Content uploaded by Frances Claire Rind
Author content
All content in this area was uploaded by Frances Claire Rind on Nov 06, 2014
Content may be subject to copyright.
JOURNAL OF NEUROPHYSIOLOGY
Vol. 75. No. 3. March 1996. Prirtred in U.S.A.
Neural Network Based on the Input Organization of an Identified
Neuron Signaling Impending Collision
F. CLAIRE RIND AND D. I. BRAMWELL
Division of Neurobiology, University
of
Newcastle-upon-Tyne, Newcastle-upon-Tyne NE1 7RU, United Kingdom
SUMMARY AND CONCLUSIONS
I. We describe a four-layered neural network (Fig. 1)) based
on the input organization of a collision signaling neuron in the
visual system of the locust, the lobula giant movement detector
(LGMD). The 250 photoreceptors ( “P” units) in layer 1 are
excited by any change in illumination, generated when an image
edge passes over them. Layers 2 and 3 incorporate both excitatory
and inhibitory interactions, and layer 4 consists of a single output
element, equivalent to the locust LGMD.
2. The output element of the neural network, the “LGMD”,
responds directionally when challenged with approaching versus
receding objects, preferring approaching objects (Figs. 2-4). The
time course and shape of the “LGMD” response matches that of
the LGMD (Fig. 4). Directionality is maintained with objects of
various sizes and approach velocities. The network is tuned to direct
approach (Fig. 5). The “LGMD” shows no directional selectivity
for translatory motion at a constant velocity across the “eye”, but
its response increases with edge velocity (Figs. 6 and 9).
3. The critical image cues for a selective response to object
approach by the “LGMD” are edges that change in extent or in
velocity as they move (Fig. 7). Lateral inhibition is crucial to the
selectivity of the “LGMD” and the selective response is abolished
or else much reduced if lateral inhibition is taken out of the network
(Fig. 7). We conclude that lateral inhibition in the neuronal net-
work for the locust LGMD also underlies the experimentally ob-
served critical image cues for its directional response.
4. Lateral inhibition shapes the velocity tuning of the network
for objects moving in the X and Y directions without approaching
the eye (see Fig. 1). As an edge moves over the eye at a constant
velocity, a race occurs between the excitation that is caused by
edge movement and which passes down the network and the inhibi-
tion that passes laterally. Excitation must win this race for units in
layer 3 to reach threshold (Fig. 8). The faster the edge moves over
the eye the more units in layer 3 reach threshold and pass excitation
on to the “LGMD” (Fig. 9).
5. Lateral inhibition shapes the tuning of the network for objects
moving in the 2 direction, toward or away from the eye (see Fig.
1). As an object approaches the eye there is a buildup of excitation
in the “LGMD” throughout the movement whereas the response
to object recession is often brief, particularly for high velocities.
During object motion, a critical race occurs between excitation
passing down the network and inhibition directed laterally, excita-
tion must win this race for the rapid buildup in excitation in the
“LGMD” as seen in the final stages of object approach (Figs.
lo- 12). The buildup is eliminated if, during object approach,
excitation cannot win this race (as happens when the spread of
inhibition laterally takes < 1 ms Fig. 13, D and E). Taking all
lateral inhibition away increases the “LGMD” response to object
approach, but overall directional selectivity is reduced as there is
also a lot of residual network excitation following object recession
(Fig. 13B).
6. Directional selectivity for rapidly approaching objects is fur-
ther enhanced at the level of the “LGMD” by the timing of a
feed-forward, inhibitory loop onto the “LGMD”, activated when
a large number of receptor units are excited in a short time. The
inhibitory loop is activated at the end of object approach, truncating
the excitatory “LGMD” response after approach has ceased, but
at the initiation of object recession (* Figs. 2, 3, and 13). Eliminat-
ing the feed-forward, inhibitory loop prolongs the “LGMD” re-
sponse to both receding and approaching objects (Fig. 13F).
INTRODUCTION
As an object moves directly toward the head, both the
size of the image on the eye and the disparity between the
images on the two eyes increase. Binocular interactions, such
as the use of binocular disparity, have only exceptionally
been found to underlie range estimation by invertebrates,
mainly because there is little overlap between the visual
fields of the left and right eyes and the absolute distances
separating the two eyes are small (for a review see Schwind
1989). For many animals, a rapidly expanding dark image is
a powerful stimulus eliciting an avoidance or escape reaction
(Gibson 1958; Holmqvist and Srinivasan 199 1; Schiff et al.
1962; Wang and Frost 1992). In the locust, two identified
neurons, the lobular giant movement detector (LGMD)
(O’Shea and Williams 1974) and the postsynaptic descend-
ing contralateral movement detector (DCMD) (Rind 1984;
Rowe11 197 1 ), respond selectively to the images of an object
approaching toward, as opposed to receding from, their eye
(Rind and Simmons 1992). The DCMD can discriminate
between approaching and receding objects using cues de-
rived from one eye. The strongest response is given to an
object approaching on a collision course with the eye, when
collision is imminent. The critical image cues for the selec-
tive response to approaching objects have been isolated as
an increase in the velocity of motion of the boundary edges
of the image and a rapid increase in the amount of edge in
the image (Simmons and Rind 1992). The critical image
cues are extracted locally without reference to global image
patterns. The use of more than one cue adds robustness to
the DCMD response, enabling the neuron to respond reliably
and quickly to an approaching object. When an object is on
a collision course with the locust, both these cues will be
maximized.
The receptive field organization of the LGMD and DCMD
neurons had been explored extensively before their selective
response to rapidly approaching objects was appreciated.
The LGMD is the sole source of compound eye input to the
DCMD, and spikes in the DCMD follow those in the LGMD
one for one (Rind 1984). In the optic lobe, the LGMD
receives excitatory input from a retinotopic array of small-
field neurons, each excited transiently by changes in illumi-
nation (O’Shea and Rowe11 1976). The excitatory inputs to
0022-3077/96 $5.00 Copyright 0 1996 The. American Physiological Society 967
F. C. RIND AND D. I. BRAMWELL
the LGMD occur over the dendritic fan of the neuron in the
distal lobula. Lateral inhibition, which is a prominent feature
of the input organization of the LGMD, occurs between the
retinotopic afferent neurons responding to edge transitions
of either the same (Edwards 1982; Rowe11 et al. 1977), or
the opposite contrast polarity (Simmons and Rind 1992).
This lateral inhibition occurs before the convergence of the
retinotopic input onto the LGMD, and thus before the decre-
ment-prone synapse between the afferents and the LGMD
(O’Shea and Rowe11 1975, 1976). Direct inhibition of the
LGMD occurs in a region of the neuron proximal to the
convergence of the excitatory afferents on the dendritic fan
and is mediated by two classes of neuron excited either by
light-dark or dark-light transitions (Rowe11 et al. 1977).
These two classes of neuron constitute a feed-forward loop
bypassing one or more tiers of processing distal to the
LGMD ( Rowe11 et al. 1977). The input organization of the
LGMD and DCMD neurons are known to the extent that
it should be possible to incorporate these features into a
computational model. Edwards ( 1982) incorporated details
of the input organization of the cockroach DCMD into a
model to examine the effect of lateral inhibition on the re-
sponse to a small spot of light whose intensity could be set
experimentally. The model was used as an initial framework
for developing the present network. For this network to be
an adequate representation of the input organization of the
LGMD neuron, its output must share the response properties
of this neuron as described by Rind and Simmons ( 1992) : in
particular, it should show a selective response to approaching
versus receding objects. This selectivity should be main-
tained over a range of approach speeds, object sizes, ap-
proach distances, trajectories, and contrasts (light vs. dark
objects). The network should show a nondirectional re-
sponse to objects that move with a constant velocity at a
fixed distance from the eye and it should respond best to
large objects moving rapidly. The network should share the
same critical image cues for a selective response to object
approach: directional responses should be produced to edges
that change in either extent or velocity as they move. If the
model performs in the same way as the LGMD neuron, it
then will be possible to examine the mechanisms within the
network that underlie the directional selectivity for objects
moving in depth and, by analogy, to explore the possible
mechanisms in the circuits that feed the LGMD neuron. For
example, it will be possible to determine how the properties
of the LGMD input organization generate the critical image
cues for a selective response to an object approaching on a
collision course (Simmons and Rind 1992).
In this paper, we describe a neural network that meets the
above criteria and, therefore, could be considered an ade-
quate representation of the input organization of the LGMD
neuron. The network is quite simple and demonstrates the
importance of the relative timing between excitation and
inhibition for the selective response to approaching objects.
A critical race between excitation passing down the network
and inhibition directed laterally is essential to the rapid
buildup of excitation in response to approaching objects. A
feed-forward inhibitory loop, activated only when a large
number of “photoreceptors”
are excited, also contributes
to directional selectivity. The feed-forward loop is strongly
activated and truncates the excitatory “LGMD” response at
the end of object approach but at the beginning of object
recession.
METHODS
The
computer program is written
and runs on a Research Ma-
chine PC with a 486, 33MHz processor, using software written in
Borland Turbo C. Both the image and the neural network are
realized in software. Input to the neural network is provided when a
simulated object moves in three-dimensional space, creating image
motion over the “eye” of the network (Fig. 1). The network
incorporates the general features of a locust eye, including the
input organization of the LGMD and DCMD neurons described
above. The photoreceptors (“P” units) are excited by changes in
levels of illumination, generated when an image edge passes over
them. Excitation passes retinotopically down the network through
layers l-3 and is summed by the output unit in layer 4: the
“LGMD”. Inhibition passes forward and laterally or loops forward
arriving after the convergence of the retinotopic projection onto
the LGMD. Both inhibitory inputs are delayed, by 2-5 ms relative
to the excitation passing down the network.
Network and its inputs
The inputs to the network are a series of computer-generated
images of a moving object, one per millisecond of simulated time.
The size of the object, its initial and final position in three-dimen-
sional space, and its velocity are controlled for each simulation
(Table 1). In layer 1, each image is mapped onto the array of
photoreceptors, each of which views a narrow region of space
separated from that of its neighbors by a minimum of 3.3 deg (Fig.
1 and Table 2). This angle is outside the locust range of 1.2-2.3
deg (Horridge 1978)) but was chosen to spread the combined field
of view of all 250 photoreceptors in space. Each facet is treated
as having just one photoreceptor, a simplification which is justified
functionally because all seven receptors making up the rhabdome
in the locust eye look at the same region in space (Nilsson 1989).
The angle between neighboring photoreceptors and the size of their
receptive field increases progressively toward the edges of the
array, mimicking the curvature of the locust eye. Each photorecep-
tor (layer 1, P unit) in the model responds with a brief ( 1 ms)
excitation to a change in level of illumination (Fig. 1). The layer
1, P unit is thus a composite between a photoreceptor and one or
more postsynaptic neurons in which responses to light on and off
are processed to give the same signals (O’Shea and Rowe11 1976).
