Transcript Motion detection with movement detectors

Motion detection
with movement detectors
Requirements on movement
detectors
• It is a non-linear device: response to
velocity a and velocity b is not equal to
velocity a+b
a
a+b
b
• movement detection may be asymmetric
(response to velocity a is not opposite to
response to velocity -a) or symmetric
Asymmetric movement detector
V = Δx/Δt
Movement detector
V = Δx/Δt
Note:
• the same velocity v is detected for
various Δx and Δt as long as
Δx/Δt = constant
Velocity dependence of movement
detector
v
response
v
Relation between temporal and
spatial gradients
I ( x, t ) I ( x, t  t )  I ( x, t )

t
t
I ( x, t ) I ( x  x, t )  I ( x, t )

x
x
dI ( x, t ) I ( x, t ) x I ( x, t )
0


dt
x t
t
I ( x, t )
x
 t 
v
I ( x, t ) t
x
Δx
Δx
Movement detector
Step-like
response
functions are
not very likely
Movement detector
responsie
Δt
Movement detector
Movement detector in fly visual system
Response to
spatial
sinewave
pattern with
wavelength 16o
and τ = 50 ms.
The aperture problem
The aperture problem
Δx
Receptive field of movement
detector
The aperture problem
The aperture problem
Identical responses
for v=v0/cosα
α
v0
The aperture problem
A single cell cannot
solve the aperture
problem; only an
ensemble of cells can
under the assumption
of a rigid body
Example 1
Example 2
Various types of cells
-
+ -
+
+
-
-
+
End-stop
cell
Example 3
Hypothetical solution
Optic/flow detectors
Divergence operator
Rotation operator
Deformation operator
Schematic overview of monkey
brain
Responses of neurons in VIP to
various optic-flow patterns
Responses of neurons in VIP to
various optic-flow patterns
Be aware : position of receptive field relative to stimulus !
Retinal motion
• Due to object motion
• due to eye movements
Schematic overview of monkey
brain
Responses of MST neurons to active
vs passive optic flow
Perceptual responses to moving
stimuli
Movement detector
V = Δx/Δt
Detectors have all
orientations
Transparent motion
Percept ?
Movement detector
V = Δx/Δt
Variation in v is achieved
by both:
• larger
Δx
• smaller Δt
Transparent motion
Percept :
two different separately
moving patterns
References