Depth Perception Not Found in Human Observers for Static or Dynamic Anti-Correlated Random Dot Stereograms

One of the greatest challenges in visual neuroscience is that of linking neural activity with perceptual experience. In the case of binocular depth perception, important insights have been achieved through comparing neural responses and the perception of depth, for carefully selected stimuli. One of the most important types of stimulus that has been used here is the anti-correlated random dot stereogram (ACRDS). In these stimuli, the contrast polarity of one half of a stereoscopic image is reversed. While neurons in cortical area V1 respond reliably to the binocular disparities in ACRDS, they do not create a sensation of depth. This discrepancy has been used to argue that depth perception must rely on neural activity elsewhere in the brain. Currently, the psychophysical results on which this argument rests are not clear-cut. While it is generally assumed that ACRDS do not support the perception of depth, some studies have reported that some people, some of the time, perceive depth in some types of these stimuli. Given the importance of these results for understanding the neural correlates of stereopsis, we studied depth perception in ACRDS using a large number of observers, in order to provide an unambiguous conclusion about the extent to which these stimuli support the perception of depth. We presented observers with random dot stereograms in which correlated dots were presented in a surrounding annulus and correlated or anti-correlated dots were presented in a central circular region. While observers could reliably report the depth of the central region for correlated stimuli, we found no evidence for depth perception in static or dynamic anti-correlated stimuli. Confidence ratings for stereoscopic perception were uniformly low for anti-correlated stimuli, but showed normal variation with disparity for correlated stimuli. These results establish that the inability of observers to perceive depth in ACRDS is a robust phenomenon.     

A Bayesian model of stereopsis depth and motion direction discrimination

 The extraction of stereoscopic depth from retinal disparity, and motion direction from two-frame kinematograms, requires the solution of a correspondence problem. In previous psychophysical work [Read and Eagle (2000) Vision Res 40: 3345–3358], we compared the performance of the human stereopsis and motion systems with correlated and anti-correlated stimuli. We found that, although the two systems performed similarly for narrow-band stimuli, broad-band anti-correlated kinematograms produced a strong perception of reversed motion, whereas the stereograms appeared merely rivalrous. I now model these psychophysical data with a computational model of the correspondence problem based on the known properties of visual cortical cells. Noisy retinal images are filtered through a set of Fourier channels tuned to different spatial frequencies and orientations. Within each channel, a Bayesian analysis incorporating a prior preference for small disparities is used to assess the probability of each possible match. Finally, information from the different channels is combined to arrive at a judgement of stimulus disparity. Each model system – stereopsis and motion – has two free parameters: the amount of noise they are subject to, and the strength of their preference for small disparities. By adjusting these parameters independently for each system, qualitative matches are produced to psychophysical data, for both correlated and anti-correlated stimuli, across a range of spatial frequency and orientation bandwidths. The motion model is found to require much higher noise levels and a weaker preference for small disparities. This makes the motion model more tolerant of poor-quality reverse-direction false matches encountered with anti-correlated stimuli, matching the strong perception of reversed motion that humans experience with these stimuli. In contrast, the lower noise level and tighter prior preference used with the stereopsis model means that it performs close to chance with anti-correlated stimuli, in accordance with human psychophysics. Thus, the key features of the experimental data can be reproduced assuming that the motion system experiences more effective noise than the stereoscopy system and imposes a less stringent preference for small disparities. Received: 2 March 2001 / Accepted in revised form: 5 July 2001     

Fine discrimination training alters the causal contribution of macaque area MT to depth perception

When a new perceptual task is learned, plasticity occurs in the brain to mediate improvements in performance with training. How do these changes affect the neural substrates of previously learned tasks? We addressed this question by examining the effect of fine discrimination training on the causal contribution of area MT to coarse depth discrimination. When monkeys are trained to discriminate between two coarse absolute disparities (near versus far) embedded in noise, reversible inactivation of area MT devastates performance. In contrast, after animals are trained to discriminate fine differences in relative disparity, MT inactivation no longer impairs coarse depth discrimination. This effect does not result from changes in the disparity tuning of MT neurons, suggesting plasticity in the flow of disparity signals to decision circuitry. These findings show that the contribution of particular brain area to task performance can change dramatically as a result of learning new tasks.     