The excitation in the P unit is extremely transient and marks the
passage of an edge with great precision. Similar response time
courses with a tight coupling of response and stimulus timing have
been observed in “transient cells” in the locust medulla responding
to small light increments or decrements (O’Carroll et al. 1992;
Osorio 1987, 1991).
The excitation from the P units is passed on to two units in layer
2: an excitatory “E” unit, and an inhibitory “I” unit. Excitation
and inhibition from the layer 2 units are summed by “S” units in
layer 3, which excite the “LGMD” in layer 4. Synaptic and con-
duction delays within and between layers can be set independently.
However, for the simulations described here, delays at excitatory
connections between layers are set to 0 ms, whereas delays on
inhibitory connections vary between l-4 ms. Excitation of a layer
2 E unit follows activation of the P unit feeding it, unless the unit
is within its refractory period. In layer 2, each E unit passes excita-
tion to one layer 3 S unit in the same retinotopic position and each
I unit passes inhibition laterally to two rings of S units, centered
on the I unit. The 6 nearest and 12 next-nearest neighbors of each
I unit are specified using look-up tables. The inhibition passed
from the I unit to each nearest and next-nearest S unit is always
divided by the number of such connections made by the I unit,
thus l/6 of the input excitation is passed to each nearest and l/
NEURAL NETWORK FOR COLLISION AVOIDANCE 969
Layer-l Layer-2
Layer-3 Layer-4
I I /
i-r------
Basic Retinotopic Unit
Information ---w
‘P’
001
Feed Forward
(s Inhibition (‘F’)
‘LGMD’
FIG.
1. Schematic representation of neural network. Inputs to network were a series of computer-generated images of a
moving object. Input organization of the basic retinotopic unit of the network is labeled. Output activity of 250 of these
units converge on the “lobula giant movement detector” (“LGMD”) unit. In layer 1, images were mapped onto the
hexagonally packed photoreceptors, each of which viewed a narrow region of space, separated from that of its neighbors by
3.3 deg. Each photoreceptor (P unit, layerl) in the model responded with a brief ( 1 ms) excitation to a change in level of
illumination. In layer 2, this excitation was passed to 3 units: E, I, and F. When excited, E passed excitation to a layer 3, S
unit in the same retinotopic position; I passed inhibition laterally to the 6 nearest and 12 next-nearest layer 3 S units and F
fed inhibition forward bypassing layer 3. F was only active when a large number of photoreceptors were activated in a short
time. E and I inputs were summed linearly by each S unit in layer 3 until a threshold level of excitation was reached and a
spike was produced. A refractory period followed such activation, during which the neuron could not be activated, and
excitation decayed exponentially. Layer 4 of the model consisted of a single “LGMD” unit, which summed excitation from
all active S units and inhibition from the F unit. In each layer, proximity to the central retinotopic unit is indicated by the
shade of grey. Time course of activation of each different unit is shown at
bottom.
P, photoreceptive unit (layer 1); I,
laterally projecting, inhibitory unit (layer 2); E, excitatory unit (layer 2); F, feed-forward inhibitory unit; S, excitatory
summing unit (layer 3); and “LGMD”, final output unit (layer 4).
12 to each next-nearest S unit. This inhibition passed on by an I
unit to each nearest and next-nearest S unit then can be altered
further by changing the synaptic weighting of the I unit input. This
synaptic weighting is expressed as the percent of I unit activation
TABLE 1.
Stimulus for simulated edge translation and object
approach
Stimulus Edge Translation Obiect Annroach
Initial position x, z, mm y, -99, 0, 50 0, 0, 400
Dimensions 1
X
h, mm
100 x 80 75 x 75
Plane of motion, (x. y, or 2)
x
z
Direction and distance, mm
70 -400
Velocity, m/s
0.75 10
Neural network responding selectively to approaching objects.
TABLE
2. Parameters for neural network
Network
P-unit Delay, ms Inter P Spacing, 0 Distance to Screen, mm
0 3.3 100
T
cO”IIFL, ms T,r,, ms IThres, 0- 1 Delay, ms
Weight, %
E-unit
12.33 0 0 0 100
I-unit
n
55.00 0 0 2 170
n+l
4 70
S-unit
22.20 2 0.1 0 100
F-unit * 0 0.05 4.5 *
* Depends on the rate of change in total P activity. T,,,,,, time constant;
T,,, refractory time; IThresh, threshold activation.
970
F. C. RIND AND D. I. BRAMWELL
A
180
160
80
60
40
20
B
200
180
-6
160
80
velocity
Simulated Response of'LGMD'Neuron
(m/s)
--
4
-
6
8
.
-w
8
I
.
,
i
I i
.a.
10
I
. ' i
I
I
---
12
I
i
I
I
i
I
I
. I
. . .* 14
. 1
i I
. I
. (
i
I
0 20 40 60 80
Time (ms)
Simulated Response of'LGMD'Neuron
Velocity
(m/s>
-- 4
--. 10,12
1
. . .
14
FIG. 2. Response of “LGMD“ to object motion. A :
object approach on a collision trajectory. B: object reces-
sion along the same path. Velocities of 4- 14 m/s were
simulated. Other stimulus details and network parameters
were as in Table 1. Activity in the “LGMD” was plotted
at 1-ms intervals throughout each simulation.
0
20 40 60 80
Time (ms)
passed across to each S unit and is (I unit activity/6)
X
percent
for nearest S units and (I unit activity/ 12)
x
percent for next-
nearest S units. Unless specifically mentioned, these weightings
are 170% to the nearest and 70% to the next-nearest S units. The
I unit inhibition to the nearest, and to the next-nearest layer 3 S
units also is delayed by a selected amount, relative to the excitatory
input. This results in a balance between excitation passing from
layer to layer down the network and inhibition directed laterally.
The maximum possible inhibition onto an S unit when all sur-
rounding I units are active, expressed as a percent the initial P unit
activation entering the pathway, is (6
X
l/6
X
170%) from the
nearest neighbor I units plus ( 12
X
I/ 12
X
70%) from the next-
nearest neighbor I units = 240%. However, for the 2 or 4 ms
conduction delays to the nearest, and to the next-nearest S units,
the time constant for the I unit results in only a proportion of this
activation ( 170%
X
0.96) plus (70%
X
0.93) = 228% being passed
to S units. The lateral inhibition exhibited by the LGMD network
has been shown to be stimulus rather than response dependent,
which means that the system remains stable even when the total
inhibition generated by the network is greater than the response
that produced it (Edwards 1982; O’Shea and Rowe11 1975). This
means that it is not essential to the stability of the network for the
100
total inhibition, induced by each I unit, to balance the excitation
received by the I unit initially.
The E and I inputs are summed linearly by each S unit in layer
3 until a given threshold level of excitation is reached and a “spike”
is produced (Fig. 1). After the peak of a spike, voltage declines
exponentially with time and is followed by a refractory period. This
phase of the S unit response is independent of any inhibitory input.
Buildup of excitation in an S unit is not shown, only its suprathresh-
old output. Layer 4 of the model consists of a single “LGMD”
unit, which linearly sums excitation from all active S units and
inhibition, delayed by 2-5 ms, from the inhibitory F unit. This sum
is expressed as a voltage, rather than a spiking output because the
input-output function of the LGMD neuron is not known. The F
unit in the network constitutes a feed-forward pathway, by-passing
layer 3, and is only active when a set number of P units (-50) are
activated in a short time. For each simulation, the threshold number
of photoreceptors excited before activation of the loop occurs and
the activity in the feed-forward inhibitory F unit can be set. The
initial increase in activity and then the rate of decay both are con-
trolled by the rate of P unit activation or inactivation.
After activation, of an E, I, or S unit excitation in it declines
exponentially (Fig. 1). This form of activation is of a similar form
NEURAL NETWORK FOR COLLISION AVOIDANCE
971
A
.
2oo - Toward .’
l
* ’
l .
Away
loo-
.
l
l .
l
.
.
. l
.
. .
.
,’
I-.
--._
Dimensions (mm) 50x50
,=:
--._
,I
--._
--s_
8’
---_
- I
---_
:
---_
1’
:
/
4
0’ 0
C
_ Tiee (ms) Time (ms) _
40
w -
_
.
.
.
.
. l b . l b
. ’ . ’
. .
. . . .
. . . .
9 9
. .
0’ 0’
, ,
. . . .
l . . l . . l . l .
. .
’ l ’ l
. .
l . ’ l . ’
b b
0 0
**.e/** ’ l **.e/** ’ l
b b l l l a l a b b
l . l .
. .
l . l .
l l
. .
b b
l l
l .** . l ’ l .** . l ’
l . l .
l l 6 l 6 l
l b
l b
l l
. .
. . 0 0 * * l l . ‘0‘ 0’.
. ‘0‘ 0’.
’ . ’ .
1 . 1 . 4 4 l l * ’ * ’
. . . . l l l l l l
0 0
l l l l . .
40
C
D
0
10
FIG. 3. FIG. 3. Effects of object size (A-E) and starting distance (F) on directional selectivity. Response of “LGMD” is plotted Effects of object size (A-E) and starting distance (F) on directional selectivity. Response of “LGMD” is plotted
to objects ranging in size from 50-70 mm and approaching on (-), to objects ranging in size from 50-70 mm and approaching on (-), or receding from ( - - - ), a collision course with or receding from ( - - - ), a collision course with
eye. Object size in millimeters, all objects were square: A, 50; B, 55; C, 60; D, 65; E and F, 70. In F, object was closer eye. Object size in millimeters, all objects were square: A, 50; B, 55; C, 60; D, 65; E and F, 70. In F, object was closer
to the eye: it approached from, and receded to, 300 mm from “eye”. to the eye: it approached from, and receded to, 300 mm from “eye”. Other stimulus conditions and network parameters Other stimulus conditions and network parameters
were as in Table 1. Activity in the were as in Table 1. Activity in the
“LGMD” was plotted at 1 -ms intervals throughout simulation. *, onset of feed-forward “LGMD” was plotted at 1 -ms intervals throughout simulation. *, onset of feed-forward
loop inhibition onto loop inhibition onto
“LGMD”. Insets show image of object mapped onto input array, at object’s closest distance to eye. “LGMD”. Insets show image of object mapped onto input array, at object’s closest distance to eye.
to that used by Werblin ( 1991) to model activity in the tiger
salamander retina. Time constants are all set within physiological
limits. The time constant for the I unit is the longest at 55 ms, a
value consistent with y-aminobutyric acid-B (GABA,) -mediated
inhibition (Werblin 1991). Unless otherwise stated, in each simula-
tion the network is allowed to adapt to the presence of the object
on the eye before motion begins. This process of adaptation is
defined relative to the declining activity of E units in layer 2.
