Modelling the spatio-temporal modulation response of ganglion cells with difference-of-Gaussians receptive fields: relation to photoreceptor response kinetics

castleCSF - A contrast sensitivity function of color, area, spatiotemporal frequency, luminance and eccentricity

The contrast sensitivity function (CSF) is a fundamental visual model explaining our ability to detect small contrast patterns. CSFs found many applications in engineering, where they can be used to optimize a design for perceptual limits. To serve such a purpose, CSFs must explain possibly a complete set of stimulus parameters, such as spatial and temporal frequency, luminance, and others. Although numerous contrast sensitivity measurements can be found in the literature, none fully explains the complete space of stimulus parameters. Therefore, in this work, we first collect and consolidate contrast sensitivity measurements from 18 studies, which explain the sensitivity variation across the parameters of interest. Then, we build an analytical contrast sensitivity model that explains the data from all those studies. The proposed castleCSF model explains the sensitivity as the function of spatial and temporal frequencies, an arbitrary contrast modulation direction in the color space, mean luminance, and chromaticity of the background, eccentricity, and stimulus area. The proposed model uses the same set of parameters to explain the data from 18 studies with an error of 3.59 dB. The consolidated contrast sensitivity data and the code for the model are publicly available at https://github.com/gfxdisp/castleCSF/.

Enhancing the dark side: asymmetric gain of cone photoreceptors underpins their discrimination of visual scenes based on skewness

Psychophysical data indicate that humans can discriminate visual scenes based on their skewness, i.e. the ratio of dark and bright patches within a visual scene. It has also been shown that at a phenomenological level this skew discrimination is described by the so-called blackshot mechanism, which accentuates strong negative contrasts within a scene. Here, we present a set of observations suggesting that the underlying computation might start as early as the cone phototransduction cascade, whose gain is higher for strong negative contrasts than for strong positive contrasts. We recorded from goldfish cone photoreceptors and found that the asymmetry in the phototransduction gain leads to responses with larger amplitudes when using negatively rather than positively skewed light stimuli. This asymmetry in amplitude was present in the cone photocurrent, voltage response and synaptic output. Given that the properties of the phototransduction cascade are universal across vertebrates, it is possible that the mechanism shown here gives rise to a general ability to discriminate between scenes based only on their skewness, which psychophysical studies have shown humans can do. Thus, our data suggest the importance of non-linearity of the early photoreceptor for perception. Additionally, we found that stimulus skewness leads to a subtle change in photoreceptor kinetics. For negatively skewed stimuli, the impulse response functions of the cone peak later than for positively skewed stimuli. However, stimulus skewness does not affect the overall integration time of the cone. KEY POINTS: Humans can discriminate visual scenes based on skewness, i.e. the relative prevalence of bright and dark patches within a scene. Here, we show that negatively skewed time-series stimuli induce larger responses in goldfish cone photoreceptors than comparable positively skewed stimuli. This response asymmetry originates from within the phototransduction cascade, where gain is higher for strong negative contrasts (dark patches) than for strong positive contrasts (bright patches). Unlike the implicit assumption often contained within models of downstream visual neurons, our data show that cone photoreceptors do not simply relay linearly filtered versions of visual stimuli to downstream circuitry, but that they also emphasize specific stimulus features. Given that the phototransduction cascade properties among vertebrate retinas are mostly universal, our data imply that the skew discrimination by human subjects reported in psychophysical studies might stem from the asymmetric gain function of the phototransduction cascade.

Temporal vision: measures, mechanisms and meaning

Time is largely a hidden variable in vision. It is the condition for seeing interesting things such as spatial forms and patterns, colours and movements in the external world, and yet is not meant to be noticed in itself. Temporal aspects of visual processing have received comparatively little attention in research. Temporal properties have been made explicit mainly in measurements of resolution and integration in simple tasks such as detection of spatially homogeneous flicker or light pulses of varying duration. Only through a mechanistic understanding of their basis in retinal photoreceptors and circuits can such measures guide modelling of natural vision in different species and illuminate functional and evolutionary trade-offs. Temporal vision research would benefit from bridging traditions that speak different languages. Towards that goal, I here review studies from the fields of human psychophysics, retinal physiology and neuroethology, with a focus on fundamental constraints set by early vision.

