# Presentation: 472307

## Image by stereo photo company Underwood & Underwood c. 1900. 

- Image by stereo photo company Underwood & Underwood c. 1900.

- the author Samuel Clemens (1835-1910) (=“Mark Twain”).

**Notes:**
Any ideas who this guy is?
I’ll give you  a clue: the photo was taken around 1900.
It’s the author Samuel Clemens, better known as Mark Twain.

## Cortical computations underlying stereo vision 

- Jenny Read
- Bruce Cumming

- Laboratory of Sensorimotor Research,
- National Eye Institute,
- National Institutes of Health

**Notes:**
I’m going to be talking today about the cortical computations that support stereo vision. I’m going to tell you something about the work I do with Bruce Cumming at the laboratory of sensorimotor research at the National Eye Institute. 

Abstract
Current models of binocular simple cells assume that input from left and right eyes is combined linearly. Model cells of this type underlie the successful energy model of disparity-tuned complex cells (Ohzawa et al., 1990, Science 249:1037). An alternative hypothesis is that input from each eye is passed through a threshold non-linearity prior to binocular combination. This is physiologically entirely plausible – for instance, it would occur if some binocular simple cells receive input via monocular simple cells rather than directly from the LGN – and explains a number of observations. (i) We have shown previously (Read et al., 2000, Abstr. Soc. Neurosci. 26:1845) that using simple cells of this form in the energy model yields disparity tuning curves whose amplitude is reduced when the stimuli are anti-correlated, in agreement with experiment. The energy model predicts the same amplitude for anti-correlated as for correlated. (ii) For some cells, comparing monocular and binocular responses suggests that the input from one eye is always inhibitory. This is hard to explain if binocular combination is linear. (iii) If the input from both eyes is excitatory, the pattern of the cell’s response to disparate drifting gratings shows a distinctive dependence on interocular phase, changing from one burst of firing per stimulus cycle to two bursts at a particular interocular phase. Observation of such “frequency doubling” would be a strong indication that the postulated cells actually exist, but has never been reported.  This may be because no one has looked for it, compounded by the difficulty of discerning such behaviour in data from awake animals. A study of our data revealed several simple cells which showed disparity-dependent frequency-doubling, supporting the view that binocular combination is non-linear in some cases. 

## Put red lens over left eye, blue lens over right eye

- Stereo anaglyph by Prof. Michael Greenhalgh, Australian National University (with permission).

**Notes:**
Because your eyes are in slightly different positions, they get slightly different views of the world. This picture demonstrates that – here we have a statue from the momument to Wellington in St Pauls’ Cathedral.Scholar differ as to what it is indented to represent. Michael Greenhalg, the professor of art who took this photo, told me it symbolised Valour and Cowardice. Lance Optican, my colleague at the NIH, told me it symbolised the invention of the manbhole cover.. You can decide which is more approprite. Here we have two photographs of the statue, taken with two cameras held slightly apart. One image is displayed in red, the other in blue, and you can see the slight differences between the images. Now if you put your glasses on, then each of your eyes will see the appropriate image. And I hope you’re getting a clear illusion of depth – the statue should appear to stand out of the screen. Everyone getting that? It’s striking just how powerful the illusion is. This picture already contains many cues to depth – we have shape from shading, we have occlusion, we have size – the fact that this guy’s face subtends a larger angle than this lady’s. But somehow none of these monocular cues give you the impression that you could reach out and touch the sculpture in the way that the stereo disparities do. You can even fool your brain into thinking it sees motion parallax – try moving your head from side to side.

The work I’m doing with Bruce Cumming at the National Eye Institute is aimed at understanding what may be going on in our brains that gives us this perception of depth.

## stereopsis

- R

- L

- 

**Notes:**
In theory, the geometry of stereopsis is simple enough.
If you are looking at an apple over here, [click], and there’s another apple over here in front of here, [click], then the image of the green apple will appear in different positions on the two retinae. With a little bit of geometry, [click], it’s then possible to deduce where the green apple must be in relation to the red one.

