Limits of phase and amplitude sensitivity in the torus semicircularis ofEigenmannia

Eigenmannia can detect modulations in the time disparity of signals received by different regions of the body surface as small as several hundred nanoseconds. This study presents recordings of single units in the torus semicircularis that are sensitive to time disparities (differential-phase) between a sinusoidal signal received by the head region and a similar signal received by the body surface caudal to the fish's pectoral fins. The sensitivity of units to differential phase, measured by the change in spike rate per unit change in time disparity, was greatest when small phase modulations, rather than stationary phase differences, were presented. Thresholds of differential-phase coders ranged from 6.5 microseconds to several hundred microseconds, with approximately 20% of the units having thresholds in the 5-10 microseconds range. For most cells, sensitivity to small modulations of differential-phase was relatively unaffected by time disparity 'offsets' within a range of several hundred microseconds. A threshold of 5-10 microseconds is still an order of magnitude higher than that measured in the Jamming Avoidance Response (JAR). Neurons that were sensitive to amplitude modulations (AMs) had thresholds as low as 0.05%. This value is comparable to that observed at the behavioral level.     

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     

Similar Mechanisms Underlie the Detection of Horizontal and Vertical Disparity Corrugations

Our aim was to compare sensitivity for horizontal and vertical disparity corrugations and to resolve whether these stimuli are processed by similar or radically different underlying mechanisms. We measure global disparity sensitivity as a function of carrier spatial frequency for equi-detectable carriers and found a similar optimal carrier relationship for vertical and horizontal stimuli. Sensitivity as a function of corrugation spatial frequency for stimuli of comparable spatial summation and composed of optimal, equi-detectable narrowband carriers did not significantly differ for vertical and horizontal stimuli. A small anisotropy was revealed when fixed, high contrast broadband carriers were used. In a separate discrimination-at-threshold experiment, multiple mechanisms of similar tuning were revealed to underlie the detection of both vertical and horizontal disparity corrugations. We conclude that the processing of the horizontal and vertical disparity corrugations occurs along similar lines.     

Visual depth encoding in populations of neurons with localized receptive fields

 Stereopsis is the ability to perceive three-dimensional structure from disparities between the two-dimensional retinal images. Although disparity-sensitive neurons have been proposed as a neural representation of this ability many years ago, it is still difficult to link all qualities of stereopsis to properties of the neural correlate of binocular disparities. The present study wants to support efforts directed at closing the gap between electrophysiology and psychophysics. Populations of disparity-sensitive neurons in V1 were simulated using the energy-neuron model. Responses to different types of stimuli were evaluated with an efficient statistical estimator and related to psychophysical findings. The representation of disparity in simulated population responses appeared to be very robust. Small populations allowed good depth discrimination. Two types of energy neurons (phase- and position-type models) that are discussed as possible neural implementations of disparity-selectivity could be compared to each other. Phase-type coding was more robust and could explain a tendency towards zero disparity in degenerated stimuli and, for high-pass stimuli, exhibited the breakdown of disparity discrimination at a maximum disparity value. Contrast-inverted stereograms led to high variances in disparity representation, which is a possible explanation of the absence of depth percepts in large contrast-inverted stimuli. Our study suggests that nonlocal interactions destroy depth percepts in large contrast-inverted stereograms, although these percepts occur for smaller stimuli of the same class. Received: 21 December 2001 / Accepted: 29 April 2002 RID="*" ID="*" Present address: Bayer AG BTS-PT-MVT-MKM, Geb. K9, 51368 Leverkusen, Germany Acknowledgement. This work was supported by a scholarship from the Studienstiftung des deutschen Volkes to J.L. Correspondence to: J. Lippert (e-mail: joerg.lippert.jl@bayer-ag.de)     

Interocular orientation disparity and the stereoscopic perception of slanted surfaces

The orientation threshold for two-dimensional filtered noise stimuli was estimated using forced-choice procedures with both dioptic and dichoptic viewing. In the dioptic case the two patterns were co-rotated. In the dichoptic case the stimuli were counter-rotated to produce an orientation disparity, which yields a percept of slant about the horizontal axis orthogonal to the cyclopean line of sight. Dioptic thresholds increased with the orientation bandwidth of the stimuli. In contrast, dichoptic thresholds were essentially constant across a wide range of conditions. In all cases, dichoptic orientation acuity was much finer than conventional estimates. In a second experiment, the dichoptic threshold was estimated for patterns superimposed on a depth pedestal. Acuity was affected significantly by the presence of the pedestal, and was an inverse function of pedestal amplitude. The results suggest that stereoscopic slant caused by dichoptic counter-rotation arises because of neural processing of the overall pattern of disparities of position produced by counter-rotation, rather than specialised encoding of orientation disparity.     