Summary: Simple measures of temporal vision such as the critical flicker frequency can be useful for modelling natural vision only if their relationship to photoreceptor responses and retinal processing is understood.

Experimentally derived model shows that adaptation acts as a powerful spatiotemporal filter of visual responses in the rat collicular neurons

Adaptation of visual responses enhances visual information processing mainly by preserving the full dynamic range of neuronal responses during changing light conditions and is found throughout the whole visual system. Although adaptation in the primate superior colliculus neurons has received much attention little is known about quantitative properties of such adaptation in rodents, an increasingly important model in vision research. By employing single unit recordings, we demonstrate that in the rat collicular neurons visual responses are shaped by at least two forms of adaptation. When visual stimuli were repeatedly presented in the same location, visual responses were reduced in the majority of single units. However, when the adaptor stimulus was outside a small diameter receptive field (RF), responses to stimulus onset but not offset were enhanced in the majority of units. Responses to stimulus offset were reduced less and recovered faster than responses to stimulus onset and the effect was limited to a fraction of RF area. Simulations showed that such adaptation acted as a powerful spatiotemporal filter and could explain several tuning properties of collicular neurons. These results demonstrate that in rodents the adaption of visual responses has a complex spatiotemporal structure and can profoundly shape visual information processing.

Mechanistic modeling of vertebrate spatial contrast sensitivity and acuity at low luminance

The validity of the Barten theoretical model for describing the vertebrate spatial contrast sensitivity function (CSF) and acuity at scotopic light levels has been examined. Although this model (which has its basis in signal modulation transfer theory) can successfully describe vertebrate CSF, and its relation to underlying visual neurophysiology at photopic light levels, significant discrepancies between theory and experimental data have been found at scotopic levels. It is shown that in order to describe scotopic CSF, the theory must be modified to account for important mechanistic changes, which occur as cone vision switches to rod vision. These changes are divided into photon management factors [changes in optical performance (for a dilated pupil), quantum efficiency, receptor sampling] and neural factors (changes in spatial integration area, neural noise, and lateral inhibition in the retina). Predictions of both scotopic CSF and acuity obtained from the modified theory were found to be in good agreement with experimental values obtained from the human, macaque, cat, and owl monkey. The last two species have rod densities particularly suited for scotopic conditions.

Sequential processing in vision: The interaction of sensitivity regulation and temporal dynamics

The goal of this work was to describe the interaction of sensitivity regulation and temporal dynamics through the primate retina. A linear systems model was used to describe the temporal amplitude sensitivity at different retinal illuminances. Predictions for the primate H1 horizontal cell were taken as the starting point. The H1 model incorporated an early time-dependent stage of sensitivity regulation by the cones. It was adjusted to reduce the effects of gap junction input and then applied as input to a model describing temporal amplitude sensitivity of Parvocellular and Magnocellular pathway retinal ganglion cells. The ganglion cell model incorporated center-surround subtraction. The H1 based model required little modification to describe the Parvocellular data. The Magnocellular data required a further time-dependent stage of sensitivity regulation that resulted in Weber's Law. Psychophysical data reflect the sensitivity regulation of the retinal ganglion cell pathways but show a decline in temporal resolution that is most pronounced for the post-retinal processing of Parvocellular signals.

