Responses of Time-to-Collision Neurons in the Nucleus Rotundus
of the Pigeon to Accelerating and Decelerating Stimuli
Hongjin Sun and Barrie J. Frost Department of Psychology, Queen's University, Kingston, Ontario, K7L 3N6, Canada
2 RESULTS
750cm/s
10cm
Change of movement parameters and optical
variable during the movement
t
instantaneous visual angle substense of the looming object.
For four kinds of movement with:
1. constant velocity
2. constant acceleration, starting from
zero velocity
3. constant deceleration, stopping at the
position of the eye
4. constant deceleration, stopping after
passing the eye
an optical variable which equals the inverse of relative rate of
expansion of the retinal image of the looming object.
20cm
500cm/s
30cm
300cm/s
t
t ]
NEURONAL RESPONSES
1.5
d t
dt
Tc time-to-collision is the time that will elapse before the object
collides with the observer's eye
Time of Onset of Response
Before Collision (Tc) (sec)
40
THEORETICAL PREDICTIONS
SYMBOLS
T0 duration of the "visible" part of the movement, from the start of
the movement to the moment the object reaches the eye
Ts duration of the total movement, from the start of the movement
observer's (or neuron's) latency of the response
150cm/s
50cm
3
2
1
0
sec
3
2
MOVEMENT WITH A CONSTANT VELOCITY:
1
0
sec
This figure shows the response pattern, PeriStimulus Time Histograms (PSTHs), for a rotundal
looming detecting neurons to a series of stimuli
(soccer-ball pattern) of varying sizes (left portion)
and varying velocities (right portion) swept along
the direct collision course path toward the bird.
Responses are the sum of 5 sweeps and are
referenced to time zero, which is the time when the
stimulus would have contacted the bird. Note the
response remains invariant in timing over substantial
changes in sizes and velocity. Moreover, the
magnitude of responses (maximal firing rate) were
similar across different object sizes and velocities.
The simulated path was 15 m in length. In left side of
the figure, the simulated object size varied from a
diameter of 10 cm to 50 cm (with velocity in 500
cm/s), in right side of the figure, the simulated
velocity varied from 150 to 750 cm/s (object size was
30 cm).
When object is some distance D t away from the eye, t
if movement velocity V is constant, and for a small value of
Tc = D t
V
=
t
500
0
-1500
-1000
Movement with a constant deceleration:
When the object moves toward the eye, ending at zero velocity,
if Ts > T0, then the object stops after passing the eye
if Ts = T0, then the object stops at the position of the eye
- ( Ts - T0 ) ] +
Th
2
+ ( Ts - T0 ) 2
0
500
eye position
500
eye position
0
-500
constant velocity
acceleration
deceleration & stop at the eye
decel. & stop behind the eye
-1500
-5
-4
-3
When the same object was decelerated or accelerated, the timing of the onset of the response of these
neurons matched what would be predicted if the neuron responds to the same value, as revealed in the
constant velocity situation. These results confirm that these neurons are indeed computing , and thus
signal accurately the time-to-collision when the movement velocity is constant, and provide a first-order
estimate of time-to-collision when the movement velocity is not constant.
-2
-1
0
Tc (sec)
-
1
2
3
The time when the object
reaches the eye
Change of Tau Value over Time
5
tau threshold level
constant velocity
acceleration
decel. & stop at the eye
decel. & stop behind the eye
4
3
2
1
0
-5
-4
-3
-2
Tc (sec)
10
-1
This figure shows that the time of the onset of
response before collision (Tc) from one Rt looming
detecting neuron. The Tc remained the same for
variation of movement duration in the constant
velocity condition. Tc varied as a function of total
movement duration in the constant acceleration
condition (starting from zero velocity). Theoretical
predictions for Tc in these two conditions (equation 1
and 2) are also graphed. In both conditions, starting
distance of the movement were the same across
variation of total movement duration. The small
variation in Tc for the constant velocity condition
suggests that this neuron encodes time-to-collision of
the looming object. The general trend of the variation
of Tc in the acceleration condition is consistent with
the theoretical prediction. Thus this neuron still
responded to the threshold of tau, although only
provides a rough estimation of the time-to-collision
(Tc).