## correspondence problem

- left eye’s image

- right eye’s image

**Notes:**
But before you can use your trigonometry, you have to know where the image of the apple is in each eye. You have to work out which bits of each eye’s image match up with each other. 
That doesn’t seem a taxing problem in an image like this, where there are many features to use, [click].

## experimental stimuli:random-dot stereograms

- click to initiate stimulus

**Notes:**
But you can also see depth in random dot patterns [start program].
These are the sorts of images we use in our experiments.
Here, there don’t seem to be any features to match up. Are you really matching the white dots in one eye with the right white dot in the other? But each white dot visible in the left eye has dozens of potential matches in the right eye.
I think the fact that you can see depth immediately and clearly in these random-dot patterns tells us something important about how our brains solve the correspondence problem. These images are pretty much completely unnatural – you never see anything like them in the world, they have a very different frequency spectrum from natural images, they don’t contain any recognisbale objects like faces or trees or cars. So the fact that you can see depth in them tells us that the stereo algorithm that the brain uses is extremely general, so it will work for just about any stimulus which contains disparity.
Our work is aimed at understanding what this algorithm is, and whre in the brain it is implemented.

## a completely unnatural stimulus

- random-dot patterns

- image changes every few ms

- no recognisable objects e.g. faces

- each dot has dozens of identical potential matches

- and yet a clear perception of depth!

## stereo algorithm

- stereo algorithm used by brain must be very *general.*
- it will work on more or less any image for which a disparity can be defined.

## long-term goal of our work

- to understand:

- the algorithm the brain uses for stereoscopic depth perception.

- how this algorithm is implemented physiologically.

- where this occurs within the brain.

## a new model which solves these problems
how it solves each of the 3 problems.

- how it solves each of the 3 problems.

- outline of this talk

- disparity-tuned cells in primary visual cortex.

- binocular energy model of these cells.

- problems with the energy model
- 3 areas where it does not agree with data.

## head image from Royal Holloway University of London Vision Research Group (with permission)

**Notes:**
Our starting point is primary visual cortex (V1). This is the first area in the visual system where inputs from the two eyes are combined together. So, understanding the computations carried out by neurons in V1 seems a good place to start.

## Slide 12

**Notes:**
We record from single neurons in V1 of an awake monkey, like Rufus here. Rufus sits in a chair and watches images like the random-dot patterns you’ve just seen. Meanwhile, we record the firing of neurons in his brain.

## disparity tuning curve

- -1.5

- -1

- -0.5

- 0

- 0.5

- 1

- 0

- 5

- 10

- 15

- 20

- 25

- 30

- 35

- disparity (degrees)

- firing rate (spikes / s)

- left image         right image

**Notes:**
Many neurons in V1 modulate their firing depending on the disparity of the stimulus. This shows an example – you can see that, as the disparity between left and right images changes, the cell’s mean firing rate varies accordingly.

duf092

## modelling these cells’ response

- In V1, response seems to be a simple function of retinal input.

**Notes:**
My work is aimed at understanding how these cells achieve this. We’re seeking the mathematical recipe telling us how to get from what’s on the retina, to the firing rate of the cell.
Fortunately, in V1, this recipe seems to be reasonably simple. Essentially, the image is first passed through bandpass filters, and then cross-correlated.

## basic building-block

- inner product of image with receptive field

**“****ON” region**

**“****OFF” region**

- Pos(*v*)

**Notes:**
Simple cells in the visual cortex seem to compute the convolution of the image with the receptive field.

Throughout this talk I’ll use the convention that red represents an ON region of the receptive field, and blue an OFF region.

There’s also the slight complication that simple cells implement an output threshold nonlinearity.

## stylized cell

**Notes:**
So from now on I’ll represent cells in a stylized way: where this little diagram represents the output nonlinearity.

## simple / complex cells

- simple : characterized by a linear  receptive field function
- complex : not possible to define a linear receptive field function

## modeling disparity-tuned cells

- combine information from both eyes

- need receptive fields in both eyes

- binocular energy model
- 	(Ohzawa, DeAngelis & Freeman, 1990)

## energy model

- convolution of left eye’s image with jth left receptive field

- convolution of right eye’s image with jth right receptive field

**Notes:**
Formally, the energy model looks like this.

So, what’s going on here is, [click] first you take the convolution of the retinal image with the receptive field in each eye, [click] then you add them together, [click] then you square the result. Complex cells are modelled as the sum of many such subunits.

