at. The totals
for an area are kept separate from those
for its edges. An area leaves a memory
trace for (number of receptors) times
(brightness) and the position of the centre,
but nothing about shape (Horridge, 2003b,
2005).
Bees discriminate between two
simple shapes by the cues for average
edge orientation in the local eye region for
that particular pair of patterns (Horridge,
2009), not by the form of a closed
boundary, which is lost in the summation
(Fig. 3). The positions of blue, green and
yellow areas are separately discriminated
(von Frisch, 1914; Gould, 1985; Horridge,
2000b) , but not all the areas are learned
separately, blue being the preferred and
sometimes the only position learned, even
if it lies on the unrewarded target
(Horridge, 2007). The positions of the
centres of two areas of black or colour can
be remembered as cues, but where they
are close together, the bees detect their
common centre. This merging of the two
areas diminishes as the spots move apart,
from an angle subtending 5º, until at 15º
they are quite separate (Horridge, 2003b).
Labels on landmarks
The group of cues that are detected
at the same time by a local region of the
eye form the label of a landmark,
irrespective whether there is a single or
several actual landmarks in that part of the
panorama (Horridge, 2006b, 2007). The
label can be learned. All that matters is
5
62.4%
n = 221
37.6%
train, bees land
on the reward hole
(c)
65.2%
n = 155
34.8%
train, subtending
100 deg
Figure 4 (a) Failure of discrimination at
a subtense of 50º between an irregular
pattern in which the orientation cue
cancels out versus the same pattern
rotated by 180º. Neither the whole
pattern nor the positions or orientations
of individual bars are discriminated. (b)
The patterns are discriminated when
the bees land on the target, or (c) when
the target subtends 100º in the
apparatus in Fig. 1. (after Horridge and
Zhang, 1995).
field sizes 5--60 deg
(b)
external
UV
receptors
green
receptors
blue
receptors
tonic
phasic
phasic
areas
edges
edges
tonic
channels
in colour
photoreceptors
green sensitive
modulation
monopolar cells, amplified
colour blind
other lamina
cells
feature detec
-tors for
orientation
motion
detection
radial
hub
(3)
average
orientation
radial
hub
(6)
tangential
hub
modulation
detectors
colour blind cues
49.4% 50.6%
n = 447
3.5 deg
2.5 deg
2.5 deg
train subtending 50 deg
reward
hole
cues in colour
(a)
colour
size
coincidences of cues
labels on landmarks
feature
detectors
formed
cues
formed
by sums
and
differences
of
feature
detectors
range piloting
directs
fixation
flight
control
internal
that the bee remembers the coincidence of
responses of cues in that local region of
the eye. Landmark labels are therefore
remembered retinotopically, i.e., at a place
on the eye.
The group of landmark labels at
wide angles to each other that are detected
at the same time by the whole eye make
the key to the recognition of a place
(Collett et al., 2002; Fry and Wehner,
2002). At each level, the coincidence of
inputs is the signal to pass the response to
the next level. The whole process from
receptors through to feature detectors and
then to cues and landmark labels (Fig. 5),
is done region by region on the eye, and
therefore in coordinates related to the
position of the head and body axis. For
this reason, bees scan the scene in the
horizontal direction as they fly, and orient
Figure 5. A map of the formal
interactions between the different
processing channels in a single local
region of the eye. The receptors at the
top feed through the lamina to feature
detectors
and
then
to
cues.
Approximate field sizes are shown on
the left. Any resemblance to the bees’
optic lobe is not accidental.
their head and body to detect landmark
labels and find the place of the reward. In
Skinner’s terminology, learning the labels
to recognize a place must be done by
‘operant’ conditioning, which is now part
of ‘active vision’.
6
The effect of pattern size
In the earliest experiments, it was
thought that the bees learned the whole
pattern because they recognized circles
and radial patterns, apparently as a whole,
irrespective of exact size and number of
radial arms. The natural inference was that
the bees learned the abstract idea of the
shape, possibly in any orientation (Hertz,
1933). This idea was eventually rejected
by experiments in which the trained bees
were presented with the training pattern
versus quite a different pattern which
displayed the preferred cues and no
unfamiliar cues. The trained bees could
then not tell the difference between the
new pattern and the one they were trained
on, showing that they were interested in
the cues, not the pattern (Horridge, 2006a,
2009).
The lay-out of very large patterns
subtending 130º is also learned (Wehner,
1969) because they overlap more that one
local region of the eye and allow the bees
to learn something about the configuration
of its regional differences (Fig. 4c). Large
patterns are discriminated by their
peripheral parts (Horridge, 1996b).
