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.

Identification of facial images in peripheral vision.

Contrast sensitivity for face identification was measured as a function of image size to find out whether foveal and peripheral performance would become equivalent by magnification. Size scaling was not sufficient for this task, but when the data was scaled both in size and contrast dimensions, there was no significant eccentricity-dependent variation in the data, i.e. for equivalent performance both the size and contrast needed to increase in the periphery. By utilising spatial noise added to the images we found that in periphery information was utilised less efficiently and peripheral inferiority arose completely from lower efficiency, not from increased internal noise.

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.

The effect of contrast and size scaling on face perception in foveal and extrafoveal vision.

PURPOSE: To determine whether face perception can be equalized across the visual field by scaling size and contrast simultaneously. METHODS: Contrast sensitivities were measured for detection (N = 1) and identification (N = 2-8) of a target face as a function of size (0.4 degrees-10 degrees) across eccentricities (E = 0 degrees-10 degrees). RESULTS: In all conditions contrast sensitivity first increased and then saturated, as a function of stimulus size. Maximum sensitivity (Smax) decreased, whereas critical size (where S = Smax/square root(2)) increased with eccentricity and set size (N). At each set size, sensitivities from all eccentricities could be equated by double scaling--i.e., translation in horizontal (size) and vertical (contrast) dimensions on log-log axes. Similarly, at each eccentricity, data from all set sizes could be superimposed using double scaling. Furthermore, all data could be superimposed onto the foveal detection curve when double scaled according to the equation F = 1 + E/E2i + logN/logN2i + E(logN)/K, where i is horizontal or vertical. This equation incorporates the eccentricity (E2) and set size (N2), where contrast and size double, as well as the interaction term (K). CONCLUSIONS: Double scaling superimposes data. Not only is this possible across set sizes or eccentricities separately, but by combining their effects, a function is provided that collapses all data to a single curve, explaining all performance variation across eccentricity and set size. Our results support the proposition based on numeral recognition that failures of spatial scaling across eccentricities may simply reflect the need for scaling both size and contrast.

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.

Neon colour spreading in three-dimensional illusory objects in humans.

We studied whether neon spreading can be induced within three-dimensional illusory triangles. Kanizsa triangles were induced by black pacman disks consisting of red sectors with curved sides. Viewing our stimuli monocularly produced two-dimensional illusory contours and surfaces as well as neon spreading in each figure. Triangles appeared concave or convex under stereoscopical viewing. Neon colour spreading was induced within illusory figures bending in three-dimensional space, suggesting that neural contour completion and surface filling-in interact across depth. Surprisingly, neon spreading was induced above the intervening surface even when the inducers were below the surface. Neon colour and illusory configuration were preserved behind the intervening surface only when it appeared transparent.

Scaling extrafoveal detection of distortion in a face and grating.

Peripheral performance involving simple visual tasks and stimuli can be equated with foveal performance by spatial scaling, whilst more complex tasks and stimuli seem to need additional scaling of image contrast. We therefore determined whether the contrast manipulation needed to compensate for eccentricity-dependent performance changes is due to an increase in stimulus or task difficulty. We measured contrast sensitivities to determine foveal and peripheral ability to discriminate between an original and a distorted version of a polar-circular sinusoidal grating and a face image. Contrast sensitivities as a function of image size were spatially scaleable across eccentricities for both the face and grating. Furthermore, irrespective of stimulus, performance could be scaled with the same individual E2 value. Thus task simplicity overrides the nature of the stimulus in determining scaling requirements, suggesting that it is the complexity of the task, not of the stimulus, that makes contrast scaling necessary in complex tasks.

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.

Illusory motion capture and release in rotating 3-D figure in humans.

An illusory bar emerges in a cleft between two opposing gratings. When the gratings rotated around the vertical axis in three-dimensional (3-D) space, the illusory bar was seen either (i) rotating with the inducing gratings or (ii) as a stationary and opaque tape located in front of gratings. This illusion seems to be caused by the different temporal dynamics of the illusion and its inducers, especially by the slower extinction rate for the illusory bar than its inducers. The illusion is a psychophysical demonstration of an illusory figure becoming spatially and temporally loose from its inducers, suggesting that they are processed separately in the brain. This indicates that illusory figures are not only by-products of normal vision but have their own important function.

Spatial integration and effective spectral density of one-dimensional noise masks.