## energy model

**BS**

**Cx**

- binocular simple cell

- complex cell

- images

- excitatory
- inhibitory

- receptive fields

- other subunits

**Notes:**
That’s all a bit abstract and mathematical, so let’s see what that might mean physiologically.

The basic building blocks of the energy model are binocular simple cells, which have receptive fields in both eyes. Many binocular simple cells feed into a single complex cell, which is then sensitive to the disparity between the left and right images.

So [click], we’ve got retinal images and [click] receptive fields; [click] each eye tells the binocular simple cell the value of the convolution of the image with the receptive field; [click] the binocular simple cell sums all its inputs and sends them to the complex cell after passing them through a squaring nonlinearity, which is what this little diagram is meant to represent.
[click] The complex sums all its inputs, including contributions possibly from many different subunits.

## energy model simulation

- disparity

- simulated firing rate

- correlated stimuli

- uncorrelated stimuli

**Notes:**
The energy model predicts that when you make this manipulation, the disparity tuning curve should turn upside down.
And amazingly enough, it does turn upside down. That strikes me as quite a strong confirmation that it’s got something right; after all, anticorrelated stimuli don’t even occur in real visual scenes.

## what the energy model gets right

-  qualitatively correct disparity tuning curves with random-dot patterns.

## binocular receptive field

- right eye’s image

- left eye’s image

- position of left bar

- position of right bar

- binocular RF

**Notes:**
The energy model also gives good matches to the binocular receptive fields found with bar stimuli.
Here, the idea is that you present a bar in each eye, at different positions. You note the response of the cell, and mark

## Ohzawa et al., 1990, Science: 249, 1037

## what the energy model gets right

-  qualitatively correct disparity tuning curves with random-dot patterns.
-  qualitatively correct binocular receptive fields with bar stimuli.

## anti-correlated stimuli

- black  white

- left eye’s image

- right eye’s image

**Notes:**
Now, I’m going to spend the rest of the talk criticising the energy model, so I wanted to start off by stressing how much it gets right. 
One result which I think is particularly striking is how well it predicts the response to binocularly anticorrelated stimuli. 
These are stimuli in which the contrast in one eye is inverted, with black becoming white and vice versa.

## experimental stimuli:anti-correlated random-dot stereograms

- click here to initiate stimulus

**Notes:**
But you can also see depth in random dot patterns [start program].
These are the sorts of images we use in our experiments.
Here, there don’t seem to be any features to match up. Are you really matching the white dots in one eye with the right white dot in the other? But each white dot visible in the left eye has dozens of potential matches in the right eye.
I think the fact that you can see depth immediately and clearly in these random-dot patterns tells us something important about how our brains solve the correspondence problem. These images are pretty much completely unnatural – you never see anything like them in the world, they have a very different frequency spectrum from natural images, they don’t contain any recognisbale objects like faces or trees or cars. So the fact that you can see depth in them tells us that the stereo algorithm that the brain uses is extremely general, so it will work for just about any stimulus which contains disparity.
Our work is aimed at understanding what this algorithm is, and whre in the brain it is implemented.

## energy model simulation

- disparity

- simulated firing rate

- correlated stimuli

- anti-correlated stimuli

**Notes:**
The energy model predicts that when you make this manipulation, the disparity tuning curve should turn upside down.
And amazingly enough, it does turn upside down. That strikes me as quite a strong confirmation that it’s got something right; after all, anticorrelated stimuli don’t even occur in real visual scenes.

## Cumming & Parker, 1997, Nature: 389, 280

- correlated stimuli

- anti-correlated stimuli

- disparity (degrees)

- firing rate (spikes / s)

## what the energy model gets right

-  qualitatively correct disparity tuning curves with random-dot patterns.
-  qualitatively correct binocular receptive fields with bar stimuli.
-  qualitatively correct response to anti-correlation.