Patterns that subtend 40º or less in the Ychoice apparatus are learned by a single
eye region (Fig. 4a), unless they are
strongly radial (Horridge, 2006b, 2009).
By varying the angle that the target
subtends at the eye (Fig. 1), we have a way
to measure the local regions in which each
cue is summed, which is not necessarily
the same for each cue. For a black area, it
is about 50º; for the position of the centre
of a black spot about 15º (Horridge,
2003b); for the summation of orientation
also 15º; for the separation of two colours
about 10º (Gould, 1985; Horridge, 1999b);
for the summation of a circular or radial
elements, at least 45º; for the position of
the hub only about 10º (Horridge, 2006b).
The ability of the bee to
discriminate the shape of an object by the
positions of peripheral bits is therefore
governed by its angular size, because the
size of the local regions appears to be
fixed. The bee eye has a total angle of
about 300º, which is probably divided into
10-20 regions for coincidences of cues
(Fig. 6). This is plenty for the
discrimination of a pattern when the bee
lands on it and discriminates the lay-out of
patches of black (Lehrer and Campan,
2006) or recognizes a familiar place by a
few landmarks (Fry and Wehner, 2002).
field
fields
*
*
*
*
*
*
*
*
small blue here
yellow here
large size here
horizontal average
orientation here
modulation
size
centres of areas
radial cue
average orientations
tangential cue
*
*
cues in
order of
preference
Figure 6. The display in the panorama that is
detected by the bee. Each oval subtending
about 30º represents a local region in the bee
eye. Within each region no more than one cue
of each kind is detected. Some of the cues that
are familiar enable the bee to recognize a
place.
Resolution in the processing hierarchy
Resolution depends on the angular
subtense and shape of the field of the
detector and on the separation between
detectors. The size of the summation field
that determines the resolution of cues is not
the same for each cue (Horridge, 2005). At
the level of coincidences of receptor
7
responses that form feature detectors, we
have:- for modulation, a resolution of 2º. On
account of the lateral inhibition, this is
better than for a single receptor. For
directional edge detection, bees have 3º; for
detection of a small black spot, 2º-3º. At the
level of coincidences of feature detector
responses to form cues, they are:modulation in regions of 20º across;
orientation in regions of 15º-20º across;
position of areas of black or colour, 12º-16º;
for the position of the centre, 5º. At the
level of coincidences of cues to form a
landmark label, we have areas up to 45º
across for the summation, and a resolution
of 15º-20º for the separation between
neighbouring landmarks. The resolution of
the angle of orientation of an edge is poor
because the feature detectors are
independent and so short; a difference of
45º is the limit for a single bar, 30º for a
parallel grating. At each stage in processing,
there is a compromise between the
resolution, which is better in small
summation fields, and the ability to find the
target, or the sensitivity, which is better in
large fields
Generalization of patterns
Generalization is the acceptance of
an unfamiliar pattern by trained bees in
the place of the familiar training pattern.
Early last century it was found that bees
could be trained with a variety of different
squares or equilateral triangles that were
presented simultaneously or in succession,
called generalization in the training
(Hertz, 1933; Anderson, 1977). The
trained bees could also recognize the
familiar training pattern when it was
presented at a different size. It was
concluded that the bees learned an abstract
feature that was common to the different
targets. These abstract features turned out
to be the usual cues that were detected in
parallel.
When bees are trained in the Ychoice apparatus, the patterns are
interchanged every 5 min to make the bees
look at them (Fig. 1). The bees learn the
preferred cues displayed within the pattern
and ignore local cues outside the pattern.
In the experimental apparatus, the patterns
are approximately the size of the local eye
region, so that only one cue of each type is
learned on each side of the pattern. This is
sufficient for the task in hand but
insufficient information to distinguish the
training patterns from many other patterns
that display the same cues.
The trained bees accept an
unfamiliar pattern as long as the familiar
cues are detected in the expected
positions, and no unfamiliar cue is added.
The behaviour of a bee trained on a 40º
pattern is similar to that of a cheap lock
that is opened by several keys. A bee
trained on a natural place with several
landmarks resembles an expensive lock
that is opened by only one key.
Generalization is therefore nothing
to do with cognition or recognition of an
abstract similarity. It is a sign of a poor
education. Errors of recognition are less
likely when the training pattern is very
large, so that it extends over several eye
regions (Figs 4c, 6). In the natural
situation with several landmarks, each
displaying several cues, the trained bees
ignore small changes but do not accept
any substitutes.
