Jenny Read,

1
Local models can account for the reduced response
of disparity-tuned V1 neurons to binocularly
anti-correlated images

• Jenny Read,
• Bruce Cumming,
• Andrew Parker

2
outline

• disparity-tuned complex cells in V1
• described well by energy model
• but this model fails for certain stimuli.
• simple modification rescues the model.

3
disparity tuning curve
firing rate
disparity
preferred disparity
4
describing the tuning curve
amplitude
?
phase
Gaussian envelope
5
anti-correlated stimuli
black ?? white
6
energy model tuning curve inverts
correlated
firing rate
anti-correlated
disparity
7
experiment not simply inversion
correlated
firing rate
anti-correlated
disparity
8
reason for reduced amplitude ?
correlated
anti-correlated
V1 complex cells
V1 complex cells
inhibition
find global solution
no global solution exists
depth percept
9
binocular simple cells
square of half-wave rectified sum of convolutions
Pos( ILRL IRRR ) 2
NB Pos half-wave rectification Pos(x)x
if xgt0, 0 otherwise. convolution.
10
circuitry of the energy model
left right
binocular simple cells
complex cell
BS
Cx
BS
Disparity-sensitive term is the product of left
and right convolutions D (ILRL) ? (IRRR)
11
energy model disparity tuning

• disparity-sensitive term is the product of left
  and right convolutions
• Dcorr (ILRL) ? (IRRR)
• anti-correlation inverts one image
• thus invert disparity tuning curve
• Danti -(ILRL) ? (IRRR)
• due to the linearity of binocular summation in
  the energy model

12
a new model

• to avoid this symmetry, we must introduce an
  extra non-linearity.
• we include an extra layer of monocular simple
  cells.

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new binocular simple cells
Pos( ILRL)
square of sum of half-wave rectified convolutions

MS
BS
Pos( ILRL) Pos( IRRR ) 2
Pos( IRRR)
14
circuitry of our new model
left right
binocular simple cells
complex cell
MS
BS
MS
Cx
MS
BS
MS
Disparity-sensitive terms now go as D Pos
(ILRL) ? Pos(IRRR)Pos (-ILRL) ? Pos(-IRRR)
15
example small amplitude ratio
correlated
firing rate
anti-correlated
disparity
16
example phase shift ? ?
correlated
firing rate
anti-correlated
disparity
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conclusions

• straightforward modification to highly successful
  energy model.
• purely local, feedforward model.
• now captures response to anti-correlated as
  well as to correlated stimuli.

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symmetry of tuning curve

• tuning curves with any phase ? are observed.
• arbitrary phase can be obtained by combining even
  (?0) and odd (??/2) curves.
• response of model complex cell depends on left
  and right eyes images write D(IL,IR).
• even tuning if D(IL,IR) D(IR,IL) .
• odd tuning if D(IL,IR) -D(IR,IL) .
• phase of model tuning curve depends on
  relationship between left and right RFs.

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example two subunits

• two subunits, each with left and right RFs
• total of 4 RF profiles RL1, RR1, RL2, RR2.

L
R

• even tuning if the left and right RF profiles are
  identical in each subunit
• RL1 RR1 RL2 RR2 .

1
2

• odd tuning if
• RL1 RR2 RL2 RR1 .

1
2
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circuitry of the old energy model
left right
binocular simple cells
BS
OFF ON
odd RFs
complex cell
BS
Cx
BS
even RFs
OFF ON
BS
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circuitry for even tuning curve
left right
binocular simple cells
BS
OFF ON
odd RFs
complex cell
BS
Cx
BS
even RFs
OFF ON
BS
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circuitry for odd tuning curve
left right
binocular simple cells
BS
OFF ON
odd RFs
complex cell
BS
Cx
even RFs
OFF ON
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binocular receptive field
bar stimuli
position of right bar
position of left bar
preferred disparity
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correlated stimuli strong firing
BS
Cx
BS
anti-correlated stimuli no firing
BS
Cx
BS
25
circuitry of our new model
left right
binocular simple cells
complex cell
MS
BS
MS
Cx
MS
BS
MS
26
correlated stimuli strong firing
MS
(2f)2
BS
4f2
MS
Cx
MS
BS
MS
anti-correlated stimuli weak firing
MS
f2
BS
2f2
MS
Cx
MS
f2
BS
MS
27
circuitry of the energy model
left right
binocular simple cells
complex cell
BS
Cx
BS
KEY
ON region (fires in response to bright stimuli)
OFF region (fires in response to dark stimuli)
28
new binocular simple cells
square of sum of half-wave rectified convolutions

MS
BS