## what the energy model gets wrong

## Cumming & Parker, 1997, Nature: 389, 280

- weaker response for anti-correlated stimuli

- disparity (degrees)

- firing rate (spikes / s)

**Notes:**
Let’s start with the response to anti-correlated stimuli. I said that the energy model predicted that anti-correlating the stimuli turned the tuning curve upside down. So you might have expected the example cell I just showed you to look like this. In fact, it looked like this [click]. what do we notice? THe response is a lot weaker for anti-correlated stimuli. This is typical for real cells.

## what the energy model gets wrong

-  quantitative response to anticorrelation
- real cells respond more weakly to anticorrelated stimuli

**Notes:**
So here’s one thing we can write down that the energy model gets wrong.

For the next one, let me introduce you to a particular cell we recorded from our monkey Dufus:

## right monocular stimulus

- 0

- 5

- 10

- 15

- 20

- 25

- 30

- 35

- firing rate (spikes / s)

- left      right

**Notes:**
duf092

## left monocular stimulus

- 0

- 5

- 10

- 15

- 20

- 25

- 30

- 35

- firing rate (spikes / s)

- left      right

**Notes:**
duf092
** stress that it obviously DOES recveive input from left eye!!!! Hence input must be inhibitory.

## “this cell is monocular”

- 0

- 5

- 10

- 15

- 20

- 25

- 30

- 35

- firing rate (spikes / s)

- left      right

- “this cell is monocular”

**Notes:**
duf092
** stress that it obviously DOES recveive input from left eye!!!! Hence input must be inhibitory.

## disparity tuning curve

- -1.5

- -1

- -0.5

- 0

- 0.5

- 1

- 0

- 5

- 10

- 15

- 20

- 25

- 30

- disparity (degrees)

- firing rate (spikes / s)

- left      right

- left      right

- left image         right image

- left      right

**Notes:**
As you can see, it modulates its firing rate strongly as a function of the disparity between the left and right images.
duf092

## left eye has purely inhibitory effect

- -1.5

- -1

- -0.5

- 0

- 0.5

- 1

- 0

- 5

- 10

- 15

- 20

- 25

- 30

- 35

- disparity (degrees)

- firing rate (spikes / s)

**-**

**Notes:**
We know that because of cells like this one, recorded from V1 of an awake monkey. As you can see, it modulates its firing rate strongly as a function of the disparity between the left and right images.
duf092

## but -!

- this isn’t possible in the energy model.

## the energy model says that each eye sends both excitatory and inhibitory input

**BS**

- receptive fields

**Notes:**
To see why, consider this example. Here, one eye consists of a single ON region, and the other eye’s RF is a single OFF region. So if I present two bright stimuli, then yes, the left eye has an inhibitory effect.

## the energy model says that each eye sends both excitatory and inhibitory input

**BS**

- receptive fields

**Notes:**
But if I change the stimulus, so that now there’s a dark spot in the left eye’s receptive field, it now has an excitatory effect.
So, in the energy model, you can’t characterise an eye as having a purely inhibitory or excitatory effect. The left eye may have an inhibitory effect for one particular stimulus, but you could always find another stimulus such that the left eye will have an inhibitory effect.
Within the energy model, you will always get a response to monocular random dot patterns, unless the RF is zero .

## what the energy model gets wrong

-  quantitative response to anticorrelation
- real cells respond more weakly to anticorrelated stimuli
-  cells where one eye always inhibits firing
- not possible within the energy model

**Notes:**
So here’s one thing we can write down that the energy model gets wrong.

The third error I want to draw your attention to is more abstract

## energy model:

- disparity tuning curve is the cross-correlation of the left and right eye’s receptive fields.

- C = [vL+vR]2 = vL2 + vR2 + 2 vLvR

## left eye’s receptive field

- right eye’s receptive field

- 0.35

- 0.35

**Notes:**
To see what this means, consider a unit whose RFs in the left and right eyes are like this. If we stimulate the unit with random dot patterns, we’ll get a disparity tuning curve like this. And note that the scale of the disparity tuning curve is determined by the scale of the structure in the receptive fields.
So hre’s a definite quantiative prediction of the enregy model. And ew know what we do with quantitative predictions. We test them!

## shape of disparity tuning

- a *key prediction* of the energy model.
- demonstrating this result would be strong evidence for the energy model.