Misleading terminology
Words and phrases borrowed from
the cognitive sciences, such as “perception
of shape”, “similarity”, “triangularity” and
“recognition”, supported anthropomorphic
ideas about mysterious cognitive abilities
of the bees. To avoid unjustified
conclusions,
a
phrase
such
as
“discrimination of difference”, when
translated for the bee, becomes “cue in
one but not the other” or perhaps “avoid
unfamiliar cue”.
In
examples
where
bees
discriminated between A and B, it was
sometimes concluded that they actually
saw or at least recognized A and B (for
example, Dyer et al., 2005). The bees,
however, detected only a difference in the
8
cues and their positions in that one task in
hand, so that they could recognize the
place. There was no evidence for
perception of A or B as patterns or
objects. Training to discriminate two
patterns is an entirely artificial situation in
which the bees adopt their usual strategy
of looking for cues to identify the place of
the reward.
Design of the bee visual system
The extremely wide visual field of
the compound eye is useful to detect
approaching enemies and the direction of
an open flight path. In the bee, the wide
field has two additional functions. When
bees return to a familiar feeding place,
they make use of the wide visual field to
remember at every moment the direction
that the axis of the body and head points
relative to the sun-compass and the
direction of home. They also recognize a
place by landmarks detected at large
angles on the eye (Collett et al., 2002). A
landmark is not necessarily an isolated
object, it can be parts of distributed
branches, flowers or pebbles, that display
sufficient coincidences of cues.
It will be noticed that nowhere is
the pattern of interest to the bee. Patterns
were introduced to bees as oriented bars,
spots, stars or triangles in the early days of
bee training and persisted as experimental
tools for a century. Bees appear to
distinguish between the patterns but
actually they detect only a difference in
the cues. Bee vision is designed to pick up
the flow field in flight and the labels on
landmarks when finding a place.
Problems of analysis
For the whole of the past century
bee vision was a mystery. In particular,
the kind of system involved was unknown.
There was no systematized way, no
paradigm, to help find the crucial
questions to ask. First, it was not
understood that bee vision is adapted to
the recognition of places. That requires a
300º not a 40º field. The effect of pattern
size was ignored. It was a major problem
discover what the bees actually detected.
Work on other visual systems was of little
help. The convictions of the experimenters
about the cognitive abilities of the bees
delayed progress. It was thought that bees
actually see the world or some aspects of
the panorama, even if fuzzy. It was
thought that landmarks were isolated
outstanding objects that the bees used as
beacons.
The bees learned to come to
patterns that were shuffled about, and the
experimenters were convinced that the
bees recognized and remembered the
patterns. But bee vision was hopelessly
counter-intuitive. Many tests of the trained
bees are required before the actual cues
are identified, and further tests before
alternative explanations can be ruled out.
The experimenters could not detect the
cues. The bees could not detect the
patterns, only the cues and their
coincidences to identify the place of the
reward. Anything could be a landmark.
Finally, it was shown that when trained
bees were tested with the training pattern
versus a different pattern that displayed
the same cues, and no unfamiliar cues,
they could not remember which pattern
they were trained on. This experiment was
repeated for all the kinds of patterns that
had been used to train bees (Horridge,
2006a, 2009).
Half a visual system
This analysis of the formal
interactions of the inputs and cues would
be little more than elementary common
sense in computer vision. There are three
successive stages of coincidences of
inputs of filters laid out in the angular coordinates of the compound eye. The edge
detectors resemble Canny detectors (Fig.
2) and are only 3º in size. Individually
their positions are not recorded. Each type
is summed to form one cue in each local
eye region. The coincidence of cues in a
local region is the only retained
9
information about that part of the image.
The coincidence of landmark labels is
recalled only for the recognition of a
place. There is little sign of central control
of field sizes or top-down adjustment.
That is only half the mechanism, however,
because the visual processing is
retinotopic and the eye is carried on the
head on the body. The posture and
movement is controlled by the vision itself
and learning is operant, that is,
instrumental, with instant feedback. The
eye is useless without its control of its
own moving platform. That is the next
frontier.
References
chromatic properties of orientation
analysis. Journal of Comparative
Physiology A 178, 763-769.
Gould, J.L., 1985. How bees remember flower
shapes. Science, New York 227, 1492-1494.
Hertz, M., 1933. Über figurale Intensität und
Qualitäten in der optische Wahrnehmung der
Biene. Biologische Zentralblatte 53, 10-40.
Horridge, G.A., 1996a. Vision of the honeybee
Apis mellifera for patterns with two pairs of equal
Anderson, A.M., 1977. Shape perception in the
orthogonal bars. Journal of Insect Physiology 42,
honeybee. Animal Behaviour 25, 67-79.
131-138.
