Evans NW, Read JCA ( 1998 )
Stability of power-law discs I. The Fredholm integral equation

Monthly Notices of the Royal Astronomical Society Vol: 300 Pages: 83-105

Comment: It seems a lifetime away now, but I began my scientific career in astrophysics, with a doctorate on galactic dynamics supervised by Wyn Evans. For my thesis work, we modelled a disk galaxy as an infinitesimally thin disk, whose density (mass per unit area) varied as an inverse power law of radius. We calculated the stability of this disk to gravitational perturbations within the plane of the disk. The stars in the disk have a tendency to clump together because of their mutual gravitational attraction, so you might think the disk would just collapse into its centre. However, if the disk is spinning fast enough, the tangential motion of the stars will counteract this tendency, and the disk may remain stable. We examined the circumstances under which stable modes are possible, for a variety of different assumptions about the density profile of the disk. This paper is basically the mathematical methods we used to do the analysis.

Evans NW, Read JCA ( 1998 )
Stability of power-law discs II. The global spiral modes.

Monthly Notices of the Royal Astronomical Society Vol: 300 Pages: 106-130

Comment: This paper contains the results of our analysis.

Read JCA, Eagle RA ( 2000 )
Reversed stereo depth and motion direction with anti-correlated stimuli

Vision Research Vol: 40 Pages: 3345-3358

ERRATA Comment: This was my first paper in the field of neuroscience. It represents work I did as an M.Sc. project with Richard Eagle, in the psychology department of Oxford University. Richard died very suddenly, aged 32, while we were working on this project, a personal tragedy for his friends and family and a great loss to vision science. I am very grateful to Simon Prince and Bruce Cumming for their kindness in helping me to write this up, and to Randy Blake, who as editor of Vision Research understood that it was difficult for me to submit my first paper in the field after Richard had died, and wrote me an encouraging letter to accompany the referees' reports.

A stereogram and a two-frame kinematogram presents analogous correspondence problems, in that both require matching features in one image with partners in a second. So one might expect there to be similarities in the way the visual system solves the correspondence problem in each case. On the other hand, there are also obvious differences which one would expect the visual system to exploit: most notably, although we used only horizontal motion in our experiments, motion can in principle occur in any direcion, whereas stereoscopic disparities are overwhelmingly horizontal (a point I later investigated in Read & Cumming 2004b). Richard was interested in examining further a result in the literature which suggested quite a fundamental difference between the two systems. This concerned anti-correlated stimuli, in which one image is replaced with its photographic negative. Anti-correlated random-dot kinematograms produce a reversed perception of depth, whereas anti-correlated random-dot stereograms produce no depth percept at all. Yet, for sinusoidal gratings, both systems must produce a reversed percept, since an anti-correlated sine-grating stereogram with near disparity is exactly the same stimulus as a correlated stereogram with far disparity. So for sufficiently narrow-band stimuli, the two systems must produce the same result, whereas at broader bandwidths, the literature showed they produced different results. With Richard, I examined human perception for filtered 1/f noise at a range of spatial frequency and orientation bandwidths. We found that for one-dimensional stimuli, containing only vertical orientations, both motion and stereo produced rather similar results, with anti-correlated stereograms causing weak reversed depth. However, for two-dimensional stimuli, containing all orientations, anti-correlated stereograms caused no depth percept, in agreement with previous studies, whereas anti-correlated kinematograms caused reversed motion. We suggested that this might be related to the anisotropy in stereo -- that disparities are overwhelmingly horizontal -- and that therefore conflict between different channels had a more devastating impact on depth perception.

Read JCA ( 2002 )
A Bayesian model of stereo depth / motion direction discrimination.

Biological Cybernetics Vol: 82 Pages: 117-136

ERRATA Comment: While working with Richard, I had begun trying to build a quantitative model of the stereo and motion systems which could explain our psychophysical results. After his death, I continued this work, and eventually wrote it up as the paper above. Again, I'm very grateful to Bruce, Simon and Andrew Glennerster for reading drafts of this and giving me feedback.

An interesting property of anti-correlated stimuli is that, under almost all reasonable assumptions about how disparity might be encoded, different spatial-frequency/orientation channels return different estimates of stimulus disparity. The problem in the model was finding a good way to combine the answers from different channels. In the end, I decided that the best way was to convert each channel's output into a common language, namely a Bayesian probability estimate of disparity. Suppose you have a binocular neuron tuned to disparity D, and you know that the input from the left eye is L. Then you can calculate the expected response of the neuron under the assumption that the stimulus disparity is D, because then the input from the right eye should be the same as that from the left, apart from small differences due to noise. If the actual response of the neuron is very different from this, then it isn't very likely that D really is the disparity of the stimulus.

I was expecting to have to build different ways of combining the different channels' outputs for the two systems, motion and stereo, in order to explain the differences in perception. But, to my surprise, I found that I could use the same mathematical structure. Differences in performance could be captured quite well by just assuming that the motion system is subject to a greater noise level than the stereo system, and that the stereo system prefers small disparities more than the motion system prefers lower speeds.

Read JCA ( 2002 )
A Bayesian approach to the stereo correspondence problem.

Neural Computation Vol: 14 Pages: 1371-1392

Comment: I got quite interested in the idea of converting the outputs of different channels to probability. I wondered whether the visual system might possibly represent the correspondence problem in probabilistic terms. We tend to pose the correspondence problem in terms of finding "the" matching feature in the right eye for a given feature in the left eye. However, sometimes there may be two matches for a given feature (Panum's limiting case), and sometimes none (occlusion). So, it might make sense to use a concept like probability -- where it is quite possible for two disparities to be considered likely, or none -- rather than a winner-take-all model which enforces exactly one match. I applied the model developed in the previous paper to various test stimuli, and it generally behaved sensibly. Because it was constructed from V1 neurons with a constant disparity preference across their receptive fields, it had a built-in preference for smoothly-varying disparity fields, so it gave correct percepts for the double-nail stimulus. It produced two probability peaks for Panum's limiting case, but only one for a random-dot stereogram. The question of when the visual system produces two disparity values, as in transparency, and how it handles occlusion, is a very interesting one, and this paper certainly goes nowhere near far enough in explaining this.