Time course of suppression by surround gratings: highly contrast-dependent, but consistently fast

Timing is critical for the effectiveness of a modulating surround signal. In this study, the optimal timing of a suppressing surround signal was measured psychophysically in human subjects. The perceived contrast of a fixated 1-deg circular patch of vertical sinusoidal grating (the target: 4 cpd, Michelson contrast 0.2) was measured as a function of the onset asynchrony between the target and an annular "surround" grating with the same orientation and spatial frequency. The contrast and area of the surround stimulus were varied parametrically. The suppressive signal peaked at earlier times the higher the surround contrast (0.1-0.4), following a function consistent with the contrast-dependence of retinal response dynamics. Increasing the area of the surround grating also moved peak suppression to earlier times. At ca. 2 deg annulus outer diameter the time to peak of the suppressive signal was shortest, although its amplitude grew with annulus area even beyond that. When both the contrast and the area of the centre and surround gratings were equal, suppression was maximal if the surround stimulus was presented ca. 5 ms before the target. Such a short delay of suppression is consistent with a neural implementation based on feedforward-feedback connections, but not with horizontal connections.

Modelling the effect of microsaccades on retinal responses to stationary contrast patterns

We have modelled the effect of microsaccades on retinal responses to achromatic borders and lines using physiologically realistic parameters. Typical microsaccade movement sequences were applied to the retinal image of stationary spatial contrast patterns as projected on the foveal cone mosaic after being passed through the optical transfer function of the eye. The resulting temporal contrast modulation over a cone receptive field was convolved with an analytical expression for the response waveform of primate cones (photocurrent: [Schnapf, J. L., Nunn, B. J., Meister, M. & Baylor, D. A. (1990). Visual transduction in cones of the monkey Macaca fascicularis. Journal of Physiology, 427, 681-713]; photovoltage: [Schneeweis, D. M. & Schnapf, J. L. (1999). The photovoltage of macaque cone photoreceptors: Adaptation, noise, and kinetics. Journal of Neuroscience, 19, 1203-1216]). The input to the ganglion cell was derived from the cone responses by the difference-of-Gaussians receptive field model of Donner and Hemilä [Donner, K. & Hemilä, S. (1996). Modelling the spatio-temporal modulation response of ganglion cells with difference-of-Gaussians receptive fields: Relation to photoreceptor response kinetics. Visual Neuroscience, 13, 173-186]. The modelled response waveforms suggest that microsaccades may significantly enhance sensitivity to edges, "re-sharpen" the image and, most interestingly, improve resolution of two closely spaced lines. The reason is that fine spatial structure of the retinal image when moving at suitable velocities is translated into a correlated temporal structure of responses of single cones and ganglion cells. The information content of the signal is not strongly dependent on positional accuracy and the effect is thus distinct from the presumed retinal basis of vernier acuity. Other eye movements (drift) with velocity distributions similar to that of the microsaccade's slow return phase might be similarly useful, although the microsaccade has some distinguishing features that could be functionally significant, e.g., the neural motor control and the biphasic movement pattern.

Defining the limits of flicker defined form: effect of stimulus size, eccentricity and number of random dots

We investigated the spatio-temporal limits of flicker defined form (FDF) phase contrast thresholds generated from the phantom contour illusion. Random dots (diameter 0.25 degrees, tapered edge) were used throughout the test field. FDF was generated using circular stimuli (temporal frequency 30 Hz, mean background luminance 50 cdm(-2)), the edges being defined by illusory borders generated from the out-of-phase dots within the display. Thresholds improved with increasing stimulus size and number of random dots at all eccentricities. For a constant threshold, fewer random dots were required with increasing eccentricity. Predictive mathematical relationships between contrast threshold, stimulus size and random dot number are discussed.

Contrast coding and magno/parvo segregation revealed in reaction time studies

Reaction times (RTs) are obtained for a wide range of contrasts of vertical sinusoidal gratings. The data are plotted as a function of the reciprocal of contrast. In some conditions, a single linear function accounts for the data. In others a clear bi-linear function is obtained. The low and high contrast regions of the function are interpreted as representing magno and parvo activity, respectively. RT-based supra-threshold sensitivity functions are obtained for different luminances, stimulus durations and eccentricities and these are compared with conventional threshold-based sensitivities to establish the extent to which RTs and contrast sensitivity are constrained by the same sensory processes.