Collett, M., Harland, D., Collett, T.S., 2002. The
Horridge, G.A., 1996b. Pattern vision of the
use of landmarks and panoramic context in the
honeybee (Apis mellifera); the significance of the
performance of local vectors by navigating bees.
angle subtended by the target. Journal of Insect
Journal of Experimental Biology 205, 807-814.
Physiology 42, 693-703.
Dyer, A.G., Neumeyer, C., Chittka, L.,
Horridge, G.A., 1997a. Pattern discrimination by
2005. Honeybee (Apis mellifera) vision
the honeybee: disruption as a cue. Journal of
can discriminate between and recognise
Comparative Physiology A 181, 267-277.
images of human faces. Journal of
Experimental Biology 208, 4709-4714.
Horridge, G.A., 1997b. Vision of the honeybee
Apis mellifera for patterns with one pair of equal
von Frisch, K., 1914. Der Farbensinn und
orthogonal bars. Journal of Insect Physiology 43,
Formensinn der Biene. Zoologische Jahrbucher,
741-748.
Abteilung für allgemeine Physiologie 35, 1-182.
Horridge, G.A., 1999a. Pattern discrimination by
Fry, S.N., Wehner, R., 2002. Honeybees
the honeybee (Apis mellifera): training on two
store landmarks in an egocentric frame of
pairs of patterns alternately. Journal of Insect
reference. Journal of Comparative
Physiology 45, 349-355.
Physiology A 187, 1009-1016.
Horridge, G.A., 2000a. Pattern vision of the
Giger, A.D., Srinivasan, M.V., 1996.
Pattern recognition in honeybees:
honeybee (Apis mellifera). What is an oriented
10
edge? Journal of Comparative Physiology A 186,
Horridge, G.A., 2006a. Visual
521-534
processing of pattern. In: Warrant, E.,
Nilsson, D-E. (Eds.), Invertebrate
Horridge, G.A., 2000b. Pattern vision of the
Vision. Cambridge University Press,
honeybee (Apis mellifera): discrimination of
England, pp. 494-525.
location by the blue and green receptors.
Neurobiology of Learning Memory 74, 1-16
Horridge, G.A., 2006b. Visual
discrimination of spokes, sectors, and
Horridge, G.A., 2003a. Discrimination of single
circles by the honeybee (Apis
bars by the honeybee (Apis mellifera). Vision
mellifera). Journal of Insect
Research 43, 1257-1271.
Physiology 52, 984-1003.
Horridge, G.A., 2003b. Visual
Horridge, G.A., 2006c. Some labels that are
discrimination by the honeybee (Apis
recognized on landmarks by the honeybee (Apis
mellifera): the position of the common
mellifera). Journal of Insect Physiology 52, 1254-
centre as the cue. Physiological
1271.
Entomology 28, 132-143.
Horridge, G.A., 2007. The preferences of the
Horridge, G.A., 2003c. The visual system of the
honeybee (Apis mellifera) for different visual cues
honeybee (Apis mellifera): the maximum length of
during the learning process. Journal of Insect
the orientation detector. Journal of Insect
Physiology 53, 877-889.
Physiology 49, 621-628.
Horridge, G.A., 2009. Visual discrimination by the
Horridge, G.A., 2003d. Visual resolution of the
honeybee. In: How animals see the world. Oxford:
orientation cue by the honeybee (Apis mellifera).
Oxford University Press. (in press)
Journal of Insect Physiology 49, 1145-1152.
Horridge, G.A., Zhang, S.W., 1995.
Horridge, G.A., 2003e. Visual resolution of
Pattern vision in honeybees (Apis
gratings by the compound eye of the bee (Apis
mellifera): Flower-like patterns with no
mellifera). Journal of Experimental Biology 206,
predominant orientation. Journal of
2105-2110.
Insect Physiology 41, 681-688.
Horridge, G.A., 2005. The spatial resolutions of
Lehrer, M., Campan, R., 2006.
the apposition compound eye and its neurosensory
Generalization of convex shapes by
feature detectors: observation versus theory.
bees: what are shapes made of ?
Journal of Insect Physiology 51, 243-266.
Journal of Experimental Biology 208,
3233-3247.
11
Srinivasan, M.V., Lehrer, M., 1988. Spatial acuity
honeybees. Philosophical Transactions of the
of honeybee vision, and its spectral properties.
Royal Society of London B 343, 199-210.
Journal of Comparative Physiology A 162, 159172.
Wehner, R., 1969. Der Mechanismus der optischen
Winkelmessung bei der Biene (Apis mellifica).
Srinivasan, M.V., Zhang, S.W., Witney, K., 1994.
Visual discrimination of pattern orientation by
Zoologische Anzeiger, Supplement 33, 586-592.