Read JCA, Parker AJ, Cumming BG ( 2002 )
A simple model accounts for the response of disparity-tuned V1 neurons to anti-correlated images.

Visual Neuroscience Vol: 19 Pages: 735-753

ERRATA
Matlab Code
Comment: I did my second M. Sc. project under the supervision of Bruce Cumming and Andrew Parker in the Physiology Laboratory at Oxford, and this turned out to be the beginning of a long and fruitful collaboration which saw me moving to the States for 4 years. My project related to an interesting observation Andrew and Bruce had just made in their influentual Nature paper of 1997. This tied in nicely with my project with Richard, because it also involved anti-correlated stimuli. Bruce and Andrew had measured the response of disparity-sensitive neurons in V1 to anti-correlated random-dot stereograms. The highly successful energy model of these neurons, proposed 7 years earlier by Ohzawa, DeAngelis and Freeman in Science, predicted that their disparity tuning curves should invert when they were probed with anti-correlated stimuli. Sure enough, in a triumph for theoretical neuroscience, the curves did invert. However, their amplitude also decreased, and this was not predicted by the model. Because anti-correlated stimuli do not cause a perception of depth, it was possible that this reduction in amplitude represented feedback (or the absence of expected feedback) from higher brain areas. However, it was also possible that a suitable feedforward model might also give a reduced amplitude for anti-correlated stimuli. Andrew and Bruce asked me to see if I could find such a model.
It turned out to be quite simple to modify the stereo energy model to produce this. All you have to do is apply half-wave rectification before inputs from the two eyes are combined, as opposed to after binocular combination as in the energy model. So, the reduction in amplitude does not necessarily depend on feedback from extrastriate areas.
In theory, I would have used this modified version of the energy model in all my subsequent modelling, on the grounds that it more accurately captures the behaviour of real neurons. However, the energy model is very easy to analyse mathematically, whereas the additional non-linearity makes my model almost impossible to say anything about analytically (at least, I haven't been able to!). So, in most of my subsequent population models, I have used the energy model to describe V1 cells. I feel quite fond of this paper, because it was my first encounter with the wonderful stereo energy model of Ohzawa et al. 1990. Much of my subsequent work has been trying to understand the behaviour of this deceptively simple model.

Read JCA, Cumming BG ( 2003 )
Measuring V1 receptive fields despite eye movements in awake monkeys.

Journal of Neurophysiology Vol: 90 Pages: 946-960

Comment: This was a little project we did, looking at a way of getting around uncertainties in measurements of eye position. During vision experiments in the awake monkey, scleral search coils -- hair-thin wires implanted around the animal's eyes -- are used to measure where the animal is looking. This enables you to check that the animals are fixating. However, the animals still make tiny fixational eye movements, which blur receptive field measurements. Some people have also used the coil outputs to correct for these microsaccades, but for this to be valid, the error on the coil outputs would have to be small compared to the scatter in eye position during fixation, and no one had checked that this was really the case. We found that coil measurements were subject to a slow drift. This means that you know where the animal is looking at any given moment only to within 0.1 degree of so, too rough to correct for fixational eye movements. However, because the drift is slow,you have a much more accurate idea of the difference between where the animal is looking now and where he was looking one second ago. We used this fact to do an improved Bayesian estimate of the receptive field profile, removing at least some of the smearing.

Read JCA, Cumming BG ( 2003 )
Testing quantitative models of binocular disparity selectivity in primary visual cortex.

Journal of Neurophysiology Vol: 90 Pages: 2795-2817

Comment: This paper represents the first major project I did after coming to work with Bruce. Here, we set out to test some more predictions of the energy model, and compare them with the predictions of the model proposed in Read et al. (2002). One prediction of the energy model is that the Fourier power spectrum of the disparity tuning curve is simply the product of the spatial frequency tuning measured in each of the two eyes. We showed that this isn't true in real cells. Real disparity tuning curves do not tend to have as strong oscillations as you would expect from the band-pass spatial frequency tuning in V1. You might think this could be explained by a relatively trivial modification of the energy-model -- suppose real cells receive input from several subunits with some jitter in their preferred disparity. This could smear out side-lobes which would otherwise have been observed. However, we were able to show that this simple generalisation of the energy-model could not explain the data either. It seems you need a more serious modification.

We showed that the model we'd proposed previously, Read et al. 2002, does seem to be able to account for the data. The key feature which makes this possible is that it allows non-linearities before binocular combination, whereas the energy model is linear up to binocular combination. (Unfortunately, it's this very linearity which makes the energy model so easy to handle mathematically!) We also pointed out that a non-linearity before binocular combination seems necessary in order to explain the behaviour of cells in which one eye always has a suppressive effect.

Read JCA, Cumming BG ( 2004 )
Ocular dominance predicts neither strength nor class of disparity selectivity with random-dot stimuli in primate V1.

Journal of Neurophysiology Vol: 91 Pages: 1271-1281

Comment: This paper used the same data as the previous one, but addressed a different question. It seems obvious that a cell's disparity tuning would be related to its ocular dominance -- surely monocular cells can't be disparity-tuned. However, "monocular" is often used to mean "does not respond to stimulation in the left eye" (say), which is different from "does not receive input from the left eye". We found that many cells which could not be driven by the left or right eye alone were nevertheless disparity-tuned, and so must receive input from both eyes. This is easy to understand -- one eye sends purely inhibitory input -- and yet it contradicts the energy model. This is not a rare event -- at the population level there is no correlation between ocular dominance and disparity tuning. This is rather worrying for conventional models of disparity tuning, such as the energy model. And yet I must admit I carry on using the energy model to study the encoding of disparity in visual cortex -- I think none of the stereo modellers, including myself, have really taken its limitations on board yet.