## how to test

- measure receptive fields?
- not possible for complex cells.
- make the comparison in Fourier space.
- this works for simple *and* complex cells.

- 

## energy model:

- disparity tuning curve is the cross-correlation of the left and right eye’s receptive fields:
- D = 2 L* R
- the Fourier power spectrum of the disparity tuning curve is the product of the Fourier amplitude spectra of the left and right eye’s receptive fields:
- FT2(D) = 2 FT(L)FT(R)

**Notes:**
It’s useful to use the convolution theorem to transform this prediction into Fourier space. 
I should point out that when I say the Fourier spectrum of the DTC, I mean of the DTC minus its baseline – so I’m only considering the disparity-modulated component.
If the energy model is correct, we can easily probe the Fourier transform of the receptive field by looking at the response to gratings:

## receptive field (RF)

- firing rate

- spatial frequency

- RF cross-section

- Fourier spectrum

- Fourier transform

- spatial frequency tuning curve

- amplitude

**Notes:**
If you present a receptive field like this with gratings at different frequencies, it’ll respond best to the grating at the same scale as the structure in the receptive field.
And in fact, if we take a slice through the receptive field at 90o to the orientation of the gratings, so as to get a 1d profile like this, then the spatial frequency tuning curve is just the Fourier spectrum of this profile.

Develop much more slow.y Explain what profile is. 
Why are units not the same. Normalised SFTC. Four panels.

## if the energy model is right:

- then by obtaining the cell’s spatial frequency tuning....
- we obtain the Fourier amplitude spectrum of the RF profile.

- spatial frequency

- normalized units

- firing rate

## x

- monocular spatial frequency tuning curves

- Fourier spectrum of disparity tuning curve

- spatial frequency

- spatial frequency

- spatial frequency

- =

- left eye

- right eye

**Notes:**
So, now we have another way to test the energy model. We can probe the SF tuning in both eyes, and get the DTC with RDS, and calculate its Fourier transform. 
Then, the three sets of results should be related as this.
One advantage of this is, it’s much easier to derive an SFTC than to derive an RF by reverse correlaiton. So, we can test this prediction in many more cells.
We can also generalise it to complex cells, which receive input from many receptive fields in each eye. There, instead of an equals sign, it turns  out that we can derive an inequality:

## spatial frequency tuning

- left eye

- right eye

## product of fitted monocular spatial frequency tuning curves

- 0.01

- 0.1

- 0.2

- 0.5

- 1

- 2.5

- 5

- 10

- 15

- spatial frequency (cycles per degree)

## disparity tuning curve

- disparity (degrees)

- firing rate (spikes/s)

**Notes:**
ruf139.0

## product of spatial frequency tuning curves

- 0.01

- 0.02

- 0.05

- 0.1

- 0.2

- 0.5

- 1

- 2.5

- 5

- 10

- 15

- 0

- 0.01

- 0.02

- 0.03

- 0.04

- 0.05

- normalized units

- product of fitted spatial frequency tuning curves

**Notes:**
GO SLOWER! expalin what slides are.
Lines thicker.

## Fourier transform

- 0.01

- 0.02

- 0.05

- 0.1

- 0.2

- 0.5

- 1

- 2.5

- 5

- 10

- 15

- 0

- 0.01

- 0.02

- 0.03

- 0.04

- 0.05

- Fourier transform of fitted disparity tuning curve (minus baseline)

- product of fitted spatial frequency tuning curves

- too much power at DC

- normalized units

**Notes:**
GO SLOWER! expalin what slides are.
Lines thicker.

## disparity (degrees)

- 0.02

- 0.05

- 0.1

- 0.2

- 0.5

- 1

- 2.5

- 5

- 10

- 15

- 0

- 0.01

- 0.02

- 0.03

- 0.04

- 0.05

- spatial frequency (cycles/degree)

- firing rate (spikes/s)

- firing rate (spikes/s)

- normalized units

- spatial frequency (cycles per degree)

**Notes:**
ruf139.0
Even though the SFTCs show NO response at DC, the DTC has a strong response at DC.

## what the energy model gets wrong

-  quantitative response to anticorrelation
- real cells respond more weakly than predicted to anticorrelated stimuli
-  suppressive effect from one eye
- not possible within the energy model
-  mismatch between disparity frequency and response to gratings
- real disparity tuning curves have more power at low frequencies than predicted

## how can we fix the problem?

- one simple modification to the energy model.
- keeps all the successes of the energy model.
- but fixes all these problems at a stroke!