All values chosen for the parameters of the network fall within
experimentally observed limits for the locust nervous system. The
output of the network is resistant to small alterations in these
parameters.
layer 1; activity in each I unit in layer 2; and activity in each S
unit in layer 3. The retinotopic position of each unit is preserved
in the display, with the level of excitation indicated by a circle
whose radius is proportional to excitation level. Activity in the
‘ ‘LGMD’ ‘, the output element in layer 4 of the network, is displayed
at the end of each simulation as a graph of excitation, on a scale
of O-400, against time. Taken together, these outputs allow activity
in a particular element in any layer to be related to both the object
attributes that produce it, and the phase of the final output response
to which it contributed. Tables 1 and 2 give the parameters used
for both stimulus and network to produce the results shown in the
initial figures in this paper. Object motion occurs relative to a screen
100 mm from the P units of the eye. The distance and position
Monitoring network activity during each simulation
of the object relative to the screen is given by three values: X,
corresponding to horizontal position; Y, corresponding to vertical
During each simulation, a graphical display is available at the
position; and 2 corresponding to distance (see Fig. 1). Object di-
end of each simulated ms for the image on the array of P units in mensions, object velocity, the direction and length of path are speci-
972
F. C. RIND AND D. I. BRAMWELL
B
r
/ Image size , / 5()ms
FIG.
4. Response of the network “LGMD” and the locust LGMD compared. A : object approach on a collision trajectory.
B: object recession along same path. Movements of a 75mm object occurred at a velocity of 2rn/s over a 500 mm distance,
from 600 mm to within 100 mm of the eye. In each panel,
top
trace (-) shows response of LGMD recorded from its
dendrites in optic lobe; middZe trace shows output of network
“LGMD” and bottom trace monitors image size of approaching
or receding object. An upward deflection indicates an increase in image size. Image size ranged between 7.2-41 deg at eye.
Beginning of network response was aligned with first observable response in LGMD neuron. This was necessary as network
was set up without a delay in photoreceptor unit response after stimulus movement (see P unit, Table 2).
fied, in
millimeters or meters
per second. Motion in the 2 direction
toward or away from the P units always occurs with at a constant
velocity. When a particular set of network parameters are specified
and the simulation performed repeatedly, the network activity and
“LGMD” output are identical on each occasion.
RESULTS
The results are divided into three parts. The first section
seeks to establish that the network behaves like the locust
LGMD neuron. The second section looks at processes in
the network underlying this behavior and the final section
assesses the importance of these processes by altering each
one separately and looking at the response of the network.
The response of the network is always the same to a repeated
stimulus.
‘ ‘LGMD ’ ’ response to object upproach versus recession
In the following experiments, the network “LGMD” is
challenged by the kinds of stimuli that were used to establish
the locust LGMD/DCMD neurons as collision detectors and
to examine the critical image cues for this discrimination.
(Rind and S immons 1992; Simmons and Rind 1992). Ob-
jects either move in depth relative to the eye or laterally at
a fixed distance from the eye. The activity in the “LGMD”
in layer 4 of the network is recorded at millisecond intervals
throughout each simulated movement (Table 1 for details
of the two stimulus configurations). Directionality of the
“LGMD” response to opposing directions of movement is
assessed by comparing either the peak amplitude of its re-
sponse or the duration of the rising phase of its response.
These measures were adopted because spike production by
the locust LGMD has been found to require a rising, or
maintained membrane potential (Rind 1996).
When the network is challenged with objects ap-
proaching or receding, at all velocities tested, the
‘ ‘LGMD’ ’ responds directionally, preferring object ap-
proach to recession (Fig. 2). The directionality of response
is the same for both light and dark objects-eliminating
luminance change as a cue for the directionality. Excitation
in the “LGMD” increases throughout the approach of an
object. The faster the approach, the greater the rate of
increase in excitation and also the greater the final level
of excitation, reaching a maximum level at approach veloc-
ities of 10 m/s (Fig. 2). This closely parrallels the response
of the locust LGMD as described in Fig. 6, Rind and Sim-
mons ( 1992). The response latency, measured as the first
‘ ‘LGMD” excitation, decreases with increases in approach
velocity. The
“LGMD” responds throughout object ap-
proach and its response is only brought to an end after
object motion has ceased. This contrasts markedly with
the “LGMD” response to receding objects; this response
occurs as a brief peak, with a rising phase of only 4.5-8
ms, soon after the start of object movement. Like the locust
LGMD (Fig. 6, Rind and Simmons 1992)) the “LGMD”
response amplitude increases as velocity increases but re-
sponse latency remains constant. At the slowest velocities
of object recession, there are a series of small peaks in
LGMD excitation that follow the initial peak.
Directional “LGMD” responses also are found for a wide
range of object sizes and distances from the eye (Fig. 3, A-
F). The excitatory response to approaching objects is of
greatest amplitude to the largest objects simulated as is ob-
served for the locust LGMD (Fig. 7D, Rind and Simmons
1992). In every simulation, the rising phase of the “LGMD”
response is longer in response to object approach than it is
to object recession. “LGMD” directionality increases with
increasing object size, reaching a maximum with an object
of 70
X
70 mm (Fig. 3E). With objects of this size, the
“LGMD” response to object recession is very brief, lasting
only 5 ms, with a rising phase of 2-3 ms. Objects 565
x
65 mm produce progressively less excitation in the
“LGMD” during object approach, but with the smallest ob-
jects, the response becomes prolonged after motion has
ceased. In contrast, the response during object recession
grows more prolonged as the size of object decreases. These
two effects decrease the directionality of the “LGMD” to
smaller-sized objects. Beginning the approach from closer to
NEURAL NETWORK FOR COLLISION AVOIDANCE 973
FIG. 5. Collision vs. noncollision trajectories. Response of the
“LGMD” to a square object 50 mm in size, approaching eye at 15 m/s.
Approach trajectories were successively displaced: A, in the X direction;
B. in the X and Y directions, away from a collision path (for X and Y
directions, see Fig. 1 ). Other stimulus details and network parameters were
as in Table 1. Activity in
“LGMD” was plotted at 1 -ms intervals throughout
each simulation. Greatest response was given in response to a simulated
trajectory 1.4 deg from a direct collision course.
the eye does not change the overall form or directionality of
the “LGMD” response (Fig. 3 F, note expansion of x axis).
When the responses of the network “LGMD” and the
locust LGMD (recorded as in Rind 1996) are compared with
stimuli of the same size, moving at the same velocity, from
the same distance and on the same trajectory (Fig. 4, A and
B), the shape and timing of the two responses are very
similar. The response of the network to a distant approaching
object begins after that of the neuron as there is a longer
interval before any of the image edges pass over an input
unit of the network compared with the eye. This difference
can be accounted for by the 20-fold decrease in number of
input elements in the network (250) compared with the lo-
cust eye (5,000).
The excitatory response of the “LGMD” is greatest for
obiects approaching on a collision course.
Figure 5 shows
excitation in the “LGMD” plotted as a function of trajec-
tory. In all these simulations an object 50
x
50 mm in size
approaches the eye at a velocity of 15 m/s. These particular
attributes are chosen to maximize both the time the object
stays within the receptive field of the eye and the excitation
evoked by the object. In a series of 10 approaches, the object
is made to deviate by successive increments of 1.43 deg
from a collision trajectory (other stimulus details as in Table
1). Deviations occur either in the horizontal plane alone
(Fig. 5A) or in a plane midway between the horizontal and
vertical (Fig. 5B). The greatest “LGMD” response is given
to objects approaching within 3 deg of a direct collision
course with a peak in response with a slight ( 1.4 deg) devia-
tion from a direct collision course (Fig. 5, A and B). As the
object was 5
X
5 mm in size, trajectories within 3 deg of a
direct approach will still result in collision between object
and eye.
‘ ‘LGMD ’ ’ directional selectivity to horizontal motion in
the X -Y plane
The network does not respond directionally to constant
velocity motion in the X -Y plane (parameters in Table 1).
The leading edge of a bar is made to move laterally at 0.75
m/s, corresponding to an angular velocity over the “eye”
of 287 deg/s, a velocity of motion similar to that used in a
study of the response of the LGMD neuron (Fig. 5, Simmons
and Rind 1992). The overall form and amplitude of the
“LGMD” response to rightward (solid line Fig. 6) versus
leftward (dashed line Fig. 6) edge movement is very similar
(the saw-toothed appearance of each the curve is due to
successive stimulation of aligned P unit receptive fields in
the input array). From these curves, it is seen that the net-
work, like the LGMD, does not respond preferentially to
one particular direction of motion in the X -Y plane. This
result is confirmed for a range of edge velocities and extents.
Similar responses are recorded for motion of a bar rather
than a single edge. With constant velocities of edge move-
ment, the ‘ ‘LGMD” response increases as edge velocity
increases over the range tested: 380 deg/s ( 1 m/s) - 1,150
deg/s (2.75 m/s). The network responds most strongly to
large objects moving at high velocities.
Processes shuping network responses to moving objects
In the second part of this paper, we examine the mecha-
nisms underlying the response of the “LGMD” to moving
objects. We will look into the network to see what happens
in layers l-3 during object motion and test the importance
of specific features of the network, such as lateral inhibition
and feed-forward inhibition, by altering each process in turn
and examining its effect on the selective response of the
network.
First we will examine the critical image cues for a direc-
tional response by the network “LGMD” and the impor-
tance of lateral inhibition in shaping them. In the locust
LGMD neuron, the critical image cues for a directional re-
sponse to an approaching object have been identified as an
increase in the velocity of edge motion and an increase in
the amount of edge (Simmons and Rind 1992). Either of
these cues presented in isolation from each other induced a
selective response in the neurons (Simmons and Rind 1992).
F. C. RIND AND D. I. BRAMWELL
Simulated Response of 'LGMD'Neuron
-
Right
Movement
--
Left
Movement
I
1 I I I I I
30 40 50 60 70 80 90
Time (ms)
When each of these cues is presented in isolation to the
network “LGMD”, the response, measured as peak excita-
tion, is also selective (Fig. 7). The preferred stimuli for the
“LGMD” are an increase in the velocity of edge motion
(Fig. 7A) or an increase in edge extent (Fig. 7B). The
importance of lateral inhibition in shaping this selectivity is
revealed by examining the
‘ ‘LGMD” response when this
inhibition is removed from the network. In the absence of
any lateral inhibition, the selective response of the
“LGMD” to edges that move with an increase in velocity
or extent is either much reduced or abolished (Fig. 7). These
results show that lateral inhibition is important in shaping
the selective response in the “LGMD” and emphasize the
match between the “LGMD” and the locust LGMD/DCMD
neurons in the critical image cues for a directional response
to approaching objects. These simulations establish that the
“LGMD” responds in the same way as the locust LGMD/
DCMD neurons to moving objects.