Stereoscopic correspondence for ambiguous targets is affected by elevation and fixation distance

Binocular correspondence must be determined if disparity is to be used to provide information about three-dimensional shape. The current study investigated whether knowledge of the statistical distribution of disparities in the natural environment is employed in this process. A simple model, which produces distributions of distances similar to those found in the natural environment, was used to predict the distribution of disparities in natural images. This model predicts that crossed disparities will be more likely as (i) stimulus elevation decreases below fixation and (ii) fixation distance increases. To determine whether these factors influence binocular correspondence for human observers, ambiguous stereograms were presented to observers, as stimulus elevation and fixation distance were manipulated. Clear biases were observed in the depth perceived in these stereograms, which were more likely to be seen as closer than fixation (i) for stimuli presented below fixation and (ii) as fixation distance increased. These results suggest that binocular correspondence is determined in a manner consistent with the distributions of disparities expected in natural scenes.     

Spike propagation synchronized by temporally asymmetric Hebbian learning

 Synchronously spiking neurons have been observed in the cerebral cortex and the hippocampus. In computer models, synchronous spike volleys may be propagated across appropriately connected neuron populations. However, it is unclear how the appropriate synaptic connectivity is set up during development and maintained during adult learning. We performed computer simulations to investigate the influence of temporally asymmetric Hebbian synaptic plasticity on the propagation of spike volleys. In addition to feedforward connections, recurrent connections were included between and within neuron populations and spike transmission delays varied due to axonal, synaptic and dendritic transmission. We found that repeated presentations of input volleys decreased the synaptic conductances of intragroup and feedback connections while synaptic conductances of feedforward connections with short delays became stronger than those of connections with longer delays. These adaptations led to the synchronization of spike volleys as they propagated across neuron populations. The findings suggests that temporally asymmetric Hebbian learning may enhance synchronized spiking within small populations of neurons in cortical and hippocampal areas and familiar stimuli may produce synchronized spike volleys that are rapidly propagated across neural tissue. Received: 28 May 2002 / Accepted: 3 June 2002 RID="*" ID="*" Correspondence to: R. E. Suri Intelligent Optical Systems (IOS), 2520 W 237th St, Torrance, CA 90505-5217, USA (e-mail: rsuri@intopsys.com, Tel.: +1-310-5307130 ext. 108, Fax: +1-210-5307417)     

Shape Invariant Coding of Motion Direction in Somatosensory Cortex

Invariant representations of stimulus features are thought to play an important role in producing stable percepts of objects. In the present study, we assess the invariance of neural representations of tactile motion direction with respect to other stimulus properties. To this end, we record the responses evoked in individual neurons in somatosensory cortex of primates, including areas 3b, 1, and 2, by three types of motion stimuli, namely scanned bars and dot patterns, and random dot displays, presented to the fingertips of macaque monkeys. We identify a population of neurons in area 1 that is highly sensitive to the direction of stimulus motion and whose motion signals are invariant across stimulus types and conditions. The motion signals conveyed by individual neurons in area 1 can account for the ability of human observers to discriminate the direction of motion of these stimuli, as measured in paired psychophysical experiments. We conclude that area 1 contains a robust representation of motion and discuss similarities in the neural mechanisms of visual and tactile motion processing.     

Direct extraction of curvature-based metric shape from stereo by view-modulated receptive fields

Any computation of metric surface structure from horizontal disparities depends on the viewing geometry, and analysing this dependence allows us to narrow down the choice of viable schemes. For example, all depth-based or slant-based schemes (i.e. nearly all existing models) are found to be unrealistically sensitive to natural errors in vergence. Curvature-based schemes avoid these problems and require only moderate, more robust view-dependent corrections to yield local object shape, without any depth coding. This fits the fact that humans are strikingly insensitive to global depth but accurate in discriminating surface curvature. The latter also excludes coding only affine structure. In view of new adaptation results, our goal becomes to directly extract retinotopic fields of metric surface curvatures (i.e. avoiding intermediate disparity curvature).To find a robust neural realisation, we combine new exact analysis with basic neural and psychophysical constraints. Systematic, step-by-step ‘design’ leads to neural operators which employ a novel family of ‘dynamic’ receptive fields (RFs), tuned to specific (bi-)local disparity structure. The required RF family is dictated by the non-Euclidean geometry that we identify as inherent in cyclopean vision. The dynamic RF-subfield patterns are controlled via gain modulation by binocular vergence and version, and parameterised by a cell-specific tuning to slant. Our full characterisation of the neural operators invites a range of new neurophysiological tests. Regarding shape perception, the model inverts widely accepted interpretations: It predicts the various types of errors that have often been mistaken for evidence against metric shape extraction.     