Temporal visual filtering in diabetes mellitus

The background modulation method was used to investigate the temporal response of the magnocellular pathway in diabetic patients and controls. The luminance threshold for detecting a moving, 2 degrees, achromatic target was measured as a function of background flicker frequency from 5 to 45 Hz. A model of photoreceptor kinetics integrated with difference of Gaussian receptive fields [Vis. Neurosci. 13 (1996) 173] was used to analyse the data. Diabetic patients with significant maculopathy showed raised thresholds at 8.75, 12.5, 15 and 17.5 Hz. Estimates of photoreceptor summation time were the same in both groups, but receptive field centre-to-surround delay showed an increasing trend in the diabetic patients.

A mechanistic inter-species comparison of flicker sensitivity

The general validity of both the Rovamo [Vision Res. 39 (1999) 533] and Barten (Contrast sensitivity of the human eye, SPIE Optical Engineering Press, 1999), modulation transfer function models for describing flicker sensitivity in vertebrates was examined using published data for goldfish, chickens, tree shrews, ground squirrels, cats, pigeons and humans. Both models adequately described the flicker response in each species at frequencies greater than approximately 1 Hz. At lower frequencies, response predictions differed between the two models and this was due, in part, to dissimilar definitions of the role played by lateral inhibition in the retina. Modelled flicker sensitivity for a matched retinal illuminance condition enabled a direct inter-species comparison of signal processing response times at the photoreceptor level. The modelled results also quantified differences between species in post-retinal signal processing capability. Finally, the relationship between flicker frequency response curves and the perception of temporal signals in real visual scenes was examined for each species. It is proposed that the area under the flicker sensitivity function may offer a single "figure of merit" for specifying overall sensitivity to time signals in a species' environment.

Spatial visual filtering in diabetes mellitus

PURPOSE

To investigate spatial visual filtering in a group of diabetic patients and compare the results with those of a group of controls.

METHODS

The luminance threshold of a moving 2 degrees achromatic target, viewed against a 17 degrees achromatic background grating, was measured as a function of grating periodicity from 0.21 to 31.4 cpd in 22 diabetic patients and 12 controls, giving a response characteristic of the spatial function of a sustained-response type of visual channel. A previously published model of spatiotemporal filtering, integrating photoreceptor kinetics with difference-of-Gaussian circularly symmetric receptive fields, was used to analyse the data.

METHODS

The model gave a good fit to the data in the control group, with a mean central space constant of 0.046 degrees and centre:surround ratio of 1:5.2 and mean R(2)=0.78 (SD 0.12). The mean central space constant in the diabetic group was 0.051 degrees and the centre:surround ratio 1:4.2, although best fit was significantly worse, at R(2)=0.54 (SD 0.19), P=0.001. The best fit for diabetic subjects with grade 2 maculopathy was significantly worse than for those with no maculopathy ( P=0.03).

CONCLUSION

The study demonstrates a disruption of circularly symmetric centre-surround receptive field structure of the sustained-response channel in the diabetic retina to a degree that is consistent with the retinal level of anatomical change in diabetic maculopathy.

Measuring and modelling the photopic flicker sensitivity of the chicken (Gallus g. domesticus)

The photopic flicker sensitivity of the chicken was determined using an operant conditioning psychophysical technique. The results show both high- and low-frequency fall-off in the sensitivity response, which peaked around 15 Hz. Flicker sensitivity was determined for a range of stimulus luminance levels, and directly compared to human flicker response measured under similar stimulus conditions. At five luminance levels (10, 100, 200, 500 and 1000 cd/m(2)), the overall chicken flicker sensitivity was found to be considerably lower than for humans, except at high frequencies. A greater degree of frequency tuning was also found in the chicken response. The critical flicker fusion values were either similar or slightly higher for chickens compared to humans (40.8, 50.4, 53.3, 58.2 and 57.4 Hz vs 39.2, 54.0, 54.0, 57.4 and 71.5 Hz respectively for humans and chickens for increasing stimulus luminance level). A recently proposed model for flicker sensitivity [Vision Research 39 (1999) 533], which incorporates low- and high-pass temporal filters in cascade, was found to be applicable to the chicken response. From this model, deductions were made concerning mechanisms controlling the transfer of temporal information.