Read JCA, Cumming BG ( 2004 )
Understanding the cortical specialization for horizontal disparity.

Neural Computation Vol: 16(10) Pages: 1983-2020

Comment: In a 2002 Nature paper, Bruce measured the response of disparity-tuned cells in V1 to a full range of two-dimensional disparities. This was unusual, because previous work had either used horizontal disparity (in awake animals), or disparity orthogonal to the preferred orientation of the cell (in anaesthetised animals). Bruce found that the 2D disparity-tuning surfaces of the cells tended to be elongated along the horizontal direction, no matter what the preferred orientation of the cell was. This was a very surprising result, as it completely contradicts the predictions of all existing models. Everyone had always assumed that the tuning to 2D disparity would reflect the cell's orientation tuning. So, my next project was to investigate what sort of model could account for this result.

We came up with two models. The first simply postulated that the cells Bruce recorded from were composed of many subunits, and these were scattered more widely horizontally than vertically. The second involved monocular normalization by appropriately elongated units.

Read JCA ( 2005 )
Early computational processing in binocular vision and depth perception.

Progress in Biophysics and Molecular Biology Vol: 87 Pages: 77-108

Comment: In 2005, I was invited to speak at the festschrift in honour of my former PI and mentor, Julian Jack FRS, who had launched my career in neuroscience by agreeing to sponsor me for a Wellcome Training Fellowship in Mathematical Biology. I took the opportunity to get my thoughts into shape on how disparity is represented in early visual cortex and talk about some of our work on the energy model and so on.

Read JCA, Cumming BG ( 2005 )
The effect of interocular delay on disparity-selective V1 neurons: relationship to stereoacuity and the Pulfrich effect.

Journal of Neurophysiology Vol: 94 Pages: 1541-1553

Comment: Bruce and I now started looking at the effect of differences in the time, as well as the position, at which corresponding features strike the eyes. Bruce recorded the response of V1 neurons to random-dot patterns with both horizontal spatial disparity, and temporal delay. I analysed this data-set, and found that the shape of the disparity tuning curve was largely independent of the delay; delay simply reduced the amplitude. This was contrary to previous reports in the cat (Anzai et al, 2002, Nature Neuroscience), which had emphasised shifts in disparity tuning as a function of delay. However, linear models (like the energy model) would predict that the disparity tuning only shifts in cells which are direction-selective. We showed that the difference between our results and those from cat could be largely explained by the relative paucity of direction-selective cells in the monkey.

Read JCA, Cumming BG ( 2005 )
The stroboscopic Pulfrich effect is not evidence for the joint encoding of motion and depth.

Journal of Vision Vol: 5(5):3 Pages: 417-434 [view on journal website]

ERRATA Comment: However, this left us with something of a puzzle, as the shifts in disparity tuning which occur with delay (in the cat) had been proposed as a neuronal substrate for the Pulfrich effect. This is a visual illusion which occurs when the image from one eye is delayed: moving objects appear to shift in depth. This had been explained on the basis of cells which are sensitive to both direction of motion and to disparity: i.e. which jointly encode motion and depth. However, in our previous paper we had found that such cells were quite rare in monkey V1 (~10%). It seemed surprising to us that these few cells would cause such an illusion, when the vast majority of cells would not be subject to the illusion on this basis. So, we looked again at whether joint encoding of motion and depth really was necessary for the Pulfrich effect. We found that it wasn't. As previous workers had noted, the Pulfrich effect arises because of cells' finite temporal integration; but finite temporal integration does not necessarily imply direction selectivity. Our results suggested that all cells in V1, even the ones which show no shift in disparity tuning with delay, could potentially support the Pulfrich illusion.

Read JCA, Cumming BG ( 2005 )
All Pulfrich-like illusions can be explained without joint encoding of motion and disparity.

Journal of Vision Vol: 5(11):1 Pages: 901-927 [view on journal website] Pubmed ID : 16441193

ERRATA Comment: The final step was to build a neuronal model, and show that it experienced the illusion. We modelled a neuronal population constructed of neurons which either encoded motion, or depth (not both), and showed that a very simple way of "reading out" this activity, so as to convert it to a perception of depth, would be subject to the Pulfrich illusion. We also examined other evidence which had been put forward in support of the joint motion/depth idea, such as the illusion of swirling motion which occurs in dynamic noise with an interocular delay. We found that this, too, could be experienced by a brain which encoded motion and depth entirely separately. So, while there certainly are primate neurons which jointly encode motion and depth (notably in MT), there is no reason to suppose that these play a privileged role in supporting the Pulfrich effect and related illusions.
This series of three papers (Read & Cumming 2005abc) has recently attracted some criticism from Ning Qian and Ralph Freeman, in a paper entitled "Pulfrich phenomena are coded effectively by a joint motion-disparity process" (J Vis, 9(5): 1-16). My take on it is that we are all basically in agreement, but the situation is obscured by the lack of a clear agreed definition of "joint" vs "separate" encoding of motion and disparity. For example, we said that to be called a motion detector, a cell not only had to be tuned to speed, it also had to respond differently to opposite directions of motion, whereas Qian & Freeman required only speed tuning. I want to clear up one other point. Qian & Freeman say that our model is "non-causal", apparently because it responds to the disparity between a stimulus in one eye and a stimulus which arrives in the other eye at a later time. At the time that stimulus 1 occurs, stimulus 2 is still in the future. However, at the time the neuron responds to the disparity between the two stimuli, both stimuli have already occurred. Thus, the model is firmly causal. Indeed, our derivation of its properties explicitly sets the temporal kernel to zero for future times.