Network response to trunslation
of
single edges in the X-Y
.
plane
The leading edge of a bar is made to move laterally to the
right, across the eye at a constant 0.75 m/s, corresponding to
an angular velocity at the eye of 287 deg/s (Fig. 8). As in
most visual experiments, the network is allowed to adapt to
the presence of the object on the screen before motion be-
gins. Adaptation lasts for 66 ms, until excitation in the E
units decayed completely, although there is still activity in
I units (see Fig. 1). As the edge begins to move (t = 0
ms), excitation passes down the network to S units located
in a position in the retinotopic array corresponding to the
leading edge of the stimulus. Inhibition in I units increases
and begins to extend in front of the moving edge, but at this
stage, inhibition is not strong enough to stop any S units
from reaching threshold and producing a spike. However,
as the movement proceeds (t = 20 ms), the inhibition gener-
ated by the moving edge is strong enough to preven t some
S units from firing when the edge passes over them. As the
FIG. 6. Response of “LGMD” to rightward, vs.
leftward, edge motion across eye. Edge that was 80
mm high and subtended 53 deg at eye moved at 0.75
m/s. Movement lasted 93 ms. Stimulus details as in
Table 2.
simulation proceeds, inhibition continues to increase and
spreads in front of the edge. Usually, some S units are pre-
vented from reaching threshold by this inhibition and only
at t = 70 ms do all the S units beneath the edge reach
threshold. For the last 20 ms of the simulation, lateral inhibi-
tion again cuts back the excitation in the S units correspond-
ing in position to the leading edge of the stimulus. After the
edge has moved over them, excitation in E units decays
rapidly (Tconst. of 12.3 ms) whereas excitation in I units
(Tconst. of 55 ms) persists, creating a trail of inhibition.
This figure shows the existence of a critical race for control
of S unit activity between laterally extending inhibition and
excitation passing retinotopically down the network.
Changing the velocity of edge motion allows the relative
times of arrival of the laterally directed inhibition and the
excitation at the S units to be altered. The responses of the
network to edge velocities of 380 deg/s ( 1 m/s), 750 deg/s
( 1.5 m/s) and 1,150 deg/s (2.75 m/s) are shown in Fig. 9.
When the activity in layers 2 and 3 of the network is examined
at the end of the simulation, a gradual diminution in the
effectiveness of the lateral inhibition is found as the velocity
of edge motion increases (Fig. 9). Although the amount of
inhibition has not changed, it is arriving at the S units of layer
3 after the edge-mediated excitation has arrived (the F unit
is not activated by any of these translatory stimuli).
Network response to object approach
In this simulation, an object approaches the eye at 10 m/
s on a collision trajectory (Fig. 10). At time 0 ms (t = 0),
the network has adapted to the presence of the object’s image
on the photoreceptor array. Some activity is still present in
the I units because these units have a longer time constant
than the excitatory units on which adaptation time is based.
As the object approach begins, the moving image edges
generate excitatory responses in the P units of the input
array. The excitation is passed on to layers 2 and 3 and the
“LGMD” and at this stage is not checked by lateral inhibi-
tion because inhibition is delayed relative to excitation (2
A
Stimulus
Edge
.
.
Position:
'LGMD' Response:
With Lateral
Inhibition
Without Lateral
Inhibition
B
Stimulus:
Edge
Position:
'LGMD' Response:
With Lateral
Inhibition
Without Lateral
Inhibition
NEURAL NETWORK FOR
0 40ms 0 40ms
0
73 65
FIG;. 7. Isolation of critical image cues for a directional response in
“LGMD” and role of lateral inhibition in shaping them. Simulations were
performed with either normal values for I unit-mediated lateral inhibition,
as given in Table 2, or with no lateral inhibition (both nearest and next-
nearest neighboring units set to 0.01 c/c). “LGMD” response was measured
as peak excitation level. A: a single edge moved across eye with same
velocity as an edge of an object either directly approaching or receding
from the eye (see Table 1 ). Edge length was constant throughout the
movement. B: a single edge moved across eye, with same extent as an edge
of an object directly approaching or receding from eye (see Table 1).
Angular velocity was constant throughout the movement.
ms to nearest neighboring and 4 ms to next-nearest neigh-
boring S units; see Table 2). As the approach proceeds (t =
10 ms), the lateral inhibition generated by the moving edges
begins to spread out in layer 3 beyond the retinotopic posi-
tion of the image and so beyond the edge-mediated excita-
tion. At t = 20, the S units are not yet prevented from
reaching threshold by this inhibition, although the strength
of the inhibition is building up rapidly and between t = 25
and f = 37 ms, some S units are prevented from reaching
threshold by the lateral inhibition. In the last stages of ap-
proach, the velocity of image edge motion continues to in-
crease rapidly (t = 38)) so that the edge-mediated excitation
in layer 3 is able to escape the influence of the lateral inhibi-
tion (I unit activity). This allows excitation to build up very
rapidly in layer 3 S units and consequently the “LGMD”
(Figs. 2 and 10). In this phase of the object’s approach, the
large extent and rapid movement of the image edges also
activate the feed-forward inhibition (F unit, * Fig. 2). This
inhibition has a delay of 4.5 ms before it reaches the
COLLISION AVOIDANCE
97s
“LGMD” so that, in this simulation, the cut back in re-
sponse it causes occurs after object approach has ceased. At
the end of object approach a pool of strong inhibition is left
in layer 2 in the wake of the rapidly moving image edges.
For approaching objects, increased velocity results in an
increased number of S units in layer 3 reaching threshold.
As the velocity of object motion increases, the object’s image
moves with sufficient speed over the eye that the E-unit-
mediated excitation of S units is able to escape the sup-
pressive influence of the laterally directed inhibition, carried
by I units in layer 2. This is clearly seen in Fig. 11 where
the activity present in the network at the ends of approaches
of different speeds are shown. At the lowest velocity of
object approach, the response of S units in layer 3 (Fig. 1 1,
left, 4 m/s) is suppressed by the lateral inhibition (Fig. 11,
right, 4 m/s). With approach velocities of 6 and 8 m/s,
the excitation that passes down the network following edge
motion escapes the suppressive influence of the lateral inhi-
bition in the latter stages of object approach (Fig. 1 1). With
a further increase in approach velocity (u = lo- 14 m/s),
the critical race, between excitation and lateral inhibition for
control of the output of the S units in layer 3, is won by the
excitation at successively earlier stages in the object ap-
proach until at 14 m/s very little suppressive influence of
the lateral inhibition remains.
Network response to object recession
In this simulation, an object recedes from the eye at a
velocity of 10 m/s (Fig. 12). As object recession is initiated,
the moving image edges generate an excitatory response,
which passes down the network and is not checked by any
lateral inhibition. In this initial phase of the object’s reces-
sion, the large extent and rapid movement of the image edges
activate the feed-forward inhibition (F unit). This inhibition
has a 4.5ms delay before it reaches the “LGMD”. In this
simulation F unit inhibition acts at t = 6 ms to cut back
excitation rapidly in the “LGMD” (“‘Fig. 2). At the same
time, lateral inhibition extends in front of the edge-mediated
excitation. Unlike the case for an approaching object, with
a receding object the image edges move with ever decreasing
velocity as the recession progresses, and this allows inhibi-
tion to prevent any excitation in the S units (Fig. 1 1). After
t = 10 the edge-mediated excitation is progressively sup-
pressed at layer 3, as excitation is overtaken by a growing
area of inhibition (t = 20, 30, and 40 ms).
Movement of large objects at high velocities away from
the eye lead to strong activation of the feed-forward inhibi-
tory loop and a rapid and complete shut down of “LGMD”
excitation (‘“Fig. 2, u = lo- 14). Small objects moving at
low velocity lead to weak activation of the feed-forward
inhibitory loop and a partial or temporary shut down of
excitation in the “LGMD” with residual network excitation
in S units causing further “LGMD” excitation in the latei
stages of object recession (Figs. 2 and 3). This residual
excitation after object recession is greatly accentuated in the
absence of any lateral inhibition (see Fig. 13 below).
Importunce of the critical race fiw directional selectivity
These experiments reveal the existence of a critical race
between excitation, passing down the network, and inhibi-
976
F. C. RIND AND D. I. BRAMWELL
‘S’-unit Response
I
‘I’-unit Response
. . .
_
OOO
Ooo
O”o
0 0
0 0.
0 0
0 l
‘Irr
a
. -
- . e t=Oms
‘t =30ms
‘t=6Oms
‘t =90ms
FIG. 8. Response of neural network “LGMD” to motion of an edge across eye. Edge that was 80 mm high and subtended
53 deg at eye moved at 0.75 m/s. Movement lasted 93 ms. Position of edge on array at 30-ms intervals during simulated
motion is indicated by a solid line superimposed on the activity of layer 2, I units (Inhibition, right) and of layer 3, S units
(level 3 response,
lqft).
I unit output onto layer 3 is shown.
NEURAL NETWORK FOR COLLISION AVOIDANCE
velocity =
T-unit Response
.
l
‘S-unit Response
380%
750%
1150%
FIG. 9. Response of the network to movement of a single edge across eye at 1 of 3 velocities. Each
snapshot shows
activity in network in last 1 ms of simulation: l@ (level 3 response), S unit activity; right (inhibition), I unit
output oilto
layer 3. Edge dimensions were as in Fig. 6.
tion passing laterally, for the selective response of the net-
work. To test the importance of such a critical race, we alter
first the strength and then the timing of lateral inhibition
within the network and examine the response of the
“LGMD” to approaching/ receding objects and to translat-
ing edges (Fig. 13, A-E, stimulus details as in Table 1).
Reducing the strength of both the nearest neighbor and
next-nearest neighbor I-unit-mediated lateral inhibition to 0
causes a small increase in the peak amplitude of the
“LGMD” response in the final 9 ms of the simulated object
approach (dotted line, Fig. 13A) but lead to a dramatic
increase in “LGMD” excitation in the latter part of simu-
lated object recession (dotted line, Fig. 13B), greatly reduc-
ing the directional selectivity of the network. With no lateral
inhibition, the “LGMD” response to lateral movement of
single edges is increased (Fig. 13C). The response of the
“LGMD” during the initial 12 ms of the simulation is not
affected by the change in weight of lateral inhibition. Left-
ward and rightward movements are equally affected. Thus
altering the strength, or timing, of lateral inhibition is found
to alter the tuning of the “LGMD” for rapid motion of
edges.