Stabilized structure from motion without disparity induces disparity adaptation

3D structures can be perceived based on the patterns of 2D motion signals. With orthographic projection of a 3D stimulus onto a 2D plane, the kinetic information can give a vivid impression of depth, but the depth order is intrinsically ambiguous, resulting in bistable or even multistable interpretations. For example, an orthographic projection of dots on the surface of a rotating cylinder is perceived as a rotating cylinder with ambiguous direction of rotation. We show that the bistable rotation can be stabilized by adding information, not to the dots themselves, but to their spatial context. More interestingly, the stabilized bistable motion can generate consistent rotation aftereffects. The rotation aftereffect can only be observed when the adapting and test stimuli are presented at the same stereo depth and the same retinal location, and it is not due to attentional tracking. The observed rotation aftereffect is likely due to direction-contingent disparity adaptation, implying that stimuli with kinetic depth may have activated neurons sensitive to different disparities, even though the stimuli have zero relative disparity. Stereo depth and kinetic depth may be supported by a common neural mechanism at an early stage in the visual system.     

Analysis of higher-order neuronal interactions based on conditional inference

 Higher-order neural interactions, i.e., interactions that cannot be reduced to interactions between pairs of cells, have received increasing attention in the context of recent attempts to understand the cooperative dynamics in cortical neural networks. Typically, likelihood-ratio tests of log-linear models are being employed for statistical inference. The parameter estimation of these models for simultaneously recorded single-neuron spiking activities is a crucial ingredient of this approach. Extending a previous investigation of a two-neuron system, we present here the general formulation of an exact test suited for the detection of positive higher-order interactions between m neurons. This procedure does not require the estimation of any interaction parameters and additionally optimizes the test power of the statistical inference. We apply the approach to a three-neuron system and show how second-order and third-order interactions can be reliably distinguished. We study the performance of the method as a function of the interaction strength. Received: 18 January 2002 / Accepted in revised form: 26 November 2002 / Published online: 13 March 2003 RID="*" ID="*" Present address: Institute for Theoretical Biology, Humboldt University, 10115 Berlin, Germany Correspondence to: R. Gütig (e-mail: r.guetig@biologie.hu-berlin.de, Tel.: +49 30 2093 9112, Fax: +49 30 2093 8801) Acknowledgements. We thank Shun-ichi Amari and Hiro Nakahara for valuable discussions on the information geometry of the exponential family of probability distributions underlying the present approach. Supported in part by the Studienstiftung des deutschen Volkes, the German-Israeli Foundation for Scientific Research and Development (GIF), the Deutsche Forschungsgemeinschaft (DFG), and the Institut für Grenzgebiete der Psychologie, Freiburg.     

Stereopsis and the random element in the organization of the striate cortex.

Receptive field position and orientation disparities are both properties of binocularly discharged striate neurons. Receptive field position desparities have been used as a key element in the neural theory for binocular depth discrimination. Since most striate cells in the cat are binocular, these position disparities require that cells immediately adjacent to one another in the cortex should show a random scatter in their monocular receptive field positions. Superimposed on the progressive topographical representation of the visual field on the striate cortex there is experimental evidence for a localized monocular receptive field position scatter. The suggestion is examined that the binocular position disparities are built up out of the two monocular position scatters. An examination of receptive field orientation disparities and their relation to the random variation in the monocular preferred orientations of immediately adjacent striate neurons also leads to the conclusion that binocular orientation disparities are a consequence of the two monocular scatters. As for receptive field position, the local scatter in preferred orientation is superimposed on a progressive representation of orientation over larger areas of the cortex. The representation in the striate cortex of visual field position and of stimulus orientation is examined in relation to the correlation between the disparities in receptive field position and preferred orientation. The role of orientation disparities in binocular vision is reviewed.     

Two-dimensional substructure of stereo and motion interactions in macaque visual cortex

The analysis of object motion and stereoscopic depth are important tasks that are begun at early stages of the primate visual system. Using sparse white noise, we mapped the receptive field substructure of motion and disparity interactions in neurons in V1 and MT of alert monkeys. Interactions in both regions revealed subunits similar in structure to V1 simple cells. For both motion and stereo, the scale and shape of the receptive field substructure could be predicted from conventional tuning for bars or dot-field stimuli, indicating that the small-scale interactions were repeated across the receptive fields. We also found neurons in V1 and in MT that were tuned to combinations of spatial and temporal binocular disparities, suggesting a possible neural substrate for the perceptual Pulfrich phenomenon. Our observations constrain computational and developmental models of motion-stereo integration.     