Spatial neural modulation transfer function of human foveal visual system for equiluminous chromatic gratings

To determine the spatial modulation transfer function (MTF) of the human foveal visual system for equiluminous chromatic gratings we measured contrast sensitivity as a function of retinal illuminance for spatial frequencies of 0.125-4 c/deg with equiluminous red-green and blue-yellow gratings. Contrast sensitivity for chromatic gratings first increased with luminance, obeying the Rose-DeVries law, but then the increase saturated and contrast sensitivity became independent of light level, obeying Weber's law. Critical retinal illuminance (I(c)) marking the transition point between the laws was found to be independent of spatial frequency at 165 phot. td. According to our detection model of human spatial vision the MTF of the retina and subsequent neural visual pathways (P(c)) is directly proportional to radicalI(c). Hence, P(c) is independent of spatial frequency, reflecting the lack of precortical lateral inhibition for equiluminous chromatic stimuli in spatiochromatically opponent retinal ganglion cells and dLGN neurons.

Flicker sensitivity as a function of target area with and without temporal noise

Flicker sensitivities (1-30 Hz) in foveal, photopic vision were measured as functions of stimulus area with and without strong external white temporal noise. Stimuli were circular, sinusoidally flickering sharp-edged spots of variable diameters (0.25-4 degrees ) but constant duration (2 s), surrounded by a uniform equiluminant field. The data was described with a model comprising (i) low-pass filtering in the retina (R), with a modulation transfer function (MTF) of a form derived from responses of cones; (ii) normalisation of the temporal luminance distribution by the average luminance; (iii) high-pass filtering by postreceptoral neural pathways (P), with an MTF proportional to temporal frequency; (iv) addition of internal white neural noise (N(i)); (v) integration over a spatial window; and (vi) detection by a suboptimal temporal matched filter of efficiency eta. In strong external noise, flicker sensitivity was independent of spot area. Without external noise, sensitivity increased with the square root of stimulus area (Piper's law) up to a critical area (A(c)), where it reaches a maximum level (S(max)). Both A(c) and eta were monotonic functions of temporal frequency (f), such that log A(c) increased and log eta decreased linearly with log f. Remarkably, the increase in spatial integration area and the decrease in efficiency were just balanced, so A(c)(f)eta(f) was invariant against f. Thus the bandpass characteristics of S(max)(f) directly reflected the composite effect of the distal filters R(f) and P(f). The temporal equivalent (N(it)) of internal neural noise (N(i)) decreased in inverse proportion to spot area up to A(c) and then stayed constant indicating that spatially homogeneous signals and noise are integrated over the same area.

Calculating the contrasts that retinal ganglion cells and LGN neurones encounter in natural scenes

Visual responses are known to depend on stimulus contrast and not simply on the absolute levels of retinal illumination. Here, we have determined the contrasts that mammalian retinal ganglion cells and lateral geniculate neurones (LGN) are likely to encounter in real world scenes. Local contrasts were calculated in 135 calibrated images of a variety of real world scenes using contrast operators that closely mirror the characteristic receptive-field organisation of mammalian retinal ganglion cells and LGN neurones. We have found that the frequency distribution of the calculated local contrasts has a pronounced peak at zero contrast and that it tails off roughly exponentially with increasing positive and negative contrasts; about 90% of the contrasts in the images were within the equivalent range of +/-0.5 Michelson and Weber contrasts. Further analysis suggests that the characteristic forms of the contrast-response functions of mammalian retinal and LGN neurones are matched to the range of contrasts that they experience when viewing real world images.

Contrast matching across spatial frequencies for isoluminant chromatic gratings

Contrast matching was performed with isoluminant red-green and s-cone gratings at spatial frequencies ranging from 0.5 to 8 c/deg. Contrast threshold curves were low-pass in shape, in agreement with previous findings. Contrast matching functions resembled threshold curves at low contrast levels, but became flat and independent of spatial frequency at high contrasts. Thus, isoluminant chromatic gratings exhibited contrast constancy at suprathreshold contrast levels in a similar manner as has been demonstrated for achromatic gratings.

