Shading Beats Binocular Disparity in Depth from Luminance Gradients: Evidence against a Maximum Likelihood Principle for Cue Combination

Perceived depth is conveyed by multiple cues, including binocular disparity and luminance shading. Depth perception from luminance shading information depends on the perceptual assumption for the incident light, which has been shown to default to a diffuse illumination assumption. We focus on the case of sinusoidally corrugated surfaces to ask how shading and disparity cues combine defined by the joint luminance gradients and intrinsic disparity modulation that would occur in viewing the physical corrugation of a uniform surface under diffuse illumination. Such surfaces were simulated with a sinusoidal luminance modulation (0.26 or 1.8 cy/deg, contrast 20%-80%) modulated either in-phase or in opposite phase with a sinusoidal disparity of the same corrugation frequency, with disparity amplitudes ranging from 0’-20’. The observers’ task was to adjust the binocular disparity of a comparison random-dot stereogram surface to match the perceived depth of the joint luminance/disparity-modulated corrugation target. Regardless of target spatial frequency, the perceived target depth increased with the luminance contrast and depended on luminance phase but was largely unaffected by the luminance disparity modulation. These results validate the idea that human observers can use the diffuse illumination assumption to perceive depth from luminance gradients alone without making an assumption of light direction. For depth judgments with combined cues, the observers gave much greater weighting to the luminance shading than to the disparity modulation of the targets. The results were not well-fit by a Bayesian cue-combination model weighted in proportion to the variance of the measurements for each cue in isolation. Instead, they suggest that the visual system uses disjunctive mechanisms to process these two types of information rather than combining them according to their likelihood ratios.     

Colour contrast influences perceived shape in combined shading and texture patterns

The 'colour-shading effect' describes the phenomenon whereby a chromatic pattern influences perceived shape-from-shading in a luminance pattern. Specifically, the depth corrugations perceived in sinusoidal luminance gratings can be enhanced by spatially non-aligned, and suppressed by spatially aligned sinusoidal chromatic gratings. Here we examine whether colour contrast can influence perceived shape in patterns that combine shape-from-shading with shape-from-texture. Stimuli consisted of sinusoidal modulations of texture (defined by orientation), luminance and colour. When the texture and luminance modulations were suitably combined, one obtained a vivid impression of a corrugated depth surface. The addition of a colour grating to the texture-luminance combination was found to enhance the impression of depth when out-of-phase with the luminance modulation, and suppress the impression of depth when in-phase with the luminance modulation. The degree of depth enhancement and depth suppression was approximately constant across texture amplitude when measured linearly. In the absence of the luminance grating however, the colour grating had no phase-dependent affect on perceived depth. These results show that colour contrast modulates the contribution of shading to perceived shape in combined shading and texture patterns.     

Linear and nonlinear transparencies in binocular vision.

When the product of a vertical square-wave grating (contrast envelope) and a horizontal sinusoidal grating (carrier) are viewed binocularly with different disparity cues they can be perceived transparently at different depths. We found, however, that the transparency was asymmetric; it only occurred when the envelope was perceived to be the overlaying surface. When the same two signals were added, the percept of transparency was symmetrical; either signal could be seen in front of or behind the other at different depths. Differences between these multiplicative and additive signal combinations were examined in two experiments. In one, we measured disparity thresholds for transparency as a function of the spatial frequency of the envelope. In the other, we measured disparity discrimination thresholds. In both experiments the thresholds for the multiplicative condition, unlike the additive condition, showed distinct minima at low envelope frequencies. The different sensitivity curves found for multiplicative and additive signal combinations suggest that different processes mediated the disparity signal. The data are consistent with a two-channel model of binocular matching, with multiple depth cues represented at single retinal locations.     

Anisotropy in the chromatic channel: a horizontal-vertical effect

We compared the chromatic contrast thresholds of drifting (2Hz) red-green sine-wave gratings of horizontal, vertical, and two oblique orientations at three spatial frequencies (2, 4, 8 cpd). Luminance contrast thresholds for yellow-black gratings were also obtained. The classic oblique effect was found for high spatial frequency luminance and chromatic stimuli. For chromatic thresholds, a significant difference was found between the horizontal and vertical thresholds of all observers. One observer was retested with her head tilted 45 deg and demonstrated that the anisotropy was specific to retinal coordinates. These results give evidence for orientation selectivity in the chromatic channel which is at least partially independent of that in the luminance channel. We estimated the degree of lateral chromatic aberration in our observers' eyes and discuss the possible contribution of this aberration to the horizontal-vertical difference in the chromatic channel.     