When masking one-dimensional gratings, the strongest masking effect is achieved by using one-dimensional spatial noise, which can be regarded as a special case of two-dimensional noise where the noise check height is equal to the grating height. The extent of spatial integration in the human visual system is limited, however. Hence, our aim was to investigate whether the effective height of noise checks of one-dimensional noise is similarly limited. We measured detection thresholds for vertical sinusoidal gratings with added spatial noise. The width of the noise checks remained constant, but their height increased until equal to the height of the image window which made noise one-dimensional. The contrast energy thresholds increased in direct proportion to increasing noise check height and the spectral density of noise, calculated by taking into account both the height and the width of the noise checks. The increase levelled off, however, after the critical noise check height (nyc). The critical noise check height in grating cycles changed as a function of spatial frequency (f) as nyc = 4.7 [1 + (1.4/f)2]-0.5. According to our results the effective height of noise checks was thus limited in accordance with studies on spatial integration, showing scale invariance above 1.4 c/deg.

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.

Spatial integration of signal information in Gabor stimuli.

We studied spatial integration of Gaussian weighted cosine gratings (Gabor gratings) in contrast detection by using a two-alternative forced-choice method. The Gabor gratings, which were either complete or sharply truncated to a square shape, were presented either in the presence or absence of static noise. Contrast thresholds were determined for different truncation areas and different widths of the two-dimensional Gaussian weighting function. Contrast detection performance was found to depend only on the effective spatial spread of the stimuli. The spatial spread is a physical description of signal area, which takes into account the spatial inhomogeneity of the signal. The highest detection efficiencies were obtained when the spatial spread was small independently of whether the stimuli were sharply truncated or complete smooth Gabor gratings. The results show that the contrast detection mechanism takes into account the shape of the signal window and does not collect information outside the area of the signal.

Contrast restoration model for contrast matching of cosine gratings of various spatial frequencies and areas.

The purpose of the model presented in this paper is to explain the well known fact that perceived contrast becomes independent of optical low-pass and neural high-pass filtering as well as areal integration with increasing stimulus contrast. In the model we assume that perceived contrast is computed by two different parallel mechanisms. One of them integrates signal information across space to improve the signal-to-noise ratio and is affected by the optical low-pass and neural high-pass filtering. The other mechanism estimates external local contrast by using inverse filtering. These two factors are combined by a 'restoration' mechanism so that the first mechanism affects the perception of low contrast and the latter that of high contrast stimuli. The behaviour of the model was tested against experimental results obtained with normal human observers. At low contrast levels, contrast matching curves were similar in shape to the detection threshold curves both as a function of the spatial frequency and area of the grating. At high contrast levels, contrast matches became physically correct. The model described the experimental results accurately.

Foveal optical modulation transfer function of the human eye at various pupil sizes.

We determined the foveal optical modulation transfer functions of the human eye (O) for pupil sizes of 1-8 mm by using two simple psychophysical techniques. O as a function of spatial frequency f could be described by exp[-(f/fc)n] at any pupil size in our data as well as in the data available in the literature [J. Physiol. (London) 186, 558 (1966); Opt. Acta 21, 395 (1974); Vision Res. 33, 15 (1993); J. Opt. Soc. Am. A 11, 246 (1994)]. When all these estimates of fc and n were pooled the parameters were found to depend on the pupil diameter as fc = 16.6 - 1.49p and n = exp(0.840/p - 0.318). This result indicates that at 1 mm O(f) is close to the diffraction-limited system.

Effects of spatial configuration and number of fixations on Kanizsa triangle detection.

PURPOSE: Illusory figures, created by the visual system between visualizing real objects, are probably caused by processes designed to segregate objects from background. Support ratio--that is, the ratio between the physically specified and total triangle side length--has been suggested to be the main spatial determinant for suprathreshold perception of a Kanizsa-type illusion. To test this scale invariance hypothesis at threshold, illusory figure perception was studied by determining the effects of inducer size and distance at various exposure durations and fixation strategies on the frequency of seeing (FoS) an illusory Kanizsa triangle. METHODS: The effect of various support ratios was studied in the first experiment by varying the intercenter distance between constant-size inducers viewed at various distances. In the second experiment, the effects of various exposure durations and fixation strategies were investigated; and the third experiment repeated the second one, with backward masking to control the processing time. In the fourth experiment, the magnification of the stimulus configuration was varied, with a support ratio that had yielded 100% FoS in the first experiment, to study the range of scale invariance in illusory figure perception. RESULTS: The support ratio was the main determinant for the perception of an illusory figure at various inducer sizes, exposure durations, and masking conditions when fixation was steady; FoS always increased from 0% to 100% with the support ratio of 0.30 to 0.37. However, free viewing, with and without masking, resulted in 100% illusory figure perception at all support ratios tested. Furthermore, when fixation was steady and support ratio and exposure duration were held constant, stimulus magnification reduced FoS from 100% to 0% at the smallest and largest stimulus sizes. CONCLUSIONS: The support ratio seems to be the main spatial determinant for illusory figure perception. However, scale invariance in Kanizsa triangle perception broke down in the smallest and largest configurations, probably because of the limitations of visual acuity and spatial integration, respectively. Integration of information from several fixations enhances FoS at small support ratios, emphasizing the importance of the binding process between separate fixations for illusory figure perception.