Existence of traveling wave solutions in a diffusive predator-prey model

 We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R ⁴ and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R ⁴ . The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem. Received: 25 May 2001 / Revised version: 5 August 2002 / Published online: 19 November 2002 RID="*" ID="*" Research was supported by the National Natural Science Foundations (NNSF) of China. RID="*" ID="*" Research was partially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. On leave from the Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada. Mathematics Subject Classification (2000): 34C35, 35K57 Key words or phrases: Traveling wave solution – Wazewski set – Shooting argument – Hopf bifurcation Acknowledgements. We would like to thank the two referees for their careful reading and helpful comments.     

Sensing without touching: psychophysical performance based on cortical microstimulation

Unequivocal proof that the activity of a localized cortical neuronal population provides sufficient basis for a specific cognitive function has rarely been obtained. We looked for such proof in monkeys trained to discriminate between two mechanical flutter stimuli applied sequentially to the fingertips. Microelectrodes were inserted into clusters of quickly adapting (QA) neurons of the primary somatosensory cortex (S1), and the first or both stimuli were then substituted with trains of current pulses during the discrimination task. Psychophysical performance with artificial stimulus frequencies was almost identical to that measured with the natural stimulus frequencies. Our results indicate that microstimulation can be used to elicit a memorizable and discriminable analog range of percepts, and shows that activation of the QA circuit of S1 is sufficient to initiate all subsequent neural processes associated with flutter discrimination.     

The Role of Binocular Disparity in Stereoscopic Images of Objects in the Macaque Anterior Intraparietal Area

Neurons in the macaque Anterior Intraparietal area (AIP) encode depth structure in random-dot stimuli defined by gradients of binocular disparity, but the importance of binocular disparity in real-world objects for AIP neurons is unknown. We investigated the effect of binocular disparity on the responses of AIP neurons to images of real-world objects during passive fixation. We presented stereoscopic images of natural and man-made objects in which the disparity information was congruent or incongruent with disparity gradients present in the real-world objects, and images of the same objects where such gradients were absent. Although more than half of the AIP neurons were significantly affected by binocular disparity, the great majority of AIP neurons remained image selective even in the absence of binocular disparity. AIP neurons tended to prefer stimuli in which the depth information derived from binocular disparity was congruent with the depth information signaled by monocular depth cues, indicating that these monocular depth cues have an influence upon AIP neurons. Finally, in contrast to neurons in the inferior temporal cortex, AIP neurons do not represent images of objects in terms of categories such as animate-inanimate, but utilize representations based upon simple shape features including aspect ratio.     

A discrete,size-structured model of phytoplankton growth in the chemostat: introduction of inhomogeneous cell division size

 We introduce inhomogeneous, substrate dependent cell division in a time discrete, nonlinear matrix model of size-structured population growth in the chemostat, first introduced by Gage et al. [8] and later analysed by Smith [13]. We show that mass conservation is verified, and conclude that our system admits one non zero globally stable equilibrium, which we express explicitly. Then we run numerical simulations of the system, and compare the predictions of the model to data related to phytoplankton growth, whose obtention we discuss. We end with the identification of several parameters of the system. Received: 9 February 2000 / Revised version: 10 October 2001 / Published online: 23 August 2002 RID="*" ID="*" Present address: Department of Mathematics and Statistics, University of Victoria, B.C., Canada. e-mail: jarino@math.uvic.ca Key words or phrases: Chemostat – Structured population models – Discrete model – Inhomogeneous division size     

Time representing cortical activities: two models inspired by prefrontal persistent activity