Decreasing the delay of the spread of I unit inhibition to
nearest and next-nearest neighbor to 1 ms from 2 and 4 ms,
respectively, reduces the “LGMD” response to both object
approach and recession (dotted line, Fig. 13, D and E). The
effect is to make it harder for excitation in S units to win
the critical race. The usual peak in “LGMD” response to an
approaching object is abolished because the edge-mediated
excitation no longer overcomes the suppressive influence of
the laterally spreading inhibition. By contrast, the response
to receding objects is much less affected by reducing the
978
F. C. RIND AND D. I. BRAMWELL
Toward
Time= Oms
Time= 1Oms
Time=20ms
Stimulus . _ .
.
.
l l l
.
.
.
. .
. 0
. .
.
l .
. l .
. .
.
.
.
.
.
.
.
. l .
.
.
.
.
. .
.
.
.
.
. .
l .
.
.
. .
. .
.
. .
.
.
b
’ . . .
l .
.
.
.
. .
. l .
.
. .
,:: .;:,:+: ::::
*.::::‘:.. ..I:< +
c3
..: .;:;,;+,: :_ .:
..:. :.
* y...... : fi l ;
:_ ,.:.,: y . . :.
:.
.
.
.
l . l
Response
Response
.
.
.
l
b
.
.
l
l .
.
.
.
l .
.
l .
.
.
l
.
. .
l
.
b
. l
.
l
.
l
.
.
l
.
.
.
l
.
.
.
.
l
.
.
.
.
l
l a
l . l
.
l
l l
l
l
.
l l
l
.
.
l
l . l
l
.
.
l l .
. l
0
l
.
.
.
.
l
l
. l
l
l
l
l .
.
l
l
.
.
.
l
l
.
.
.
l b:*:ie.
OO
zo 0:
O0
@
O0
9:
OO
. :0:
l l
.
l l
l
.
l .
.
l .
.
.
l l
0
.
l l
.
.
l .
.
.
.
l
.
l
. .
.
.
l
. l
.
.
. l
.
.
. l l
.
l . .
.
l
.
.
.
.
. .
.
.
l .
.
.
.
.
.
.
. .
FIG. 10. Neural network response to an object 75 X 75 mm in size, approaching eye at a velocity of 10 m/s on a collision
course. Initially object is 500 mm removed from “eye” and approaches to within 100 mm. Activity in layers l-3 of network
is shown at time 0, 10, 20, 37, 39, and 40 ms through the 40-ms simulation. Image of object remains on array throughout
movement, although bottom edge moves out of figure at t = 39 ms. Activity of each unit within a layer was represented as
a circle whose diameter reflects its level of excitation. Network was adapted to presence of image on eye, for 22 ms, before
object motion began. Top (stimulus), image of approaching object mapped onto photoreceptor array (P units, layer 1) ;
middle (inhibition), activity of lateral inhibitory units (I unit) at their output in layer 3; and bottom (level 3 response),
activity of summing units (S units) in layer 3.
delay on the lateral spread of I unit inhibition. As before,
the “LGMD” responds to object recession with a brief,
intense peak of activity at the beginning of object recession
but the amplitude of the response is slightly reduced (dotted
line, Fig. 13E).
Removing F unit mediated feed-forward inhibition pro-
longs “LGMD” excitation in response to both object ap-
proach and object recession. The response to object approach
is prolonged, after the end of the stimulus, and the response
to object recession is now maintained throughout movement
of the image (Fig. 13F). In the absence of F unit activity, the
‘ ‘LGMD’ ’ response to receding objects declines gradually as
activity in S units decays and no further S unit activation
occurs due to the spread of lateral inhibition into the areas
where the image edges now fall.
DISCUSSION
The neural network based on the input organization of the
LGMD neuron in the locust visual system responds direc-
tionally when challenged with approaching and receding ob-
jects. The directionality is maintained with objects of various
sizes and approach velocities and the network is tuned to
direct approach and shows no selectivity for different direc-
tions of translatory motion across the eye. The critical image
cues for a selective response to object approach by the
“LGMD” are growing edges, or edges that move with in-
creasing velocity over the eye. The network responds in the
same way as the locust LGMD neuron and meets the criteria
set out as a good challenge of the correspondence between
network and neuron. The network allows the following con-
clusions to be drawn about the mechanisms shaping the se-
lective response of the LGMD neuron to approaching ob-
jects.
Inhibition and its role in directional selectivity
The critical image cues for a selective response to object
approach by the “LGMD” are edges that change in extent
or in velocity as they move (Fig. 7). Lateral inhibition is
crucial to the selectivity of the “LGMD” and the selective
response is abolished or else much reduced if lateral inhibi-
NEURAL NETWORK FOR COLLISION AVOIDANCE 979
Time=37ms
Stimulus . . .
.
.
.
. l .
.
.
. .
. .
. .
.
I a
l
w . . :.:. l l l .
.
. *
*::; ;’ .;
8
.
j : :,,.. :.I:
l
l . .*
l ‘.
10. l
l
.
.
.
. l ’
l . ...,...:+‘.*.‘.
* _’ ., . . :. *.
‘.,. l
l .
l
l
,’ ::_ l ; !: .I., .: : ,; ‘;* _. *,
. 9
l
l .
d
.
0
‘+‘: .I:.*.., :.“::a.‘:: ‘.: : .a,,, l l .
.
l .
.*
,., ‘&.:i..: . . . . +‘. ~ ._ l : ._.
l
0 .“...
:* ,,,. .,‘.’ +‘: ._
l
l l .
l .
l
*: :.:.. ‘.* ‘*:
.
. 4 l .
.
.
l
y : ; .).“” ‘,’ : : v
0
.
: + ,,,: ,:: :,;i :‘*:,,
. l . 4’. .:; :‘:jrt,( ,,,,:I :‘*;,i.:,
*
l
.
.
.
.
l ’
.
.
.c’,(,* ,*:::,:.:: :‘, l .“. “. .
.
0 .
4. l .‘
l . . ‘.*,i : ,:‘, .Fj
.*
.
0.
. . l : .
,. . . . . .., .:
l . l * ,... ‘..i ‘...
.
.
.
1 -
.
. l .
Time=39ms
Time=40ms
l
.
.
*I’-unit Response
‘S’-unit Response
FIG. 10. ( cwntinuecl)
tion is taken out of the network (Fig.
7). We conclude “LGMD” response during object movement. A receding
that lateral inhibition in the neuronal network for the locust
LGMD also underlies the experimentally observed critical
image cues for its directional response. Lateral inhibition is
a prominent feature of the receptive field organization of the
locust LGMD neuron, and one function already suggested
is to protect the decrement prone small-field excitatory affer-
ents from habituation (Rowe11 et al. 1977). In the neural
network, lateral inhibition enhances the selective response
to approaching objects and, in conjunction with other pro-
cesses, tunes the network to objects approaching on collision
trajectories: as an object approaches the eye of the network,
there is a rapid buildup of excitation in the output element
of the network, the “LGMD”. Essential to this buildup of
excitation in the “LGMD” is a critical race between excita-
tion passing down the network and inhibition directed later-
ally in layers 2 and 3 of the network. The conduction delay
of the lateral inhibition determines at which speed of ap-
proach, and at which point in the approach, the race between
excitation and inhibition for control of the output of layer 3
will be won by excitation. Directional selectivity is enhanced
greatly by feed-forward inhibition. Whereas the feed-for-
ward loop is activated at the end of object approach, truncat-
ing the excitatory “LGMD” response to approaching ob-
jects after approach has occurred, the feed-forward loop is
activated at the initiation of object recession truncating the
object evokes only a brief, intense peak of activity, with a
rising phase of 3-5 ms, that then is cut back by feed-forward
inhibition. Without the feed-forward loop, the initial re-
sponse of the “LGMD” to object recession declines slowly,
with a time course dependant on the time constant of the S
units in layer 3 of the neural network (Fig. 13 F). As reces-
sion progresses, lateral inhibition prevents activation of fur-
ther S units, because, unlike object approach, both edge
extent and velocity are ever decreasing.
Inhibition strength and its role in direction& selectivity
The strengths of inhibition used in the model are very
modest and we were particularly cautious about overestimat-
ing the strength of the lateral inhibition because this has
been a problem with theoretical studies of the mechanism
of directional selectivity in the past. For example, Koch and
Poggio ( 1983), in their model of the inhibitory interaction
responsible for generating directional selectivity in the cat
cortex, predicted that a measurable conductance increase
should accompany shunting inhibition during motion in the
nonpreferred direction. However, Douglas, Martin, Whitter-
idge, and coworkers ( 1988, 1991) examined the synaptic
interactions underlying directional selectivity by making in-
tracellular recordings from directionally selective cortical
980
F. C. RIND AND D. I. BRAMWELL
velocity =4m/s
‘S-unit Response 1 ‘I’-unit Response
&I
0
&b
o~~o~~~o~o
0
0
0 .
0
O 0.
l .0
00
o”
0’
0
Oo..
0
0 . .
:o
0
0
o;o;;;o;o
0.
8
0
-0.
0
.o
8m/s
12m/s
14m/s
1:ic;. I 1 . Neural network response to an object approachin
g eye on a collision course. Each snapshot shows activity in
network in last millisecond of simulation. Approach velocities of 4, 8, 12, and 14 m/s are shown. At each velocity, activity
of S units in layer 3 is shown on lqfi (level 3 response) and output activity of I units from layer 2 is shown on right
( inhibition).
NEURAL NETWORK FOR COLLISION AVOIDANCE 981
L
Away
Time= Oms
Stimulus . -
.
?’
* .., ‘,.* .: .* : .’ ,. .., .m ..:. .?
,
: .‘a’,
l . . :‘A ., .‘.I : .: .::, !... ~‘.;,~,~..::..’ .: : *,
,, ,_ ,: .: * .,.:_ ._.. fi.... ,:..... ... . . . . :. . . . : .+‘: ‘..:_I ,{
. . .*,; ,: :i. ,,
.*I : ::. .* : ; ; t *+:. y :?. ,‘,:. : :
,_ :I
_, ::::_:_:...: . .
:~: ,+:::,:*~. .y, ,,; i>:.; ‘:i.::. ::.:;*:.i ). l
.
4: ‘e’..
*’ :, c ‘,I ;_; .‘. :‘g? :j:‘::j.‘: t :;;yj:. ;, &:‘,;:i:x,z __.. ::: If;;;
: .‘. ‘*
‘*:.:‘. ::.t&:. .:.:* ::*:: ::: :.,_ f ..,.: :,.::.‘j:.: :: *:
,
. . .
l
:A ,’ .;::I:..::‘:~:::.“,.:i: ::.:.::::: *::.;:: : ;:;:.;.,*~i:,~E ; ,‘>C :,;:_:::;i:
‘. :. .‘.. l : : :.. ‘:. ,f ,:,:: :.fc(: 1.; “::,:‘::.::::‘:~:i;,~~~,: :.j;;;; ::,_:. .~ ::.:: ,,<,* .,: ~ ;::
.