Hardingham NR, Bannister NJ, Read JCA, Fox KD, Hardingham GE, Jack JJB ( 2006 )
Extracellular calcium regulates postsynaptic efficacy through group 1 metabotropic glutamate receptors.

Journal of Neuroscience . Vol: 26(23) Pages: 6337-45 [view on journal website]

Matlab Code
Comment: This project began when I was in my first neuroscience post-doc, doing a Wellcome Training Fellowship in Mathematical Biology with Julian Jack in Oxford. Julian's lab had done a lot of work on synaptic physiology, in particular developing quantal analysis as a tool to examine central synapses. The physiology underlying quantal analysis is the fact that neurons are generally connected by more than one terminal. When the presynaptic neuron fires an action potential, packets - quanta - of neurotransmitter may be released from all, some or none of these terminals. If each packet of neurotransmitter contributes a similar amount to the postsynaptic depolarisation, then a histogram of the effect produced by each presynaptic action potential will have several peaks, corresponding to the release of 0, 1, 2 ... quanta of neurotransmitter. In principle, this histogram can then be analysed to estimate the effect caused by each quantum, and the probability that a quantum will be released from a terminal given an action potential. In practice, this depends critically on things like whether each quantum really does have a very similar postsynaptic effect, whether the release probability is the same at all terminals, whether these quantities are constant over time and so on. Julian's lab had already developed a lot of sophisticated tools for quantal analysis, and I took this further, developing a still more elaborate fitting algorithm to extract the quantal parameters, and also a battery of statistical tests to decide whether the resulting model of the synapse was adequate. There's quite a lot of sceptism as to how far quantal analysis can be trusted in the central nervous system (as opposed to at the neuromuscular junction, where it was originally developed), so these tests were critical in convincing people that our results were reliable. Neil Hardingham, the first author, who was a Ph.D. student and post-doc in Julian's lab when I was there, used these techniques to examine how the quantal parameters change as a function of extracellular calcium. He was able to show that calcium depletion, as well as reducing release probability, also reduces quantal size. Since calcium levels drop as neurons become active, this represents a novel mechanism for regulating information transfer between neurons.

Read JCA, Cumming BG ( 2006 )
Does depth perception require vertical disparity detectors?

Journal of Vision Vol: 6(12)1 Pages: 1323-1355 [view on journal website]

Comment: This paper represents a cool idea which turned out (probably) not to be true. There's a wealth of psychophysical evidence indicating that humans measure vertical disparity, and use this to calibrate oculomotor signals about eye position. This has been taken, without much thought, as "obviously" indicating that the brain therefore contains detectors tuned to a range of vertical disparities, and various physiological studies have looked for them (so far with little success, due to a range of interpretation problems). We realised that actually, the psychophysical performance could be explained if the brain only had access to the magnitude (not the sign) of vertical disparity. Essentially, this is because the sign has a predictable pattern, so you don't need to measure it explicitly. This is important because if all you need is the magnitude of vertical disparity, you can get this from a population of purely horizontal disparity detectors. For these detectors, vertical disparity could be deduced via its effect on binocular correlation. This seemed to us a very elegant solution for the brain to adopt. Most disparities are horizontal (see Read & Cumming 2004), so it would enable the brain to concentrate its detectors according to the statistics of natural viewing (clearly the efficient thing to do) while still being able to extract information from vertical disparities when they do occur. This also raised the exciting possibility of being able to mimic vertical-disparity illusions with binocular correlation -- stereopsis without disparity. Sadly, however, my attempts to produce these illusions failed, and I now believe that this idea is not correct. In 2010, I returned to this train of thought and developed a more sophisticated model which can deduce both magnitude and sign of vertical disparity from a population of purely horizontal disparity detectors.

Read JCA , Cumming BG (2007) ( 2007 )
Sensors for impossible stimuli may solve the stereo correspondence problem.

Nature Neuroscience Vol: 10 Pages: 1322 - 1328. [view on journal website]

ERRATA
Supplementary material
Comment on this paper in Nature's Research Highlights section, Nature, 449: 118.

Comment: Here, Bruce and I returned to the question of how to extract stimulus disparity from a population of binocular neurons such as seem to exist in primary visual cortex. Once again, we used the energy model of Ohzawa, DeAngelis and Freeman (1990). The output of this model depends on the receptive fields in the two eyes. The physiological literature shows that the receptive fields are usually well-described by Gabor functions, of similar spatial frequency and orientation tuning, but differing in their phase and/or position on the retina. It makes sense to have receptive fields which differ in retinal position -- you can view these as "position-disparity detectors" sensing objects at different positions in space. But we wondered why you find receptive fields differing in phase, "phase-disparity detectors". These do work as disparity detectors, but they seem suboptimal -- they respond best to retinal patterns that are never generated by real objects. If the brain only contained these phase-disparity detectors, instead of the more suitable position-disparity detectors, you might reckon there was some developmental constraint which meant that the brain just couldn't wire up position-disparity detectors. But since it clearly can generate position-disparity, what's the point of having phase-disparity detectors as well?
Phase-disparity detectors respond best to different patterns of light and dark in the two eyes. Real objects would always project the same pattern in both eyes, so phase-disparity detectors don't respond best to real objects. They respond best to unrelated regions of the visual scene, i.e. where the regions of the two retina viewed by this particular binocular neuron do not correspond to the same object in space. In other words, they respond best to false matches. This could be very useful, because position-disparity detectors are plagued by false matches. It's difficult to interpret their response, as a strong response does not necessarily indicate that there is an object at the disparity to which the detector is tuned; it could be a false match. We realised that you could solve this problem by using the phase-disparity detectors as "lie detectors". For each possible match provided by the position-disparity detectors, the pattern of the response of the corresponding phase-disparity detectors reveals whether the match is true or false.
At the moment, this is just an idea; we don't know if this is really how the brain uses phase-disparity detectors. We hope this paper will stimulate experimental investigations which will either confirm or rule out our suggestion, as well as prompting further consideration about the role of phase disparity in the brain.