 Timing information in the range of seconds is significantly correlated with our behavior. There is growing interest in the cognitive behaviors that rely on perception, comparison, or generation of timing. However, little is known about the neural mechanisms underlying such behaviors. Here we model two different neural mechanisms to represent timing information in the range of seconds. In one model, a recurrent network of bistable spiking neurons shows a quasistable state that is initiated by a brief input and typically lasts for a few to several seconds. The duration of this quasistable activity may be regarded as the neural representation of internal time obeying a psychophysical law of time recognition. Another model uses synfire chains to provide the timing information necessary for predicting the times of anticipated events. In this model, the neurons projected to by multiple synfire chains are conditioned to fire synchronously at the times when an external event (GO signal) is expected. The conditioning is accomplished by spike-timing-dependent plasticity. The two models are inspired by the prefrontal activities of the monkeys engaging in different timing-information-related tasks. Thus, this cortical region may provide the timing information required for organizing various behaviors. Received: 12 March 2002 / Accepted in revised form: 26 November 2002 / Published online: 28 March 2003 Correspondence to: T. Fukai (e-mail: tfukai@eng.tamagawa.ac.jp, Tel.: +81-42-7398434, Fax: +81-42-7397135) Acknowledgements. K. Kitano was supported by Japan Society for the Promotion of Science.     

Deriving physical connectivity from neuronal morphology

 A model is presented that allows prediction of the probability for the formation of appositions between the axons and dendrites of any two neurons based only on their morphological statistics and relative separation. Statistics of axonal and dendritic morphologies of single neurons are obtained from 3D reconstructions of biocytin-filled cells, and a statistical representation of the same cell type is obtained by averaging across neurons according to the model. A simple mathematical formulation is applied to the axonal and dendritic statistical representations to yield the probability for close appositions. The model is validated by a mathematical proof and by comparison of predicted appositions made by layer 5 pyramidal neurons in the rat somatosensory cortex with real anatomical data. The model could be useful for studying microcircuit connectivity and for designing artificial neural networks. Received: 11 February 2002 / Accepted: 5 November 2002 / Published online: 20 February 2003 Correspondence to: H. Markram (e-mail: Henry.Markram@epfl.ch Tel.: +41-21-6939537, Fax: +41-21-6935350) Acknowledgements. This study was supported by the National Alliance for Autism Research, the Minerva Foundation, the US Navy, the Ebner Center for Biomedical Research, and the Edith Blum Foundation.     

Neural computations in the tiger salamander and mudpuppy outer retinae and an analysis of GABA action from horizontal cells

 A neural network architecture based on the neural anatomy and function of retinal neurons in tiger salamander and mudpuppy retinae is proposed to study basic aspects of early visual information processing. The model predictions for the main response characteristics of retinal neurons are found to be in agreement with neurophysiological data, including the antagonistic role of horizontal cells in the outer plexiform layer. The examination of possible γ-aminobutyric acid (GABA) action from horizontal cells suggests that GABA_A alone, GABA_B alone, or their weighted combination can generate the response characteristics observed in bipolar cells. Received: 25 June 2002 / Accepted: 28 January 2003 / Published online: 20 May 2003 Acknowledgements. The authors would like to thank an anonymous reviewer for valuable comments. Correspondence to: S. X. Yang (e-mail: syang@uoguelph.ca)     

Spatial stereoresolution for depth corrugations may be set in primary visual cortex

Stereo "3D" depth perception requires the visual system to extract binocular disparities between the two eyes' images. Several current models of this process, based on the known physiology of primary visual cortex (V1), do this by computing a piecewise-frontoparallel local cross-correlation between the left and right eye's images. The size of the "window" within which detectors examine the local cross-correlation corresponds to the receptive field size of V1 neurons. This basic model has successfully captured many aspects of human depth perception. In particular, it accounts for the low human stereoresolution for sinusoidal depth corrugations, suggesting that the limit on stereoresolution may be set in primary visual cortex. An important feature of the model, reflecting a key property of V1 neurons, is that the initial disparity encoding is performed by detectors tuned to locally uniform patches of disparity. Such detectors respond better to square-wave depth corrugations, since these are locally flat, than to sinusoidal corrugations which are slanted almost everywhere. Consequently, for any given window size, current models predict better performance for square-wave disparity corrugations than for sine-wave corrugations at high amplitudes. We have recently shown that this prediction is not borne out: humans perform no better with square-wave than with sine-wave corrugations, even at high amplitudes. The failure of this prediction raised the question of whether stereoresolution may actually be set at later stages of cortical processing, perhaps involving neurons tuned to disparity slant or curvature. Here we extend the local cross-correlation model to include existing physiological and psychophysical evidence indicating that larger disparities are detected by neurons with larger receptive fields (a size/disparity correlation). We show that this simple modification succeeds in reconciling the model with human results, confirming that stereoresolution for disparity gratings may indeed be limited by the size of receptive fields in primary visual cortex.