Contrast transfer function of the visual system]

Visually evoked potentials were used to determine the spatial contrast response function of the visual system and the visual acuity of the pigeon. The spatial contrast response describes the relationship between the contrast in a pattern of vertical stripes, whose luminance is a function of position, and the amplitude of the visually evoked response at various spatial frequencies for a given temporal frequency (pattern reversal frequency); it indicates how particular spatial frequencies are attenuated in the visual system. The visually evoked responses were recorded using monopolar stainless steel electrodes inserted into the stratum griseum superficiale of the optic tectum; the depth of penetration was determined on the basis of a stereotactic atlas. The stimulus patterns were generated on a video monitor placed 75 cm in front of the animal's eye perpendicular to the optic axis. The spatial contrast response function measured at 10% contrast and 0.5 Hz reversal frequency shows a peak at a spatial frequency of 0.5 c/deg, corresponding to 1 degree of visual angle, and decreases progressively at higher spatial frequencies. The high-frequency limit (cut-off frequency) for resolution of sinusoidal gratings, estimated from the contrast response function, is 15.5 c/deg, corresponding to a visual acuity of 1.9 min of arc.     

Changes in perceived contrast of suprathreshold gratings as a function of orientation and spatial frequency

Orientation anisotropy for suprathreshold gratings of different spatial frequencies was measured using a contrast matching procedure. Observers matched the contrast of sine-wave gratings of various orientations to a vertical reference grating set at different reference contrasts. At threshold, the size of the anisotropy increased with spatial frequency, confirming previous results. When the reference grating contrast was set above threshold, the anisotropy declined, and eventually disappeared for gratings of medium spatial frequencies. At higher spatial frequencies, although the relative anisotropy became smaller, it did not disappear within the range of contrasts used in this study. For medium, but not for high spatial frequencies, the data are consistent with Kulikowski's (1976) model of effective contrast constancy.     

Evidence for different nonlinear summation schemes for lines and gratings at threshold

Within a wide class of multichannel models of the visual system it is suggested that spatial distributions of luminance are processed by the independent activation of grating detectors, or spatial frequency channels. Probability summation is often described in terms of Quick's nonlinear pooling model [Quick RF (1974) Kybernetik 16:65–67]. Using this model, we find evidence for the existence of different kinds of nonlinear summation at threshold; for compound gratings with well-separated spatial frequency components, the threshold functions indicate nonlinear summation which is not compatible with probability summation, while for line patterns well separated in the spatial domain the probability summation rule proves compatible with the data. Received: 24 June 1998 / Accepted in revised form: 16 March 1999     

视觉诱发电位(VEP)方位效应与刺激位置的关系

以人视觉诱发电位(VEP)反应为指标,在视野的不同位置测定了VEP对四个方位的闪烁方波光栅刺激(时间频率2.9Hz,空间频率1.4c/deg,对比度0.94)的反应幅度。在距中央凹20°视角同心圆的八个刺激位置上,VEP反应幅度对与向心线垂直方位的光栅刺激(同心圆的切线方向),有统计意义上的优势。这一规律在垂直、水平向心线上尤为明显。从总体上未发现VEP反应幅度与刺激光栅方位有着明显的关系。这说明在人视野周边区,VEP反应幅度与光栅方位和向心线的夹角(偏向角)相关,而与光栅的绝对方位无关。在相同的刺激条件下,中央区的VEP反应幅度与刺激光栅方位之间也未发现明显关系。     