Serrano-Pedraza I, Read JCA ( 2009 )
Stereo vision requires an explicit encoding of vertical disparity

Journal of Vision Vol: 9(4):3 Pages: 1--13 [view on journal website]

Comment: This work was testing Read & Cumming (2006), where we suggested that the brain could potentially deduce vertical disparity information from the pattern of (de)correlation across the visual field, without necessarily using cells tuned to a range of vertical disparities. In this paper, we tried to construct a stimulus for which this strategy would fail. We found that perception carried on just the same, thus shooting down the model of Read & Cumming (2006) in its present form.

Bredfeldt CE, Read JCA , Cumming BG ( 2009 )
A quantitative explanation of responses to disparity defined edges in macaque V2.

Journal of Neurophysiology Vol: 101 Pages: 701-713 [view on journal website]

Comment: Christine and Bruce, the first and last authors, have a previous paper on Cyclopean Edge Responses in Macaque V2 (J Neurosci, 2006, 26:7581-7596 ) , showing that many V2 cells respond to depth edges in random-dot stereograms. They suggested there that the responses they observed could result from a simple feedforward scheme in which V2 neurons receive inputs from several V1 subunits with different disparity selectivity. In this paper, we carried out quantitative modelling demonstrating this. I like this paper because much of my work has been on modelling the properties of neurons in V1. It's nice to feel that we can begin to trace how those calculations are then used beyond V1 to result in our depth perception.

Read JCA, Phillipson GP, Glennerster A ( 2009 )
Latitude and longitude vertical disparities

Journal of Vision Vol: 9(13):11 Pages: 1-37 [view on journal website]

Comment: At around this time I'd been spending a lot of time thinking about vertical disparity, and had been awarded an MRC grant to study it. To begin with, I wasn't even entirely clear what vertical disparity was, and I had difficulty following some of the other papers on it. I realised that a lot of the confusion was occurring because there are actually several different definitions of "vertical disparity" in the literature -- I've identified at least four -- and to make matters worse, different papers aren't always clear about exactly which definition they have in mind. Unsurprisingly, this has caused a lot of confusion about what the properties of vertical disparity actually are. Part of the problem, I think, is that under some circumstances you obtain the same results regardless of whether you define the elevation coordinate as a latitude or a longitude on the retina, and this may have given the impression that it doesn't ever matter -- whereas in fact, under some circumstances, the two definitions give completely different results. So with my PhD student Graeme Phillipson and my old friend and colleague from back in Oxford, Andrew Glennerster, we decided to write a paper really getting into the nitty-gritty of vertical disparity, and laying out clearly what properties follow from different definitions. It may not be the most exciting paper ever, and like many of my papers, it has masses of Appendices filled with equations. But we hoped it would be a useful reference for anyone interested in vertical disparity -- and I did at least try hard to make the pictures pretty.

Serrano-Pedraza I, Phillipson GP, Read JCA ( 2010 )
A specialization for vertical disparity discontinuities

Journal of Vision Vol: 10(3):2 Pages: 1-25 [view on journal website] Pubmed ID : 20377279

Comment: One of the first things I wanted to know about vertical disparity was how finely we are able to resolve it. This had been studied in a previous paper by Kaneko & Howard (1997, Vision Research 37 (20): 2871-2878), but there were a number of issues which made me feel the question hadn't been fully resolved. We used essentially the same stimulus as Kaneko & Howard: that is, an alternating version of Ogle's induced effect, in which vertical magnification alternated in strips across the image. We assumed that the task would be easiest when the magnification was constant across the whole image, and become progressively harder as the strip-width was reduced. To our surprise, this wasn't the case for most subjects. About a third of our observers did behave in this way, but most of us found that the abrupt switches in the sign of vertical magnification were quite salient and actually helped us do the task -- resulting in a band-pass, rather than a low-pass, performance profile. I have worried a lot about whether this result could be due to some artefact, but we've tested for everything we can think of and it keeps showing up time after time. So, there must be mechanisms in the brain which respond to discontinuities in vertical disparity. The existing literature emphasises the continuity of vertical disparity in natural viewing. But actually, discontinuities can occur under some circumstances, so it is possible that we have developed detectors for these.

Hardingham N, Read JCA, Trevelyan A, Nelson C, Jack JJB, Bannister N ( 2010 )
Quantal analysis reveals a functional correlation between pre- and postsynaptic efficacy from excitatory connections in rat neocortex

Journal of Neuroscience Vol: 30(4) Pages: 1441-51 [view on journal website]

Matlab code

Read JCA ( 2010 )
Vertical binocular disparity is encoded implicitly within a model neuronal population tuned to horizontal disparity and orientation

PLoS Computational Biology Vol: 6(4) Pages: e1000754 [view on journal website]

Comment: So, at this point the original idea we'd put forward in 2006 was pretty comprehensively disproved. However, I now realised that a more sophisticated decoding could extract both the magnitude and the sign of vertical disparity, in a way that was consistent with psychophysics including Serrano-Pedraza and Read (2009). In this paper, I demonstrated that this works in simulations. However, this way of encoding vertical disparity works very well, and as far as I can see doesn't predict any characteristic errors of perception. Thus, I think this idea can only really be tested by physiology.