3
-2000
CONCLUSIONS
Supported by an NSERC grant to BJF and an NSERC scholarship to HS.
-500
Distance (cm)
-1000
5
Movement Duration (To) (sec)
Change of Distance over Time
Movement with a constant acceleration:
When the object moves toward the eye starting from zero
2
2
velocity,
Tc = ( Th + T0 ) Th + T0
Th
0
constant velocity
acceleration
deceleration & stop at the eye
deceleration & stop behind the eye
MOVEMENT WITH VARYING VELOCITY:
When the movement velocity is not constant, the value does
not equal time-to-collision, Tc. However, if neurons still initiate
their responses at the threshold of ( Th ), the response onset
time before collision (Tc) should follow the relationships below.
0.5
0
1000
Therefore, time-to-collision can be signalled by the
instantaneous value of . If a neuron responds to a threshold of
, its response onset time before collision Tc would indicate
Th value.
Tc = Th -
Tc = [
3
Change of Movement Velocity over the Distance
to the time when the object come to stop under its own
deceleration. The object might stop after passing the observer's
eye.
214cm/s
Velocity (cm/sec)
40cm
tau threshold value
Neuronal responses to constant velocity
prediciton for response to instanteous tau
Neuronal responses to acceleration
1
0
The time when the object
reaches the eye
Time of Onset of Response
Before Collision (Tc) (sec)
B
A
spikes
Distance (cm)
Recent theoretical analyses and behavioural
studies demonstrate that when an object moves
toward an observer or an observer approaches
an object, an optic variable called
can be
utilized to control the observer's responses to the
impending collision. specifies the time that will
elapse before the object collides with the
observer, namely time-to-collision, if the velocity
of the relative movement between object and
observer is constant. Behavioural studies have
shown that even when the movement is not at a
constant velocity, animals still use
as a first
order optical variable to estimate time-to-collision
to control their visuo-motor behaviour (Lee and
Reddish, 1981). Previous studies from our lab
demonstrated that some cells in the dorsal
nucleus rotundus (nRt) of pigeons respond
selectively to objects moving on a collision
course toward the bird. Morever, the neuron's
response always started at a constant time
before collision, regardless of the value of the
object‘s velocity, as long as the velocity is held
constant during approach. In this study, we
examined the response of this type of neuron
when the object's velocity was not constant
during movement.
Visual stimuli were generated by a graphics
computer and projected onto a wide tangent
screen in front of the pigeon by a high resolution
projector. Object motion was simulated by
objects ("soccer ball-like" visual patterns) moving
against homogeneous and textured stationary
backgrounds. The movement was presented
either at constant velocity, constant deceleration,
or constant acceleration. Standard extracellular
recording techniques were used.
Neurons in dorsal nRt that were found to
specifically respond to objects moving on a direct
collision course toward the bird were identified.
Among these looming detectors, some neurons
responded at a constant time before collision
when tested with a looming object approaching at
a constant velocity. In this experiment, this kind
of neurons was tested with constant deceleration
and acceleration to further determine the exact
optical variable these neurons encode.
Tau (sec)
1 INTRODUCTION
tau threshold value
prediciton for response to instanteous tau
Neuronal responses to deceleration
2
1
0
0
1
2
3
Movement Duration - Display Duration
(Ts-To) (sec)
This figure shows, in the constant deceleration
condition, the time of the onset of response before
collision (Tc) of the same Rt neuron shown above.
The Tc was tested for variation of the portion of
movement duration between the time when the
object reached the eye and the time when it finally
stopped by its own deceleration (Ts-T0). Theoretical
prediction (equation 3) for Tc in this condition is also
graphed. In this condition, total moving distance was
the same across variation of movement duration.
The general trend of the variation of Tc in the
deceleration condition is consistent with the
theoretical prediction.
Thus this neuron still
responded to the threshold of tau, although only
provides a rough estimate of the time-to-collision
(Tc).
4