: 4 .: .::;,?*:.. .:::.j$r iy* .:::::‘, :.,.::::~6:.~,:::~~::~: :. > :.: ,_,.__:: ‘:: :
. * : ..: i ; ‘1 ‘: :
. l .j’J?
‘:::::‘:,:,.::::,.:.~~:~,~~,.:~:~,~,: :i,:.~,3::~~t:::~~:.~:~.~~.~,.~~:.~ _.,__. :.::: _;_
:. A, .1”i ye...:..:.. .::.>.
.,.,.,.,,, * :,... :.::_::..::;...: .::>. y...:...:*..>. L_.,._ .._. . .._ 4 . . . l
:.::,‘,:‘* :.;:.., ,.:;,..)‘,. .: ., . . . . _.: :.. :.. :. .:_ .:. .:.. . . . . .
:.i; .. ‘: ‘j ‘. .i:‘::.* ,( :_.:>,::: .,:. :‘:;:,:3’::::::::,~;: ::.;:::.‘~::. :* ::__::;; .:;:;,:\_. ; *,:..: 1: ‘_>I :I:_
,
. , ”
l : .:: ; ,: :) ..’ ‘1.1; 1; ;i*:::‘:; i~~:,:itl~:~~.ii:I::~~:~:~,:~~~~.~,. ~.:;~:~j..$ .$$:,il’,:,i
,
.
:.
.
.
. .
..$; 1: .1_ -:; ; 6:: .:.,I::~ :Qi:i~*Xii~iii~~:~:~~~~~~~~.:~~:~~~~~~~~~~.:~ ,:;f:;j:;il:<:;
.:.. ,:y.;,::i;,, .:..:: : :, ;i:%i~,~.:::::~~~~:::~~,~:~~~~~~.:~~,~:~~~~:~:~~~~~~~~:~:~ .:zr:p
,
.
. , .,_.,. ;,.,,..: ,’ :: i”:y;: .“I:, ,..:
.,:*: ::j ~,..y,$.yq.. ,:;~::.‘::;$;ti’i’::: i *:::.::.:.::;,. ,
. :, _..::j;.:, l ./: .* ; .:~::::ii:::i~:i~:,:,~.~,~~~~~:~ 2;: 3.iii:ii~l::,lr.‘~,:~::~~.~~~:
.,.
.
.
b ? .’ .’
‘*,::’ ,’ .,: : “I*:’ ‘::,,i: ‘1;“:’ y:i:fi::; .‘lij~~~$;~;,:~,,,; ;ti’:$::,#,:r: ,gfi :
.* ‘.. ,,: e.:.
,;,F..::::. ...:.... .:. ‘.
..(I .:.,.,... . . . . . . . . . .,.
..y...<,..: *:y.: :::: ::x::$T’.: ::_,
l
,
.*. ,.
. .:. .,. .,.,._,
._ . . . .._... . . .
b
.
. “,.,’
‘: :: +-,% ,.,
: . . . . . .
.,., ,. ,:,:;$Jy :: y.$j:jj.ji:::~,:;; :$.+, ,,y, : s ,I,:: ;,:<:‘:i:::*:: ‘<, i’:; ,.I: ;:::: ,
: l ‘J :
: : ,,, :,e f;, ;,:;; ;: j*. ;~.,:,;*,~:::,~~.,~~ .:: :
,.‘.,O :‘.’
:. *.:;:.:: ‘: F ::.:: :>:. ‘:.Y.:::‘::
:I : : ._ :_, ..:.: ..:...
f& :: _: ‘,: : : 1: :I: :;.y::+::; ::,:;*:,:I’. ‘.:,:;::::&;:y .j_ . ..z.. .j’::
.
.
‘.
.,
.* :*:
,,,;,.:: ‘*,.:“:. . . :.:.:
*:.:.: :. ,.:. _.:A:.:.: .:.,.:.:.: . ..*. :.:., “.:
‘._:, j. .:::.:+ ,...: . . . . .:j:: ..,:,: _.+_. .::;i::i’::::: .,__.:._ f:_:-,_ l
l
..* ,::. .~ -:, ‘& : y y;.::, 1-2:: .y.:;;,
:_ .,_,_. :. . . ,..). . . ,._.__ .,.,. :.: ._._. .., .:.*‘.
.: _.
_.
*:: :,_ . . . .:4. : : .‘i..,
,’ :; y. *:‘t::i, :‘:‘::: ,+::; .:__. if .; ..:.
*.: :...* . . *‘: :‘::. ::, : .‘: :.yti::: ,_, _:: : : :. :
: f.1, _,‘: :...: ::.,,..:.. : ., . . . . . . . . . .__. $, 5 .:_
.
‘I’-unit Response
.
.
. l . .
0 .
.
0
. 0
O o”
0 .OO 0
.
0 0
0
.
O 0
oo-o”o 0 0
0 0 oooooo~oo b 0
. 0
0
. 0
0 Oo
000 0 o” ’
00
0
oooooo o”
0 .
0
“00 0.
.
z”
0 0
b
o~o~oo
oOoooOb
Oo 000
“,o oo ooo oooo
0 .
.
.
0
O o”ooooo Ooobb
. .
0
0
0 0
O0 0
oooo”o ooo.
0 0
0
oooooooo 0
.
0
0
0 0 0
0
0
0
.
.
n
‘S-unit Response
Time= 5ms
Time= 1Oms
w
.
b
.
.
.
.
.
.
l b
. .
* .
. b
.
.
.
.
. .
l b
.
.
.
l
.
.
.
.
.
.
b
.
.
FIG. 12. Neural network response to an object 75 x 75 mm in size directly receding from eye at a velocity of 10 m/s.
Object is initially 100 mm from eye and recedes to 500 mm. Stimulus conditions and network parameters were as in Tables
1 and 2, except that course of object was reversed. Network was adapted to presence of image on eye, for 22 ms, before
object motion began. Activity in layers l-3 of the network is shown at time 0, 5, 10. 20, 30, and 40 ms through 40-ms
simulation. 7’~~~ (stimulus), image of approaching object mapped onto photoreceptor array (P units, layer 1 ): r~i&llc)
(inhibition), activity of lateral inhibitory units (I unit) at their output in layer 3; and hottorn (level 3 response), activity of
summing units ( S units) in layer 3.
neurons
and failed to reveal conductance changes of the
order of magnitude predicted by Koch and Poggio ( 1983,
1985). In their simulation of the “canonical” circuit under-
lying directional selectivity in the cat visual cortex,
Douglas
and Martin ( 199 1 ) found that the relative timing of the
excitation entering the circuit and the inhibition generated
within the circuit was the critical feature determining
whether inhibition or excitation will predominate the re-
sponse. In the preferred direction, the excitatory input arrives
first and is able to produce strong cortical re-excitation,
which cannot be inhibited despite the strong inhibition that
this excitation also evokes.
In the “LGMD” neural network, the maximum possible
lateral inhibition directed at an S unit in layer 3 was 2.4
times the excitation delivered from an E unit in layer 2, a
level of inhibition that was only reached with simultaneous
activation of all 6 S units neighboring and 12 next-neigh-
boring I units such as would occur during a whole-field light
on or off stimulus. The synaptic gain for transmission from
I unit to each of the 6 nearest neighboring S units was
given a value of 0.284, whereas that to the 12 next-nearest
neighboring S units was 0.058. For comparison, the inhibi-
tory synapse between photoreceptors and laminar monopolar
cells in the fly retina has a maximum gain of -6 (Laughlin
et al. 1987), and the excitatory synapse between the locust
LGMD and DCMD neurons has a gain of plus 1.2 (Rind
1984). In both the LGMD and “LGMD”, the feed-forward
inhibitory loop was able to suppress completely an ongoing
response (O’Shea and Rowe11 1975) (Figs. 2-4). The gain
of this loop in the neural network was variable, increasing
with the number of activated photoreceptors. The feed-for-
ward loop in both the locust and the neural network LGMDs
exhibited the computational features of proximal neuronal
inhibition, whereas the effects of lateral inhibition more
closely resembled those of distal neuronal inhibition (Vu
and Krasne 1992).
In the neural network, a conservative estimation of the
extent of lateral inhibition was employed, extending it only
to nearest and next-nearest neighbors. This resulted in a
spread of inhibition over a visual angle of roughly 12 deg.
Rowe11 et al. ( 1977) estimate its spread in the locust LGMD
to be 520 deg. Initially, two configurations of the neural
982
Time=20ms
Stimulus _ _
.
.
. l .
.
.
.
.
. .
. 0
.
.
.
l .
. l .
. .
. l .
0
l .
.
. l 0
.
.
.
.
.
l .
.
. .
.
. . l .
0 l
.
.
. . .
l .
. .
. l
0
l .
0 . ::
,*.:: <: ?y .). .: :.
:. ., ,._. . . . . . :. _.. .
a
.
. . l .:: : .j, ‘.I:;, .:j 1: :;:+, 0
. l
.
.
. .
‘.. .,.:*‘::, ::. : :.,:...:.:: l .
l . .
: T ;: .;‘i:::*$$ : ;;::: j
l .
. .
,:: ,,:,:; +‘,‘:“.“,,,,:,, :_“.. l . l . l .
. . . . . . .._
0
. .
ir’;:.‘i.., ::‘.I’:;$ ,::...+: :;c
. .
,.:. ._.. :..::.:.:. : .. .‘. l
.
.
.
.
.
. . . .* ;:i: ,, .
.
.
:,, #‘.:.::I.:’ .,.
.
0
.
.
.
.
. .
.
l 0 l
0
0
.
.
.
l .
.
0
. .
.
.
.
l . l .
.
.
. .
.
. .
.
.
.
. . l
.
.
. 0
.
r
‘S’-unit
Response
o o”
ooooo
Oo
0
0 o”ooooooo 0
00
* 00
0
O0
00 o”
OO
000
O0
08
o”o
8
$0:
O0
O0
O0
0 0 OoO
OO
“0 O
o”ooo
O 0”
OOoOo
0 0 oooo” .o
0
F. C. RIND AND D. I. BRAMWELL
Time=30ms
l
0 0 oooo 0 o
O o” 0
0 ooooooo 0
0
00 00’
0 0
0 0 0 O 0 0
0
OO
0
0 :O
0 000”:.