Allenmark PF, Read JCA ( 2010 )
Detectability of sine- versus square-wave disparity gratings: a challenge for current models of depth perception

Journal of Vision Vol: 10(8):17 Pages: 1-16 [view on journal website]

Comment: In 2010, my PhD student Fredrik Allenmark, my post-doctoral associate Ignacio Serrano-Pedraza and I were all thinking a lot about disparity gratings. By "gratings" here, what we mean are surfaces which are corrugated in depth, as in the two icons here. "Sine-wave gratings" are surfaces in which the corrugations are smooth waves, rather like corrugated iron, whereas "square-wave gratings" have square edges. As the corrugations get higher in frequency (i.e. up-and-down bits get closer together), it gets harder to see that the surface has this structure. "Luminance gratings", i.e. patterns of black and white stripes, have made a huge contribution to our understanding of vision. Disparity gratings have also been studied, but less extensively. We were interested in what our perception of such structures can tell us about human vision.

For his PhD project, Fredrik started with a couple of recent observations from Bruce Cumming's lab at NIH and Marty Banks' lab at Berkeley. In a linked pair of papers in The Journal of Neuroscience, these workers had shown that V1 neurons seem to respond best to frontoparallel surfaces, and had proposed that the limit of human stereoresolution -- that is, the highest-frequency gratings we can detect - is set by the size of these neurons' receptive fields. We reasoned that if this model is correct, it should be easier for us to detect square-wave gratings than sine-wave gratings. Square-wave gratings are made up of piecewise frontoparallel surfaces, to which V1 neurons respond optimally, whereas sine-wave gratings are always slanting towards or away from the observer. Fredrik first ran simulations to confirm that the model behaved as we expected, and then carried out careful experiments to see what humans perceived. To our surprise, Fredrik found that there was no difference in stereoresolution for square-wave versus sine-wave gratings. As the amplitude of high-frequency gratings increased, human performance fell to chance at the same rate for both sine-wave and square-wave gratings, whereas the model predicted that this should happen only for sine-waves.

Read JCA, Phillipson GP, Serrano-Pedraza I, Milner AD, Parker AJ ( 2010 )
Stereoscopic vision in the absence of the lateral occipital cortex

PLoS ONE Vol: 5(9) Pages: e12608 [view on journal website]

Supplementary file S1.
Supplementary file S2.
Supplementary file S3.
Comment: "D.F." is a famous neuropsychological patient who experienced carbon monoxide poisoning in an accident many years ago. This left her with long-term damage to a number of different brain areas, visible on magnetic resonance imaging. As a consequence, she has a remarkably specific visual impairment known as visual form agnosia. Although she can see colours and movement, and she can navigate the world visually without bumping into things, she cannot recognise objects visually. This is not because her vision is blurred; she has good acuity. She simply perceives objects as a meaningless jumble of elements. Fortunately for science, DF is a highly intelligent woman who is interested in her unusual brain injury, and over the past three decades she has devoted untold hours of her time to working with psychologists in order to map out the precise nature of her visual impairment. David Milner, emeritus professor at Durham, has worked extensively with DF along with his long-time colleague Mel Goodale. I highly recommend their two books, "The visual world in action" (the longer and more detailed) and "Sight Unseen" (slimmer and accessible for lay readers). On this project, I collaborated with David and with Andrew Parker from Oxford, along with my postdoc Ignacio Serrano-Pedraza and PhD student Graeme Phillipson, in order to examine DF's stereo vision.

It was already known that DF retained stereo vision, but that her stereoacuity was somewhat impaired. Standard clinical measures of stereo vision ask subjects to use stereo disparity to tell which of two surfaces was the closer. People with normal vision are incredibly precise on making such relative disparity judgments. DF could do the task, but only when the separation between the two surfaces was relatively large. Andrew had recently written a very insightful review on the neuronal basis of stereo vision in Nature Neuroscience. Based on the physiological and imaging literature Andrew reviewed, and the location of DF's most severe cortical damage, we were not surprised that DF was impaired on standard relative disparity tasks, but predicted that she would not be impaired on an absolute disparity task, i.e. judging the depth of an isolated object.

To our delight, this prediction was initially borne out. On DF's first two visits, she performed as well as age-matched controls on an absolute disparity task, but whereas they performed much better when a reference surface converted the task to a relative-disparity task, DF did not. However, this initially clean story was complicated when, after testing DF on a variety of other stimuli, she subsequently improved on the relative disparity task. It was as if we had provided training which enabled her to use information she had previously been blind to. For example, maybe her attention was not automatically drawn to the boundary demarcating the two surfaces, as controls' is, but with training she learnt where the informative region of the stimulus was. However, our results did show clearly that there is a big difference between relative disparity between adjacent surfaces (which was compromised by DF's cortical lesion) and relative disparity between transparent surfaces in relative (which DF sees perfectly). This neuropsychological evidence agrees with the predictions from physiology.

This was my first neuropsychological study, and it was a very interesting experience for me. While it is inevitably difficult working in an "n=1" situation, I found it fascinating gaining insight into DF's visual world, seeing first-hand the problems faced by someone who has a completely unique visual experience and thus no words to communicate it. I would like to record my gratitude to DF for bearing with me so patiently!

Phillipson GP, Read JCA ( 2010 )
Stereo correspondence is optimized for large viewing distances

European Journal of Neuroscience Vol: doi:10.1111/j. Pages: 1460-9568.2010.07454.x.

ERRATA Comment: This paper represents Graeme's main PhD project. Graeme was interested in how stereo vision copes with the changing epipolar geometry caused by eye movements. By cleverly manipulating the geometry of the viewed stimuli, Graeme showed that stereo correspondence does not take account of changes in vertical disparity which occur as our eyes move from viewing near to far objects, but remains optimised for far viewing. I think this is a unique situation where a pattern of vertical disparity produces no depth percept on its own, but enhances the visibility of depth due to horizontal disparity.