Vertical Binocular Disparity is Encoded Implicitly within a Model Neuronal Population Tuned to Horizontal Disparity and Orientation

Primary visual cortex is often viewed as a “cyclopean retina”, performing the initial encoding of binocular disparities between left and right images. Because the eyes are set apart horizontally in the head, binocular disparities are predominantly horizontal. Yet, especially in the visual periphery, a range of non-zero vertical disparities do occur and can influence perception. It has therefore been assumed that primary visual cortex must contain neurons tuned to a range of vertical disparities. Here, I show that this is not necessarily the case. Many disparity-selective neurons are most sensitive to changes in disparity orthogonal to their preferred orientation. That is, the disparity tuning surfaces, mapping their response to different two-dimensional (2D) disparities, are elongated along the cell''s preferred orientation. Because of this, even if a neuron''s optimal 2D disparity has zero vertical component, the neuron will still respond best to a non-zero vertical disparity when probed with a sub-optimal horizontal disparity. This property can be used to decode 2D disparity, even allowing for realistic levels of neuronal noise. Even if all V1 neurons at a particular retinotopic location are tuned to the expected vertical disparity there (for example, zero at the fovea), the brain could still decode the magnitude and sign of departures from that expected value. This provides an intriguing counter-example to the common wisdom that, in order for a neuronal population to encode a quantity, its members must be tuned to a range of values of that quantity. It demonstrates that populations of disparity-selective neurons encode much richer information than previously appreciated. It suggests a possible strategy for the brain to extract rarely-occurring stimulus values, while concentrating neuronal resources on the most commonly-occurring situations.     

The relationship between absolute disparity and ocular vergence

The relationship between disparity and ocular vergence was investigated under closed-loop as well as under open-loop viewing conditions. First we examined whether vergence responded similarly to disparity presented under open-loop and closed-loop conditions. Similar response were observed in both conditions. The direct relationship between disparity and vergence was examined by presenting constant disparities between 0.2° and 4° under open-loop viewing conditions. Such vergence responses are described as the outputs of first-order low-pass filters with different filter characteristics for each amplitude of disparity. By analyzing the latency of vergence responses induced by constant disparities with help of the transfer function of disparitycontrolled vergence, the time delay of disparity processing in the vergence loop was estimated. We suggested that the time delay was approximately between 80 and 120 ms instead of 160 ms as is generally assumed. The relationship between the rate of disparity change and vergence was examined by comparing responses to ramp and stepwise changes in target vergence. From the similar responses to ramp and staircase changes in disparity we concluded that vergence is not sensitive to the velocity of target vergence as such. On the basis of these findings we developed a model of disparity-controlled vergence. In this model disparity is processed through several parallel, imperfect integrators with slightly different low-pass filter characteristics, each of them susceptible to a limited range of disparities. Gains as well as phase lags of vergence responses to sinusoidal disparities are accurately simulated by this model. As a consequence of the limited working range of the low-pass filters, the model correctly simulates the alterations of fast and slow phases in response to step and ramps of target vergence, which are characteristic of real vergence responses.     

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.     

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.     

Invariants of spatial summation for S (short wavelength) cone vision

Spatial summation in the human visual system was studied as a function of retinal eccentricity upon selective stimulation of the short-wavelength sensitive cones. The area of complete spatial summation (Ricco's area) was found to increase with retinal eccentricity while the threshold of stimuli equal in size with Ricco's area remained constant. Comparisons with known morphology of the small bistratified retinal ganglion cells, the only cells known to be excited by S-one ON stimulation, showed that Ricco's area included 2-4 such cells and is up to 1.5 times larger than the dendritic field of a single cell. These relationships were relatively constant within the eccentricity range tested (5-20 deg along the temporal horizontal meridian) and might be the source of threshold invariance of stimuli matching Ricco's area.     

Binocular vision: an orientation to disparity coding

A new study has shown that neurons in the visual cortex are specialized to encode the larger range of horizontal - relative to vertical - disparities that occurs in central vision. These results challenge the established 'energy' model of disparity processing.     

Self-organizing maps for visual feature representation based on natural binocular stimuli

We model the stimulus-induced development of the topography of the primary visual cortex. The analysis uses a self-organizing Kohonen model based on high-dimensional coding. It allows us to obtain an arbitrary number of feature maps by defining different operators. Using natural binocular stimuli, we concentrate on discussing the orientation, ocular dominance, and disparity maps. We obtain orientation and ocular dominance maps that agree with essential aspects of biological findings. In contrast to orientation and ocular dominance, not much is known about the cortical representation of disparity. As a result of numerical simulations, we predict substructures of orientation and ocular dominance maps that correspond to disparity maps. In regions of constant orientation, we find a wide range of horizontal disparities to be represented. This points to geometrical relations between orientation, ocular dominance, and disparity maps that might be tested in experiments. Received: 9 July 1998 / Accepted in revised form: 2 June 1999     

Stereoscopic acuity and observation distance

The amount of depth perceived from a fixed pattern of horizontal disparities varies with viewing distance. We investigated whether thresholds for discriminating stereoscopic corrugations at a range of spatial frequencies were also affected by viewing distance or whether they were determined solely by the angular disparity in the stimulus prior to scaling. Although thresholds were found to be determined primarily by disparity over a broad range of viewing distances, they were on average a factor of two higher at the shortest viewing distance (28.5 cm) than at larger viewing distances (57 to 450 cm). We found the same pattern of results when subjects' accommodation was arranged to be the same at all viewing distances. The change in thresholds at close distances is in the direction expected if subjects' performance is limited by a minimum perceived depth.     