0
O0 0,o
0
0 0
0 0
0 0
0 0 0 0
O O. 0 0
0 0’0 OoOoOO 0 0
0
0 0 .“oooo, 0 0
network were created. In the first, the lateral spread of inhibi-
tion was delayed relative to the excitation passing downward
through the layers of the network: 2 ms to the nearest and
4 ms to the next nearest neighbors. In the second, lateral
inhibition was not delayed (Fig 13, D and E). No direct
experimental evidence is available to distinguish between
these two alternatives, although intracellular recordings from
the LGMD verified the responses predicted by the first con-
figuration of the network (F. C. Rind, unpublished observa-
tions) and all the results shown in this paper use this version.
These delays would be consistent with a conduction delay:
in Limulus eccentric cells the lateral processes that mediate
lateral inhibition are much finer than those conducting infor-
mation centrally (Fahrenbach 1985 ) and so lateral inhibition
travels relatively slowly. In the locust, synaptic delays be-
tween some neurons are as short as 1 ms and thus too rapid
to be solely responsible for a 2- to 4-ms delay (Rind 1984),
however, both inhibitory and excitatory synapses between
ocellar neurons are known to have delays of 3-4 ms (Sim-
mons 1982). Anatomic evidence shows that these ocellar
synapses are monosynaptic (Littlewood and Simmons
1992). In the “canonical” circuit in cat cortex, the inhibition
is thought to be mediated by GABAB receptors and outlasts
the excitatory currents in the same neurons (Douglas and
Martin 199 1 ). The slow onset and decay of the inhibition
also is seen in the neurons of the tiger salamander retina
Time =40ms
~~ ~~~ ~~~
w . w
.
l l l
.
.
.
.
. .
l .
. l
.
.
. l .
. . .
.
.
.
0
.
.
.
l l l
.
.
.
.
l l
l
l l
.
0
0 . l .
.
l l
l
. .
. l
.
l l
. .
l l 0
l l
l
. l .
l
.
.
. l l
.’ .t,:.:::.*..:. ‘, ‘_ l
l
l l .
.
. 0
, ..j.:: :...: :..:_: l
l
.
l l . .
. . . . :I::.;. *‘l:;;,: ;: .
l
l l .
l 0
. .
:.*:‘:.“.: _:, ,..*
.:. . . .
l
.
0
. l
q
l i’..:i:;::;: :,:: :,: :: l
l .
.
. l
0 .
l
. .
.
.
. l
.
l
l l
. l
.
0
. .
.
l
l . l
0
.
l
0
.
l
. l
.
.
l
.
.
l 0 l .
.
.
l .
0 .
.
. .
l . l
.
.
.
l l
.
0
l l l . .
.
.
. .
l .
l
.
0
. l .
l .
.
.
.
. .
.
.
0 0
.
.
.
.
.
. .
.
l l
.
.
0
0
.
. . . .
. 0 0 .
.
l .
.
. .
.
.
. .
l
0 0
0
l .
. .
0
.
l .
.
.
.
.
.
0 0
.
.
.
.
.
.
.
l . l
and involves GABA, and glycine receptors (Frumkes et al.
198 1; Maguire et al. 1989; Werblin 199 1) . GABAB receptors
with similar response features are known in insects and these
were used as a guide to the properties of the I units responsi-
ble for lateral inhibition in the present neural network (Bai
and Sattelle 1995). The slow onset of inhibition may com-
bine with lateral conduction delays and a synaptic delay to
produce the 2- to 4-ms delay incorporated into the lateral
spread of inhibition within the neural network. GABAergic
neurons are thought to be present in the insect medulla and
lobula and have been implicated in the shunting inhibition
mediating directional selectivity in the fly (Biiltoff and Biil-
toff 1987), however, the pattern of GABA reactivity in lo-
cust optic lobes and the involvement of GABAB receptors
is not known.
Neurons and networks signaling motion in depth using
monocular cues
In humans, a compelling impression that an object is mov-
ing in depth is given when its magnification on the retina
is increased (Wheatstone 1852). Size change neurons or
psychophysical channels have been described in a wide
range of animals including humans (Cynader and Regan
1978; Hong and Regan 1989; Regan and Beverley 1978;
Tanaka et al. 1989; Wang and Frost 1992; Zeki 1974). In
NEURAL NETWORK FOR COLLISION AVOIDANCE
983
A
Simulated Response of 'LGMD' Neuron
*
Toward :
200
.' :
-
8
With Lateral Inhibition
- -- Without Lateral Inhibition
-4
4J
2
-4
D
Toward
.
Time (ms)
I3
E
, Away
Away
9
- With Lateral Inhibition
- -With critical race
- -- Without Lateral Inhibition
- --Without critical race
C
Across
-With Lateral Inhibition
--
Without Lateral Inhibition
t
1
Away
-With Feedforward Inhibition
--Without Feedforward Inhibition
t
FIG. 13. Effects of changing network parameters on response of “LGMD”. Role of inhibition in response to objects that
move
toward, away from, or across eye (stimuli as in Table 1).
A-C:
with and without lateral inhibition.
D
and
E:
with
and without a race between excitation and lateral inhibition (without a race: delay on inhibition < 1 ms). F: with and without
feed-forward inhibition.
those size change neurons that have been studied to date,
divergent motion of image edges (or other image features)
has been a critical image cue for a directional response (Re-
gan and Cynader 1979; Zeki 1974). Liaw and Arbib ( 1993 )
have developed a neural network that mimics the direction
selective avoidance response shown by anurans to ap-
proaching objects. The sensitivity of the network to radial
edge expansions and to the net receptor dimming is modeled
on the responses of neurons in the frog tectum (T3) ,which
are direction selective for object motion in depth (Griisser
and Grusser-Cornehls 1976). In the network, each T3 neuron
receives inputs from photoreceptors looking out over a 40
X
40-deg patch. The detection of radial edge expansion is
achieved by increasing the synaptic weighting toward the
periphery of each T3’s receptive field. As a consequence,
maximal activation of the network is only achieved if the
object edges expand within the 40
X
40 deg extent of each
T3 receptive field. This means that the response is not inde-
pendent of object size or contrast and that time to collision
cannot be signalled unambiguously. In their simulations, ob-
ject distance is not calculated by the network but was mea-
sured independently and added subsequently to allow appro-
priate reactions to be timed. Even with these limitations, the
network has been effective in mimicking frog approach/
avoidance behavior in response to objects moving toward
the animal.
As the present network is the first example incorporating
the receptive field organization of an identified neuron,
which is selective for motion in depth, it is not possible to
determine the generality of the neuronal interactions in-
volved. However, the ability of animals to estimate time to
collision with either a rapidly approaching object or surface
using auditory or visual cues derived from one eye is well
documented behaviorally. Lee ( 1980) has described a vari-
able tau (r = image size/rate of change in image size) that
allows the time to contact with an approaching object to be
984
F. C. RIND AND D. I. BRAMWELL
determined without first measuring its approach velocity and
distance. Tau (r> is thought to be used to time behavior by
plunge diving gannets (Lee and Reddish 198 1 ), landing flies
(Wagner 1982)) landing pigeons (Lee et al. 1993) and bats
navigating around obstacles or through narrow openings
(Lee et al. 1992). These findings suggest the generality of
such a strategy and emphasize the importance of any solution
A probable explanation for this is that their visual stimuli were not
adequate to excite the LGMD at the end of object approach when
the rate of image change is high. Their experiments plot the failure
of their visual stimulus to excite the LGMD rather than any re-
sponse of the neuron. Consistent with this, Simmons and Rind
(1992) report that edge jumps of >5” at the eye result in a rapid
decline in LGMD excitation.
in terms of the neuronal processing involved. Wang and
Frost
( 1992) described neurons in the nucleus rotundus of
REFERENCES
the pigeon brain that responded selectively to images of an
BAI, D. AND SATTELLE, D. B. A GABAB receptor on an identified motor
object approaching the bird on a collision course. The loom-
neurone. J. Exp. Biol. 198: 889-894, 1995.
BERMAN, N. J., DOUGLAS, R. J., MARTIN, K. A. C., ANII WHITTERIDGE, D.
ing sensitive neurons used monocular cues to signal a con-
Mechanism of inhibition in cat visual cortex. J. Physiol. Lond. 440: 697-
stint time to collision of 1 s, irrespective of object size
or approach velocity. Wang and Frost concluded that these
neurons were involved in initiating and controlling the pi-
geon’s avoidance behavior to such looming objects. These
observations provide evidence that there are mechanisms in
the pigeon visual system capable of extracting tau (r ).
course.
In
the
“LGMD”,
both lateral inhibition and feed-forward
inhibition underlie selectivity for objects rapidly ap-
proaching on a collision course. Removing or altering the
The neural network described in this paper was based on
the input organization of the LGMD neuron, which has been
shaped by natural selection over millions of years, particu-
timing of either lateral inhibition or feed-forward inhibition
larly as the pathway is thought to be crucial to individual
survival, functioning in escaping imminent predation (Rind
reduced the selective response to approaching objects (Fig.
and Simmons 1992). The network, and the pathway that
inspired it, both gave a rapid and robust response to ap-
proaching objects, regardless of wether the object was lighter
13). The selectivity of the network and by analogy the
or darker than the background. The response of the system
increased rapidly as an object approached. Object collision
LGMD neuron is due to the timing of the critical race be-
was signaled independently of approach trajectory as there
was no hard-wired system for detecting the pattern of radial
tween the excitation passing down the network and both
edge expansion that accompanied object approach. The net-
work was found to be tuned to detect the time-varying fea-
forward and laterally directed inhibition. For excitation to
tures of the image of an approaching object on a collision
dominate, excitation must arrive before laterally extending
HON& X. ANII REGAN, D. Visual field def&ts for unidirectional and oscilla-
inhibition and before feed-forward inhibition is initiated.
tory motion in depth. Visiorz Rc.s. 29: 809-8 19, 1989.
Feed-forward inhibition is switched on after the stimulus
HORRIIIGII, G. A. The separation of visual axes in apposition compound
movement has ceased for an approaching object and during
eyes. Philos. Trms. R. Sot. Land. B Biol. Sci. 285: l-59, 1978.
the movement for a receding one. The model allowed the
Kocrj, C. AND POGC;IO, T. A theoretical analysis of electrical properties of
spines. Proc. R. Sot. Lmd. SW. B Biol. Sci. 2 18: 455-477, 1983.
722, 1991.
BULTHOFF, M. ANL) BULTHOIT, I. Combining neuropharmacology and be-
haviour to study motion detection in flies. Biol Cyherrwt. 55: 3 13-320,
1987.
CYNADER, M. AND REGAN, D. Neurones in cat parastriate cortex sensitive
to the direction of motion in three-dimensional space. J. Physiol. Lond.
274: 549-569, 1978.