Serrano-Pedraza I, Read JCA ( 2010 )
Multiple channels for horizontal, but only one for vertical corrugations? A new look at the stereo anisotropy

Journal of Vision Vol: 10(12):10 Pages: 1–11

Comment: While Fredrik was measuring the high-frequency limit of our ability to perceive sine- and square-wave depth corrugations, Ignacio got interested in another aspect of sine- versus square-wave corrugations. For sine-wave corrugations, Brian Rogers and Mark Bradshaw had shown that at low frequencies, horizontal corrugations were easier to detect than vertical corrugations: that is, the corrugations didn't have to be so deep in order to be visible. At high frequencies, this difference becomes weaker. This result has been replicated in many different tasks, and represents a fundamental anisotropy of stereo vision. Ignacio showed that, at low frequencies, this anisotropy is not as strong with square-wave gratings as with sine-waves: low-frequency square-waves are about equally visible whether they are horizontal or vertical. To understand why this is, Ignacio considered two different models. In one model, the waveform is analysed as a whole, and it is detected if its RMS amplitude exceeds some threshold. In the other model, the waveform is analysed in separate frequency channels, assumed to have a bandwidth narrow enough that harmonics differing by 1.5 octaves activate separate channels. The grating is detected if the Fourier amplitude of any harmonic exceeds the threshold for that frequency, which we measure using sine-wave gratings. For vertical gratings, both models worked equally well, but for horizontal gratings, only the separate-channel model can capture the improved performance at low frequencies. One plausible interpretation of these results is that there is only a single channel available to detect vertical gratings, but there are a few (three, say) for horizontal gratings. This recasts the well-known stereo anisotropy in Fourier language: horizontal gratings are more visible at low frequencies because they activate a channel dedicated to these low frequencies, whereas vertical gratings are only perceived when their amplitude is large enough to activate the all-purpose channel, which is centered on intermediate frequencies. Obviously, more work is needed to test this hypothesis, and we intend to pursue this in the future, for example with a masking technique.

Serrano-Pedraza I, Clarke MP, Read JCA ( 2011 )
Single vision during ocular deviation in intermittent exotropia

Ophthalmic and Physiological Optics Vol: 31 Pages: 45-55 [view on journal website] Pubmed ID : 21158884

Comment: Around this time Ignacio, Mike and I had been thinking a lot about intermittent exotropia as we worked on our IOVS paper, so we took this opportunity to write a little review on the subject.

Serrano-Pedraza I, Manjunath V, Osunkunle O, Clarke MP, Read JCA ( 2011 )
Visual suppression in intermittent exotropia during binocular alignment

Investigative Ophthalmology and Vision Science Vol: 52(5) Pages: 2352-2364 [view on journal website] Pubmed ID : 21220559

This paper won the 2011 Pfizer Research Prize for excellent ophthalmological research in the North East.
Comment: This is my first clinical paper. Shortly after I arrived in Newcastle, Anya Hurlbert, our Institute director, put me in touch with Mike Clarke, a consultant ophthalmologist specialising in disorders of binocular vision. She figured that we’d have plenty to talk about and she was (as usual) quite right. Mike introduced me to a condition called intermittent exotropia. It’s a form of squint where the eye deviates outwards only occasionally, mainly when the person is tired and/or looking at faraway objects. What intrigued me about it was to learn that people with this condition generally retain their stereo 3D vision, the “gold standard” of binocular function, indicating that both their eyes can see well individually and can work together. And yet when their eyes are pointing in different directions, they don’t generally report any double vision, implying that input from one of the eyes has been temporarily turned off. Ignacio and I were intrigued that the brain can learn to turn the eyes’ input on and off in this way. We wondered what triggered the switch. Was it the eye movement itself, or was it the resulting change in retinal input – the fact that the two eyes’ images no longer matched up? Ignacio came up with a cool experiment to answer that question, and we spent a lot of time fine-tuning it to make it fun and enjoyable for child participants. For example, instead of dots or lines, we used child-friendly faces, such as Igglepiggle shown in the icon.
The experiment worked really well and we got a nice clear answer to our question. It turns out that eye movements are not required; it’s the retinal input which triggers the switch. If you grow up with intermittent exotropia, then your brain learns to look out for big offsets between the retinal images. That probably means that one of your eyes has turned outwards, and to avoid being troubled by double vision, your brain apparently switches to monocular mode.

Serrano-Pedraza I, Hogg EL, Read JCA ( 2011 )
Spatial non-homogeneity of the antagonistic surround in motion perception

Journal of Vision Vol: 11(2):3 Pages: 1–9 [view on journal website] Pubmed ID : 21292831

Allenmark PF, Read JCA ( 2011 )
Spatial stereoresolution for depth corrugations may be set in primary visual cortex

PLoS Computational Biology Vol: 7(8) Pages: e1002142 [view on journal website] Pubmed ID : PMC3158043

Comment: We weren't sure at first how much of a problem this was for the existing model. In principle, it could require fundamental changes, for example indicating that stereoresolution is set at a much higher cortical level than V1. However, we thought of one pretty minor tweak which could potentially reconcile the model and data. V1 neurons are believed to show a "size-disparity correlation", i.e. the larger disparities are encoded by neurons with larger receptive fields. In our model, a single "correlation detector" represents a pool of V1 neurons tuned to different spatial frequencies and orientations. The size of the window within which interocular correlation is computed represents the minimum receptive field of neurons in this pool. In our previous model, following Gepshtein, Banks, Landy et al, we had assumed that this window was the same for all disparities. Now, we made the window larger for neuronal pools tuned to larger disparities. Now, as the amplitude of a corrugation increased, the receptive-field size of the cells encoding it also increased, limiting the ability to perceive high-frequency corrugations. It turned out that this impaired the model's ability to "see" square-wave corrugations, bringing performance down to the level of sine-waves, just as in humans.