基于视差敏感复杂细胞的聚散式眼动的生理模型

根据心理物理实验和电生理实验的结果,选用对非零视差有选择性反应的视差敏感复杂细胞来检测视差信息,并把所提取的视差信息直接投射到聚散式眼动细胞（ｖｅｒｇｅｎｃｅｃｅｌ）以控制聚散式眼动。同时,综合考虑了复杂细胞编码范围的限制、近细胞和远细胞的相位关系以及跳跃式眼动后增强效应（ｐｏｓｔ－ｓａｃｃａｄｉｃｅｎｈａｎｃｅｍｅｎｔ）等因素。得到的模拟结果与心理物理实验结果定性地符合     

Three roads to islet bursting: emergent oscillations in coupled phantom bursters

Glucose-induced membrane potential and Ca(2+) oscillations in isolated pancreatic beta-cells occur over a wide range of frequencies, from >6/min (fast) to <1/min (slow). However, cells within intact islets generally oscillate with periods of 10-60 s (medium). The phantom bursting concept addresses how beta-cells can generate such a wide range of frequencies. Here, we explore an updated phantom bursting model to determine how heterogeneity in a single parameter can explain both the broad frequency range observed in single cells and the rarity of medium oscillations. We then incorporate the single-cell model into an islet model with parameter heterogeneity. We show that strongly coupled islets must be composed of predominantly medium oscillating single cells or a mixture of fast and slow cells to robustly produce medium oscillations. Surprisingly, we find that this constraint does not hold for moderate coupling, and that robustly medium oscillating islets can arise from populations of single cells that are essentially all slow or all fast. Thus, with coupled phantom bursters, medium oscillating islets can be constructed out of cells that are either all fast, all slow, or a combination of the two.     

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.     

Gene Conversion Disparity: Factors Influencing Its Direction and Extent, with Tests of Assumptions and Predictions in Its Evolutionary Effects

The evolutionarily important characteristics of gene conversion disparity extent and direction are surveyed in fungi. Temperature and background genotype can have small or large effects, sometimes even changing the direction of disparity. Disparity results from Sordaria and Ascobolus were very similar, with between-strain, between-data set and between-locus differences being larger than those between species or genera. In general, different loci in an organism show similar disparity properties when comparable types of mutation are considered, but may not do so in pooled results containing different proportions of different mutation types. Frameshifts typically have strong disparities, usually with negative signs for single base additions and positive signs for single base deletions. Base substitutions tend to have moderate disparities, favoring wild type more often than mutant in most data sets. Large deletions usually have significant disparity, either positive or negative. For comparable molecular types of mutation, spontaneous and induced mutations had roughly similar disparity properties.--Experimental tests and theoretical considerations generally failed to support a number of assumptions and predictions made in previous treatments of gene conversion in evolution. In general, a mutation's conversion properties depend much more on its molecular type in relation to wild type than on any evolved conversion advantages or disadvantages.     

Symmetry detection across the visual field.

Humans are extremely sensitive to symmetry when it is foveated but sensitivity drops as a symmetrical region of a fixed size is moved into the periphery. A psychophysical study was undertaken to determine if eccentricity dependent sensitivity loss could be overcome by magnifying stimuli at each eccentricity (E) by a factor F = 1 + E/E2, where E2 indicates the eccentricity at which the size of a stimulus must be doubled, relative to a foveal standard, to achieve equivalent performance. The psychophysical task required subjects to decide on each trial in which of two intervals a symmetrical stimulus had been presented. Stimuli were presented at a range of sizes and eccentricities (0 to 8 degrees) and the probability of a correct discrimination was computed for each condition. In Experiment 1, thresholds were measured with stimuli set to maximum available contrast and, in Experiment 2, stimuli were presented at a constant multiple of contrast detection threshold. In both experiments, a single scaling function removed most of the eccentricity dependent variation from the data. However, the E2 value recovered for one subject tested in both experiments was larger by about 65% when stimuli were not equated for visibility. We conclude that symmetry detection can be equated across a range of eccentricities by scaling stimuli with an E2 in the range of 0.88 to 1.38 degrees. Failure to equate for visibility across all viewing conditions may result in an inflated estimate of E2.