DEHAY, C., DOUGLAS, R. J., MARTIN, K. A. C., AND NELSON, C. Excitation
by geniculocortical synapses is not vetoed at the level of dendritic spines
in cat visual cortex. J. Physiol. Lond. 440: 723-734, 199 1.
DOUGLAS, R. J. AND MARTIN, K. A. C. A functional microcircuit for cat
visual cortex. J. Physiol. Lond. 440: 735-769, 199 1.
DOUGLAS, R. J., MARTIN, K. A. C., ANI> WHITTERIDGE. D. Selective re-
sponses of visual cortical cells do not depend on shunting inhibition.
Nmmz Lond. 332: 642-644, 1988.
DOUGLAS, R. J., MARTIN. K. A. C., ANII WHITTERIDGIZ. D. An intracellular
analysis of the visual responses of neurones in cat visual cortex. J.
Physiol. Lund. 440: 659-696, 199 1.
EDWARDS, D. H. The cockroach DCMD neurone. I. Lateral inhibition and
the effects of light- and dark-adaptation. J. Exp. Biol. 99: 61-90, 1982.
FAHRENBACH, W. H. Anatomical circuitry of lateral inhibition in the eye
of the horseshoe crab, Lirmlus polyphmms. Proc. R. Sot. Lond. Ser. B
Biol. Sci. 225: 219-249, 1985.
ences on ganglion cell receptive field organisation: a model. J. Neuro-
physiol. 45: 783 - 804, 198 1.
GIBSON, J. J. Visually controlled locomotion and visual orientation in ani-
mals. Br. J. Psychol. 49: 182- 194, 1958.
GLANTZ, R. M. Defense reflex and motion detector responsiveness to ap-
proaching targets: the motion detector trigger to the defense reflex path-
way. J. Corny. Physiol. 95: 297 -3 14, 1974.
GRUSSSER, O.-J. AND GR~~SSER-CORNEHIX U. Physiology of the anuran
visual system. In: Frog Neurobiology, edited by R. Llin;-is and W. Precht.
Berlin: Springer-Verlag, 1976, p. 297 - 385.
HOI.MQVIST, M. H. AND SIIINIVASAN, M. V. A visually evoked escape
response of the house fly. J. Conlp. Phwbl. 169: 45 1 -459, 199 1.
FRUMKES, T. E., MILLER, R. F., SLAUGHTER. M., ANI> DACHEUX, R. F.
Physiological and pharmacological basis of GABA and glycine action
on neurons of mudpuppj, retina. III. Amacrine mediated inhibitory influ-
role of these processes in the selective responses of the locust
KOCH, C. ANLI POGGIO, T. Synaptic veto mechanism: does it underlie direc-
neurons to be studied.
tion and orientation selectivity in the visual cortex? In: h4od~l.s of the
Visual Cor’tclx, edited by D. Rose and V. Dobson. Chichester: John Wiley
and Sons, 1985, p. 408-420.
F. C. Rind is a Royal Society University Research Fellow.
LAUGHIAN, S. B., HOWARIX J., ANL) BI,AKF,SIA:L;, B. Synaptic limitations to
This work was supported by a grant from the Science and Engineering
contrast coding in the retina of the blowfly C’crlliphorct. PI-w. R. Sot.
Research Council ( UK) and by the Royal Society.
Lond. Ser. B Biol. Sci. 23 1: 437-467, 1987.
Address reprint requests to F. C. Rind.
LEE, D. N. The optic flow field: the foundation of vision. Philos. Trms. R.
Sot. Lond. B Biol. Sci. 290: 169- 179, 1980.
Received 20 June 1994; accepted in final form 28 September 1995.
NOTE ADDED IN PROOF
The finding that Lobula Giant Movement Detector (LGMD)
excitation builds up throughout object approach directly contradicts
the findings of Hatsopoulos et al. (Hatsopoulos, N., Gabbiani, F.,
and Laurent, G. Elementary computation of object approach by a
widefield visual neuron Science Wash. DC 270: lOOO- 1003, 1995).
LEE, D. N., DAVIES, N. N. O., GREEN, P. R., ANL) VAN DER WEEL, F. R.
Visual control of approach by pigeons when landing. J. Exp. Biol. 180:
85- 104, 1993.
LEE, D. N. AND REDDISH, P. E. Plummeting gannets: a paradigm of ecologi-
cal optics. Nature Lond. 293: 293-294, 198 1.
LEE. D. N.. VAN DER WEEI,. F. R., HITCHCOCK, T., MATEJOWSKY. E., AND
P~TTIGR~W, J. D. Common principle of guidance by echolocation and
vision. J. Camp. Physiol. 17 1: 563-57 1, 1992.
NEURAL NETWORK FOR COLLISION AVOIDANCE
985
LIAW, J.-S. AND ARBIB, M. A. Neural mechanisms underlying direction
selective avoidance behavior. In: Adaptive Behavior. Cambridge, MA:
The Massachusets Institute of Technology, 1993, vol. 1, p. 227-261.
LITTLEWOOD, P. M. H. AND SIMMONS, P. J. Distribution and structure of
identified tonic and phasic synapses between L-neurones in the locust
ocellar tract. J. Comp. Neural. 325: 493-5 13, 1992.
MAGUIRE, G., MAPLE. B., LUKASIEWICZ, P., AND WERBLIN, F. G-Ammo-
butyrate type B receptor of L-type calcium channel current at bipolar
cell terminals in the retina of the tiger salamander. Proc. Natl. Acad. Sci.
USA 86: 10144-10147, 1989.
MILDE, J. J. AND STRAUSFELD, N. J. Cluster organization and response
characteristics of the giant fiber pathway of the blowfly Calliphora eryth-
rocephala. J. Comp. Neurol. 294: 59-75, 1990.
NALBACH, H.-O. Visually elicited escape in crabs. In: Frontiers in Crusta-
cean Neurobiology, edited by K. Wiese. Basel: Birkhauser, 1990, p.
165-172.
NILSSON, D.-E. Optics and evolution of the compound eye. In: Facets
of
Vision, edited by D. G. Stavenga and R. C. Hardie. Berlin: Springer-
Verlag, 1989, p. 30-74.
O’CARROLL, D. C., OSORIO, D., JAMES, A. C., AND BUSH, T. Local feedback
mediated via amacrine cells in the insect optic lobe. J. Comp. Physiol.
171: 447-455, 1992.
O’SHEA, M. AND ROWELL, C. H. F. Protection from habituation by lateral
inhibition. Nature Lond. 254: 53-55, 1975.
O’SHEA, M. AND ROWELL, C. H. F. The neuronal basis of a sensory analyser,
the acridid movement detector system. II. Response decrement, conver-
gence, and the nature of the excitatory afferents to the fan-like dendrites
of the LGMD. J. Exp. Biol. 65: 289-308, 1976.
O’SHEA, M. AND WILLIAMS, J. L. D. The anatomy and output connections of
a locust visual intemeurone: the lobula giant movement detector (LGMD)
neurone. J. Comp. Physiol. 9 1: 257 -266, 1974.
OSORIO, D. The temporal properties of non-linear transient cells in the
medulla of the locust medulla. J. Comp. Physiol. 161: 43 l-440, 1987.
OSORIO, D. Mechanisms of early visual processing in the medulla of the
locust optic lobe: how self inhibition, spatial pooling, and signal rectifica-
tion contribute to the properties of transient cells. Vis. Neurosci. 7: 345-
355, 1991.
REGAN, D. AND BEVERLEY, K. I. Looming detectors in the human visual
pathway. Vision Res. 18: 415-421, 1978.
REGAN, D. AND CYNADER, M. Neurons in area 18 of cat visual cortex
selectively sensitive to changing size: nonlinear interactions
sponses to two edges. Vision Rex 19: 699-711 , 1979.
between re-
RIND, F. C. A chemical synapse between two motion detecting neurones
in the locust brain. J. Exp. Biol. 110: 143- 167, 1984.
RIND, F. C. Intracellular characterization of neurons in the locust brain
signaling impending collision. J. Neurophysiol. 75: 986-995, 1996.
RIND, F. C. AND SIMMONS, P. J. Orthopteran DCMD neuron: a reevaluation
of responses to moving objects. I. Selective responses to approaching
objects. J. Neurophysiol. 68: 1654- 1666, 1992.
ROWELL, C. H. F. The orthopteran descending movement detector (DMD)
neurones: a characterisation and review. 2. VgL Physiol. 73: 167- 194,
1971.
ROWELL, C. H. F., O’SHEA, M., AND WILLIAMS, J. L. D. Neuronal basis
of a sensory analyzer, the acridid movement detector system. IV. The
preference for small field stimuli. J. Exp. Biol. 68: 157- 185, 1977.
SCHIFF, W., CAVINESS, J. A., AND GIBSON, J. J. Persistent fear responses in
rhesus monkeys to the optical stimulus of “looming”. Science Wash.
DC 136: 982-983, 1962.
SCHWIND, R. Size and distance perception in compound eyes. In: Facets
of
Vision, edited by P. G. Stavenga and R. C. Hardie. Berlin: Springer-
Verlag, 1989, p. 425-444.
SIMMONS, P. J. Transmission mediated with and without spikes at connexi-
ons between large second-order neurones of insect ocelli. J. Comp. Phys-
iol. 147: 401-414, 1982.
SIMMONS, P. J. AND RIND, F. C. Orthopteran DCMD neuron: a reevaluation
of responses to moving objects. II. Critical cues for detecting approaching
objects. J. Neurophysiol. 68: 1667- 1682, 1992.
TANAKA, K., FUKADO, Y., AND SAITO, H. Underlying mechanisms of the
response specificity at expansion/contraction and rotation cells in the
dorsal part of the medial superior temporal area of the macaque monkey.
J. Neurophysiol. 62: 642-656, 1989.
Vu, E. T. AND KRASNE, F. B. Evidence for a computational distinction
between proximal and distal neuronal inhibition. Science Wash. DC 255:
1710-1712, 1992.
WAGNER, H. Flow field variables trigger landing in flies. Nature Land. 297:
147- 148, 1982.
WANG, Y.-C. AND FROST, B. J. “Time to collision” is signalled by neurons
in the, nucleus rotundus of pigeons. Nature Land. 356: 236-238, 1992.
WERBLIN, F. Synaptic connections, receptive fields and patterns of activity
in the tiger salamander retina. Invest. Ophthal. Vis. Sci. 32: 459-483,
1991.
WHEATSTONE, C. Contributions to the physiology of vision. Philos. Trans.
R. Sot. Lond. B Biol. Sci. 142: 1 - 18, 1852.
ZEKI, S. Cells responding
to
changing image size and disparity in
of the rhesus monkey.
J. Physiol. Land. 242: 827 -841, 1974
the cortex