The effects of eccentricity and stimulus magnification on simultaneous performance in position and movement acuity tasks.

We presented two tasks, spatial interval discrimination and displacement detection, simultaneously in the same location at various eccentricities. The subject was to solve (i) only the spatial interval task; (ii) only the displacement task; or (iii) both tasks simultaneously. With 500 msec stimulus duration, and using the method of spatial scaling, the E2 value (the eccentricity at which stimulus size has to be doubled to maintain performance level) was found to be 0.17-0.39 deg for spatial interval discrimination and 1.0-1.2 deg for displacement detection. These values remained unaffected whether the subject solved one task or two tasks simultaneously. This finding was confirmed using a shorter, 50 msec stimulus duration. As there is no interference between tasks, the mechanisms solving the tasks appear to be functionally independent i.e., operating in parallel at all eccentricities.

Detection of geometric image distortions at various eccentricities.

PURPOSE: Human ability to perceive spatial stimuli declines with increasing eccentricity. To study this phenomenon with natural images, the authors applied the spatial scaling method by measuring the smallest detectable amount of geometric change in a human face at several eccentricities for a series of stimulus magnifications to find out whether performance could be made equal across the visual field simply by an appropriate enlargement. METHODS: The authors used a novel method to produce subtle changes to an image of a face. The smallest change recognized was determined using a two-alternative forced-choice method and expressed in terms of correlation sensitivity, the inverse of the correlation between the images that just could be discriminated. RESULTS: The detection of changes in the facial features, presumably a spatially complex task, became equal across the visual field simply by an appropriate change of scale. The E2 value represents the eccentricity at which the foveal stimulus size must double to maintain performance at the foveal level. The E2 values, found to be 1.73 degrees to 2.45 degrees, were similar to our previously measured values for vernier acuity, orientation discrimination, and curvature detection and discrimination, obtained with the same method of spatial scaling. CONCLUSIONS: The authors' results indicate that with adequate stimulus magnification, one is capable of detecting geometric changes in complex images such as face equally at the fovea and in the periphery. In this task, there seems to be no qualitative difference between the accuracy of foveal and peripheral processing.

Effect of image orientation contents on detection efficiency.

Contrast detection performance is known to be better for single component sinusoidal gratings than for sums of gratings at different orientations. A recent study Rovamo et al. (1994) (Investigative Ophthalmology and Visual Science, 35, 2611-2619) showed that spatial integration is less effective for multiple orientation component than for single component gratings. This suggests an explanation that the size of a spatial integration window depends on the orientation contents of the stimulus. To test this hypothesis we designed a computational detection model and tested it against new experimental data. The model generates a cross-correlation template, the extent of which is limited both in the spatial and spatial frequency domain. The template is a copy of the band-pass filtered signal weighted by a spatial window function. The spatial window function, which limits spatial integration, decreases with increasing orientation range of the stimulus. The experimental stimuli were composed of side-by-side located square shaped, one cycle, grating patches. The range of either grating orientations or phases within the patches as well as the number of patches in a stimulus were varied. We also measured detection efficiency for Bessel Jo images as a function of area. Human spatial integration became considerably weaker with increasing orientation range. The increasing phase range also reduced detection efficiency to some extent. Supporting the idea of the varying size of the spatial integration window, the computational model explained the orientation, phase, and Bessel Jo data well.

Modeling spatial integration and contrast invariance in visual pattern discrimination.

PURPOSE: Human pattern discrimination performance has been reported to be largely independent of stimulus contrast but to depend on stimulus area. The authors propose a model that combines the effects of spatial integration and contrast. The model is based on the computation of similarity between pattern templates in memory and signals to be discriminated using normalized correlation. There are also two sources of additive noise, one before and one after the computation of correlation. The model was compared with human observers in an orientation discrimination task. METHODS: Orientation discrimination thresholds of human observers were measured for sinusoidal gratings of various areas, contrasts, and spatial frequencies. A two-interval, forced-choice methods was used. The performance of the model was determined by using computer simulations. RESULTS: It was found that the effects of contrast and grating area were interrelated. The decrease of orientation thresholds as a function of grating area was considerably larger at low than at high contrast. On the other hand, orientation thresholds decreased clearly as a function of contrast at the smallest grating areas but hardly at all at the largest grating areas. The model accounted well for the experimental findings. CONCLUSIONS: Because the invariance of orientation discrimination with respect to stimulus contrast depended on area, the cause of the invariance appeared to occur after spatial integration. The model explains this so that, with increasing contrast or area, the normalized correlation gradually approached a constant value. The proportion of pretemplate noise became negligible compared to the constant posttemplate noise. Thus, total noise also approached a constant value. Hence, the signal-to-noise ratio and discrimination performance became constant.

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.