## energy model

**BS**

**Cx**

- binocular simple cell

- disparity-selective complex cell

- images

- receptive fields

**Notes:**
Well, to make it work, all we have to do is postulate an additional layer of monocular simple cells, like this.

## our modified version

**BS**

**Cx**

- binocular simple cell

- disparity-selective complex cell

- images

- receptive fields

**MS**

**MS**

- monocular simple cells

**Notes:**
Well, to make it work, all we have to do is postulate an additional layer of monocular simple cells, like this.
NB mention not nec. monocular simple cells- could be dendrites.

## our modified version

**BS**

**Cx**

- binocular simple cell

- disparity-selective complex cell

- images

- receptive fields

**MS**

**MS**

- monocular simple cells

**Notes:**
In fact, that should be a plus or minus sign, because we can equally well allow an inhibitory synapse.

## suppression from one eye

**BS**

**Cx**

- binocular simple cell

- disparity-selective complex cell

- images

- receptive fields

**MS**

**MS**

- monocular simple cells

**Notes:**
In fact, that should be a plus or minus sign, because we can equally well allow an inhibitory synapse.
Yet, simulations show that when both eyes are stimulated, ie we present binocular random dot pattern, then the interaction between the excitation from the right eye and the inhibition from the left means that we do get disparity tuning.

## problems our model solves

- suppressive effect from one eye
- inhibitory synapse after monocular simple cell

- 

## mismatch in disparity frequency

## disparity (degrees)

- spatial frequency (cycles/degree)

- firing rate (spikes/s)

- firing rate (spikes/s)

- normalized units

- spatial frequency (cycles per degree)

**Notes:**
Even though the SFTCs show NO response at DC, the DTC has a strong response at DC.

## disparity (degrees)

- spatial frequency (cycles/degree)

- firing rate (spikes/s)

- firing rate (spikes/s)

- normalized units

- spatial frequency (cycles per degree)

**Notes:**
Remember that the basic problem is that the blue area is smaller than the orange area.
Everything would be fine if the blue area dipped down a bit more. [click].
So, we want something that’s basically like the energy model but with some kind of effect that truncates the dip downwards, [click] giving us a DC response.

Draw another line on top of the old one – shade out old one.

## firing rate (spikes/s)

## firing rate (spikes/s)

## energy model       our modified version

- -50

- 0

- 50

- 0

- disparity

- 0

- 0.02

- 0.04

- 0.06

- 0

- spatial frequency

- -50

- 0

- 50

- 0

- disparity

- 0

- 0.02

- 0.04

- 0.06

- 0

- spatial frequency

- Fourier power spectrum

- disparity tuning curve

- no power at DC

- increased power at DC

## threshold at zero

**BS**

**Cx**

- binocular simple cell

- complex cell

- receptive fields

**MS**

**MS**

- monocular simple cells

**Notes:**
GO SLOW.
Say: we have this threshold at 0 but we can introduce a free parameter which will enable us to explain full rnage of data

## we can vary the threshold

- threshold is an additional free parameter.
- we now have the freedom to match the range of behavior observed in real cells.
- (whereas the energy model did not have enough freedom.)

## increased threshold

**BS**

**Cx**

- binocular simple cell

- complex cell

- receptive fields

**MS**

**MS**

- monocular simple cells

**Notes:**
GO SLOW.
Say: we have this threshold at 0 but we can introduce a free parameter which will enable us to explain full rnage of data