用显示器测量办公亮度环境下的人眼对比度敏感视觉特性

对比度敏感是描述人眼视觉系统空间特性的主要指标之一,对比度敏感函数是反映不同条件下的对比度敏感与空间频率之间的关系。人眼对比度敏感数据的测量受到环境亮度较大的影响,为了研究常用办公环境条件下的人眼对比度敏感情况,对6位青年在环境亮度分别为153,312,470 cd/m2和暗室条件下,在距离为2米处观测11种空间频率的矩形光栅进行测量,光栅用显示器进行显示,其平均亮度分别为60和90 cd/m2。实验结果表明,对于相同频率的光栅,人眼对比度敏感程度随着环境亮度的增加而减小,而且人眼在暗室环境下比在办公环境条件下对亮度光栅更敏感;但是在观测平均亮度为60cd/m2的光栅时,人眼特殊地对在环境亮度为312 cd/m2的条件下更敏感。     

用显示器测量办公亮度环境下的人眼对比度敏感视觉特性

对比度敏感是描述人眼视觉系统空间特性的主要指标之一,对比度敏感函数是反映不同条件下的对比度敏感与空间频率之间的关系。人眼对比度敏感数据的测量受到环境亮度较大的影响,为了研究常用办公环境条件下的人眼对比度敏感情况,对6位青年在环境亮度分别为153,312,470 cd/m2和暗室条件下,在距离为2米处观测11种空间频率的矩形光栅进行测量,光栅用显示器进行显示,其平均亮度分别为60和90 cd/m2。实验结果表明,对于相同频率的光栅,人眼对比度敏感程度随着环境亮度的增加而减小,而且人眼在暗室环境下比在办公环境条件下对亮度光栅更敏感;但是在观测平均亮度为60cd/m2的光栅时,人眼特殊地对在环境亮度为312 cd/m2的条件下更敏感。     

Detection of sinusoidal gratings by pattern-specific detectors: further evidence for the correlation principle in human vision

 The detection of compound sinusoidal gratings of various spatial frequency separations and four different grating sizes has been studied using the summation-to-threshold paradigm. Contrast interrelation functions have been measured and spatial frequency tuning estimates, based on the slope of the contrast interrelation function at two definite points, were derived using the “negative gradient technique” proposed by Logvinenko [Logvinenko (1995) Biol Cybern 73: 547–552]. It is shown that compound grating detection can be modelled by assuming pattern-specific sensory mechanisms for each of the spatial frequency components, which adapt to the periodicity and the size of the stimulus but not to its envelope function. Further, it is shown that relative sensitivity for a given spatial frequency separation can be predicted with good accuracy by the correlation of the grating components used for superposition. It is suggested that the most plausible implementation of the pattern correlation principle in human grating detection is the “grating cell” model. Received: 10 March 2000 / Accepted in revised form: 4 December 2000     

Methods for the identification of evoked response components in the frequency and combined time/frequency domains

Two prominent frequency components designated f1 and f2 have been identified in the visual evoked response to the transient presentation of sinusoidal luminance gratings in the range of 0.5–8 c/deg. The components occur at temporal frequencies below the alpha band, with the f1 frequency roughly half that of the f2 frequency. The f1 component is largest at low spatial frequencies with f2 becoming progressively dominant as spatial frequency is increased.The frequency and amplitude of f1 and f2 change substantially over the time course of the response. This has been studied by calculating the temporal frequency spectrum of the transient evoked potential over successive short-time epochs running through the response. Using this technique, the response is shown to consist of narrow- and frequency peaks or ‘formants’ emerging at different times after stimulus onset. These formants occur at frequencies other than those of the spontaneous EEG and undergo changes in frequency and amplitude over the time course of the response.Two spectrum analysis techniques were employed: the Discrete Fourier Transform and Linear Predictive Coding. Frequency components were successfully identified in single-trial responses using the LPC technique.     

Phase channels and the square-wave illusion

We have utilized a phase-sensitive effect, the square-wave illusion, to investigate the presence and tuning of phase-sensitive mechanisms. Subjects viewed a 1 c/deg triangular-wave grating and reported the presence or absence of the illusion, before and after adaptation to square-wave gratings of various spatial frequencies. Illusion strength declined with adaptation and was a function of spatial frequency. This function may reflect the spatial frequency tuning of a 'phase channel'. We have also measured by adaptation a contrast sensitivity function, maximally sensitive to a frequency of 1 c/deg. When normalized to the same maximal depression from baseline sensitivity, the phase channel and spatial-frequency channel shared the same low frequency tuning, but the phase channel was broader, with extended sensitivity to higher frequencies. These results can be understood if the phase channel is constructed from combinations of phase sensitive spatial-frequency channels.     