Modelling spatial contrast sensitivity functions for chromatic and luminance-modulated gratings

We extended our detection model of achromatic spatial vision (Rovamo, J., Mustonen, J., & Näsänen, R. (1994a). Modelling contrast sensitivity as a function of retinal illuminance and grating area. Vision Research, 34, 1301-1314) to colour vision by taking into account the fact that due to the spatio-chromatic opponency of retinal ganglion cells and dorsal lateral geniculate nucleus (dLGN) neurons, equiluminous chromatic gratings are not affected by precortical lateral inhibition. We then tested the extended model by using Mullen's experimental data (Mullen, K. J. (1985). The contrast sensitivity of human color vision to red-green and blue-yellow chromatic gratings. Journal of Physiology, 359, 381-400). The band-pass shape of the spatial contrast sensitivity function for luminance-modulated green and yellow gratings transformed to a low-pass shape, resembling the chromatic spatial contrast sensitivity function for red-green and blue-yellow equiluminous gratings, when the effect of precortical lateral inhibition on grating contrast was computationally removed by dividing luminance contrast sensitivities by spatial frequency (i.e. by af, where a = 1 degree). After the removal of this direct effect of lateral inhibition, there still remained a residual shape difference between the spatial contrast sensitivity functions for chromatic and luminance gratings. It was due to indirect reduction of grating visibility by quantal noise high-pass filtered by precortical lateral inhibition. When this indirect effect of quantal noise was also removed, contrast sensitivity for luminance gratings was about twice the sensitivity for chromatic gratings at all spatial frequencies. This was evidently due to the fact that the chromatic contrast of the equiluminous grating at the opponent stage (Cole, G. R., Hine, T. & McIihagga, W. (1993). Detection mechanisms in L-, M-, and S-cone contrast space. Journal of the Optical Society of America A, 10, 38-51) was about half of the luminance contrast of either of its chromatic component. Thus, if the contrast of the equiluminous chromatic grating were not expressed as the Michelson contrast of one chromatic component grating against its own background (Mullen, K. J. (1985). The contrast sensitivity of human color vision to red-green and blue-yellow chromatic gratings. Journal of Physiology, 359, 381-400) but as chromatic contrast at the opponent stage, contrast sensitivity would be the same for chromatic and luminance gratings.

Noise and its effects on photoreceptor temporal contrast sensitivity at low light levels

We studied photoreceptors in the locust (Schistocerca americanus) visual system to determine the extent to which quantal noise and intrinsic neural noise limit temporal sensitivity. Typical computational models of the temporal contrast sensitivity function are deterministic, reflect only filter characteristics, and lack explicit noise sources [J. Opt. Soc. Am. 58, 1133 (1968); Vision Res. 32, 1373 (1992)]. We report here that the temporal contrast sensitivity function, at low light levels, is not simply the reflection of a filter function. Our evidence suggests that, at low backgrounds, noise, in conjunction with temporal filtering, plays a role in shaping the temporal contrast sensitivity function. At a given low adaptation level, quantal noise limits sensitivity at low temporal frequencies, while intrinsic noise limits sensitivity at relatively higher temporal frequencies.

The effects of temporal noise and retinal illuminance on foveal flicker sensitivity