## energy model       our modified version

- -50

- 0

- 50

- 0

- disparity

- 0

- 0.02

- 0.04

- 0.06

- 0

- spatial frequency

- -50

- 0

- 50

- 0

- disparity

- zero threshold

- 0

- 0.02

- 0.04

- 0.06

- 0

- spatial frequency

- -50

- 0

- 50

- 0

- disparity

- high threshold

- 0

- 0.02

- 0.04

- 0.06

- 0

- spatial frequency

- Fourier power spectrum

- disparity tuning curve

- no power at DC

- increased power at DC

- maximum power at DC

## problems our model solves

- suppressive effect from one eye
- inhibitory synapse after monocular simple cell
- mismatch between disparity frequency and response to gratings
- threshold boosts power at low frequencies

- 

- 

**Notes:**
So, we can chalk up another success for our model

## anticorrelation

-  image in one eye replaced with negative

-  one of the convolutions changes sign

-  disparity-modulated term inverts; amplitude unchanged:

-  a consequence of the **linearity** of the model

**Notes:**
So, in order to get a reduction in amplitude, we’re going to need to break the linearitry.

## modified model

- anticorrelation: convolution changes sign

- clearly disparity-modulated term no longer simply inverts

## example simulation

- disparity

- firing rate

- correlated

- anticorrelated

**Notes:**
Here is an example tuning curve obtained with our new model.
As in experiments, each point on the curve represents the mean response averaged over many different presentations of random-dot stereograms with the specified disparity.
To get this very marked amplitude reduction for anti-correlated stimuli, I had to make my model monocular simple cells incorporate a high firing threshold. Thus, in this example their output nonlinearity is even stronger than half-wave rectification.

Stress difficult to get this kind of relationship with odd tuning curve - had to do  paper and pencil analysis of symmetry relationships

## problems our model solves

- suppressive effect from one eye
- inhibitory synapse after monocular simple cell
- mismatch between disparity frequency and response to gratings
- threshold boosts power at low frequencies
- quantitative response to anticorrelation
- with high enough thresholds, arbitrarily low amplitude ratios can be obtained

- 

- 

- 

**Notes:**
So, we can chalk up another success for our model.

## heterogeneity

- real neurons vary greatly in behavior.
- some well-described by energy model.
- complex cells have many binocular subunits:
- perhaps some are like the energy model
- linear binocular combination
- others are like our modified version
- threshold prior to binocular combination

## heterogeneity

**Cx**

- some binocular subunits as in our model...

- ...others as in the original energy model

- complex cells receive input from many binocular subunits.

## plus... a prediction

- Consider case where convolutions are equal and opposite: *v**L**=-v**R*

- Our version: no cancellation

- Original energy model: they cancel out

**Notes:**
A difference between the original energy model and our version

## disparate drifting grating

- right eye

- left eye

**Notes:**
This has important implications for the response to a drifiting luminance grating like this one.

## typical simple cell response

- one burst of firing per cycle of the stimulus.

- time (one stimulus cycle)

- firing rate

## phase difference 0o

- phase difference 0o

- right eye

- left eye

**BS**

**MS**

**MS**

## phase difference 0o

- phase difference 0o

**BS**

**MS**

**MS**

- right eye

- left eye

- ...half a cycle later

## phase difference 180o 

- phase difference 180o

**BS**

**MS**

**MS**

- –

- +

- right eye

- left eye

## phase difference 180o

- phase difference 180o

**BS**

- ...half a cycle later

**MS**

**MS**

- +

- –

- right eye

- left eye

## energy model  modified version 

- energy model  modified version

## energy model	    modified version 

- energy model	    modified version

## interocular phase difference

- time (1 stimulus period)

- spikes / s

**Notes:**
**don’y say “nominally identical”. Say “for +/-180 the phase difference is the same, but the data sets are different”.
**don’t say”it’s not just noise” – say “it shows a robust and systematic tendency to freq doubling”

## summary

- the energy model gives a good qualitative account of disparity-tuned neurons.
- it has been widely used in computational models.
- there are a number of discrepancies when it is compared with quantitative data.

## summary

- we postulate that some binocular simple cells receive input via monocular simple cells.
- straightforward, physiologically plausible mechanism.
- extends our repertoire so that we can account for all known observations.
- even predicted something before it was observed!

## conclusion

- developing a good understanding of the mechanisms of disparity selectivity in primary visual cortex.
- indicates the initial processing carried out by the brain.
- provides a basis for understanding the computations enabling stereo vision.