Vuong QC, Friedman A, Read JCA ( 2012 )
The relative weight of shape and non-rigid motion cues in object perception: A model of the parameters underlying dynamic object discrimination

Journal of Vision Vol: 12(3): 16 Pages: 1-20 [view on journal website] Pubmed ID : 22427696

Comment: This is a paper with my colleague Quoc and his collaborator Alinda over in Canada. Once again, my contribution is a tedious appendix filled with equations. Quoc and Alinda were interested in how much we recognise objects by their shape, and how much by their characteristic motion. We’ve probably all had the experience of recognising a friend from behind by their gait, for example. Quoc and Alinda came up with cool stimuli which could be differentiated either by their shape, or by their movement, or both. I helped develop a cue-combination model to quantify how much weight people were giving to each cue.

Brilot BO, Bateson M, Nettle N, Whittingham MJ, Read JCA ( 2012 )
When is general wariness favored in avoiding multiple predator types?

American Naturalist Vol: in press Pages:

Comment: I’m fond of this paper because it's my first ecology paper. If you've been reading this far, you know that I'm all about stereo vision - its properties, neuronal basis, cortical location and so on. This paper, in contrast, is about predator-prey relations, e.g. a sparrow trying to avoid being eaten by a cat or a hawk. Needless to say, the ecology in this paper comes from the other authors. My contribution was to help with the mathematical modelling. Ben Brilot, the first author, and his PI Melissa Bateson (another Royal Society University Research Fellow before she became a Reader here at Newcastle), are interested in anxiety and wariness in animals. In this project, they and our colleagues Daniel Nettle and Mark Whittingham were interested specifically in how a prey animal's optimal behaviour changes if it has to avoid not one, but two or more predators which place conflicting demands on the animal. If the overall danger level rises, should the animal simply become more wary to every potential threat, or should it target its wariness towards the greater danger? We thought that signal detection theory could be a useful framework, and Ben and I spent a lot of time sitting down together trying to figure out how to make that work. As ever, the issue was how to simplify the problem enough to make progress while still retaining enough complexity to make it interesting. I think we both found it a really interesting experience. I was fascinated to get this insight into my ecological colleagues' field, and blown away by the depth and breadth of their knowledge across so many species and situations.

Read JCA, Vaz X, Serrano-Pedraza I ( 2012 )
Independent mechanisms for bright and dark image features in a stereo correspondence task

Journal of Vision Vol: 11(12):4 Pages: 1-14 [view on journal website] Pubmed ID : 21984818

Comment: I've long been intrigued by the 1995 Nature paper by Julie Harris and Andrew Parker, where they show that people perform better on a disparity task when the stimulus uses white and black dots on a grey background, than when the dots are all white or all black. They explain the effect by arguing that the stereo correspondence problem - that is, matching up which features in the two eyes correspond to the same object in space - is easier with black and white dots. Mixed colours instantly halves the complexity of the problem, because you know that a black dot can't match with a white dot. That does sound very reasonable, but my problem is that I come at stereo correspondence from the perspective of the energy model, which effectively implements cross-correlation between the two eyes' images. Cross-correlation doesn't "see" dots at all. I couldn't figure out how to implement Julie and Andrew's explanation using current models of cells in early visual cortex.
I did, however, think I could see a way round the problem. Julie and Andrew's paper started with an easy stereo task - seeing which of two adjacent planes was closer. The planes were defined by dots which were randomly scattered in X and Y, but all at the same Z (where the Z axis defines distance from the observer). They then made the task harder by introducing disparity noise, i.e. giving each dot some jitter in Z. This meant you had to average over several dots in order to get a good estimate of mean Z.
When I coded up this stimulus and had a look at it, it immediately struck me that it didn't noticeably challenge stereo correspondence. I felt I could clearly see each dot in space, indicating that my brain had successfully solved the correspondence problem. But the task was hard, because it wasn't obvious which cloud of dots was closer. Once I'd realised that, I thought I might have a way out of my difficulty. Stereo correspondence would proceed by, essentially, cross-correlation, and mixed black/white dots would offer no advantage over all-white and all-black dots. But then, in order to do Julie and Andrew's task, a higher brain area would have to figure out which dots to average over. Maybe that brain area is only able to average over a certain number of dots within each category, and therefore adding a different category ("black" as well as "white") improves performance. So when Xavier Vaz, a Biomedical Sciences undergraduate, did his project in my lab, I had him test this theory by comparing Julie and Andrew's original task with a different one designed to challenge stereo correspondence, but to be trivial once correspondence had been achieved. I was confident the mixed-colour advantage would show up on the original task and be abolished in our new experiment.
And I was completely wrong. Performance on both tasks was clearly better for mixed black-and-white dots. Julie and Andrew's result holds not only in their original task, but also in this new version of it. And I still don't have a clue how to reconcile this with my understanding of how disparity is encoded in early visual cortex.

Banks MS, Read JCA, Allison RS, Watt SJ ( 2012 )
Stereoscopy and the Human Visual System

Motion Imaging Vol: In press Pages:

Comment: In July 2011, the Society of Motion Picture and Television Engineers (SMPTE) held its 2nd International Conference on Stereoscopic 3D for Media & Entertainment in New York. Marty Banks from Berkeley, Rob Allison from York University in Toronto, Simon Watts from Bangor and I jointly presented a seminar on stereoscopy and the human visual system. The aim was to lay out some of the key findings from vision science which relate to the design of 3D displays including 3D TV and cinema. We collaborated closely on our presentations, and afterwards wrote them up together into this paper.

Read JCA ( 2012 )
Understanding visual cues to depth

Current Biology Vol: 22 (5) Pages: R163-R165 [view on journal website] Pubmed ID : 22401898

Comment on Curr Biol. 2012 Mar 6;22(5):426-31.
Comment: This is a "Dispatch" article commenting on a cool paper by Robert Held, Emily Cooper and Marty Banks in the same issue of Current Biology, "Blur and Disparity are Complementary Cues to Depth."