We measured foveal flicker sensitivity with and without external added temporal noise at various levels of retinal illuminance and described the data with our model of flicker sensitivity comprising: (i) low-pass filtering of the flickering signal plus external temporal and/or quantal noise by the modulation transfer function (MTF) of the retina (R): (ii) high-pass filtering in proportion to temporal frequency by the MTF of the postreceptoral neural pathways (P): (iii) addition of internal white neural noise; and (iv) detection by a temporal matched filter. Without temporal noise flicker sensitivity had a band-pass frequency-dependence at high and medium illuminances but changed towards a low-pass shape above 0.5 Hz at low luminances, in agreement with earlier studies. In strong external temporal noise, however, the flicker sensitivity function had a low-pass shape even at high and medium illuminances and flicker sensitivity was consistently lower with noise than without. At low luminances flicker sensitivity was similar with and without noise. An excellent fit of the model was obtained under the assumption that the only luminance-dependent changes were increases in the cut-off frequency (fc) and maximum contrast transfer of R with increasing luminance. The results imply the following: (i) performance is consistent with detection by a temporal matched filter, but not with a thresholding process based on signal amplitude; (ii) quantal fluctuations do not at any luminance level become a source of dominant noise present at the detector; (iii) the changes in the maximum contrast transfer reflect changes in retinal gain, which at low to moderate luminances implement less-than-Weber adaptation, with a 'square-root' law at the lowest levels; (iv) the changes of fc as function of mean luminance closely parallels time scale changes in cones, but the absolute values of fc are lower than expected from the kinetics of monkey cones at all luminances; (v) the constancy of the high-pass filtering function P indicates that surround antagonism does not weaken significantly with decreasing light level.

Lower-level visual processing and models of light adaptation

Before there was a formal discipline of psychology, there were attempts to understand the relationship between visual perception and retinal physiology. Today, there is still uncertainty about the extent to which even very basic behavioral data (called here candidates for lower-level processing) can be predicted based upon retinal processing. Here, a general framework is proposed for developing models of lower-level processing. It is argued that our knowledge of ganglion cell function and retinal mechanisms has advanced to the point where a model of lower-level processing should include a testable model of ganglion cell function. This model of ganglion cell function, combined with minimal assumptions about the role of the visual cortex, forms a model of lower-level processing. Basic behavioral and physiological descriptions of light adaptation are reviewed, and recent attempts to model lower-level processing are discussed.

Flicker sensitivity as a function of spectral density of external white temporal noise

Foveal flicker sensitivity at 0.5-30 Hz was measured as a function of the spectral density of external, white, purely temporal noise for a sharp-edged 2.5 deg circular spot (mean luminance 3.4 log phot td). Sensitivity at any given temporal frequency was constant at low powers of external noise, but then decreased in inverse proportion to the square root of noise spectral density. Without external noise, sensitivity as function of temporal frequency had the well-known band-pass characteristics peaking at about 10 Hz, as previously documented in a large number of studies. In the presence of strong external noise, however, sensitivity was a monotonically decreasing function of temporal frequency. Our data are well described (goodness of fit 90%) by a model comprising (i) low-pass filtering by retinal cones, (ii) high-pass filtering in the subsequent neural pathways, (iii) adding of the temporal equivalent of internal white spatiotemporal noise, and (iv) detection by a temporal matched filter, the efficiency of which decreases approximately as the power -0.58 of temporal frequency.

The effect of background luminance on visual responses to strong flashes: perceived brightness and the early rise of photoreceptor responses

The threshold intensity for large-long incremental stimuli rises proportionally to adapting background luminance IB (Weber adaptation), but the intensity required to evoke a criterion high-brightness sensation rises much less steeply. We propose that this difference originates in the very first stage of visual processing, in the phototransduction and adaptation properties of the retinal photoreceptor cells. A physiological model previously found to account for visual latency and brightness as functions of stimulus intensity in the dark-adapted state [Donner, K. (1989). Visual Neuroscience, 3, 39-51] is extended to cover different states of adaptation. It is assumed that the neural coding of high intensities is based on the rate of rise (quasi-derivative) of the photoreceptor response just after it reaches a small threshold amplitude. The shallow background adaptation functions for high-brightness criteria emerge as a consequence of the relative constancy of the leading edge of large responses under backgrounds, a phenomenon that can be formally described by compensating changes in photoreceptor sensitivity and time scale. We first test the model on supra-threshold responses in the frog retina, where the discharge rate of ganglion cells (a possible neural code for brightness) and the primary rod hyperpolarizations can be recorded under identical conditions. The two are related as predicted over at least 3 log units of background intensity. We then show that published data on the background adaptation of human foveal high brightness judgments conform to the same model, assuming that human cones accelerate as IB-b with b = 0.14-0.15.