A comparison of vernier acuity for narrowband and broadband stimuli

This study investigates the influence of contrast and exposure duration on vernier acuity thresholds for abutting and separated narrowband stimuli, and asks whether these data can predict broadband vernier performance. Vernier thresholds were determined for sinusoidal grating stimuli at two spatial frequencies (1 and 8 c/deg) across a range of contrasts (0.05-0.8) and exposure durations (35-2100 ms). Performance was assessed for the abutting configuration, and when a gap equivalent to 0.5 to 1.5 times the spatial period of the grating was introduced between the upper and lower halves of the grating. Vernier thresholds were also determined for a square-wave stimulus as a function of contrast (0.06 to 0.78). Exposure duration was fixed at 2100 ms. In addition, thresholds were determined at the appropriate contrast levels for the fundamental frequency (1.8 c/deg) of the square-wave, and for a number of the harmonics (3F, 5F, 7F, 9F). Our results provide support for filter models of vernier acuity by showing that vernier performance for abutting and closely-separated broadband stimuli represents the envelope of vernier sensitivity of those spatial frequency mechanisms that are activated by the broadband stimulus. In the case of high frequency grating stimuli presented for long exposure durations, vernier performance can be invariant across much of the contrast range. Despite this, however, contrast independence is not exhibited for abutting broadband stimuli because, within the broadband stimuli, the contrast of the higher harmonic components never reaches a level to reveal this plateau.     

Visual acuity and spatial contrast sensitivity in tree squirrels

The visual sensitivity of tree squirrels from three different species (two western gray squirrels, Sciurus griseus; three fox squirrels, Sciurus niger; and an eastern gray squirrel, Sciurus carolinensis) was measured for spatial patterns defined by luminance differences. Spatial contrast sensitivity functions were determined in behavioral discrimination experiments in which the stimuli were sinusoidally-modulated gratings. At an average luminance level of 3.4 cd/m² these squirrels were maximally sensitive to spatial frequencies of about 0.5 cycles/degree (c/d). These experiments, in conjunction with additional measurements involving discrimination of square-wave grating patterns, also indicate that the finest gratings these squirrels can discriminate average 2.2 c/d (SD = 0.42 c/d). There are no obvious differences in resolution acuity among the three species. Grating acuity also was measured at a much higher luminance level (340 cd/m²). The results of this experiment indicate that the spatial acuity of the tree squirrel increases with luminance level, reaching a maximum of 3.9 c/d at 340 cd/m².     

Saccadic eye movements and the detection of fast-moving gratings

Experiments are presented in which the effect of saccadic eye movements on the visibility of sinusoidal gratings drifting with velocities between 2 deg/s and 400 deg/s is investigated. The results demonstrate that saccades are highly useful for detecting this class of stimuli. Due to a saccade, otherwise subthreshold stimuli become visible as short, distinct flashes of the seemingly statinoary pattern. The paper analyzes in detail the dependence of the amount of facilitation on saccade size and relative direction and isolates the additional effect of saccadic suppression. A simple model is proposed which predicts the experimental findings.     

Touch Influences Visual Perception with a Tight Orientation-Tuning

Stimuli from different sensory modalities are thought to be processed initially in distinct unisensory brain areas prior to convergence in multisensory areas. However, signals in one modality can influence the processing of signals from other modalities and recent studies suggest this cross-modal influence may occur early on, even in ‘unisensory’ areas. Some recent psychophysical studies have shown specific cross-modal effects between touch and vision during binocular rivalry, but these cannot completely rule out a response bias. To test for genuine cross-modal integration of haptic and visual signals, we investigated whether congruent haptic input could influence visual contrast sensitivity compared to incongruent haptic input in three psychophysical experiments using a two-interval, two-alternative forced-choice method to eliminate response bias. The initial experiment demonstrated that contrast thresholds for a visual grating were lower when exploring a haptic grating that shared the same orientation compared to an orthogonal orientation. Two subsequent experiments mapped the orientation and spatial frequency tunings for the congruent haptic facilitation of vision, finding a clear orientation tuning effect but not a spatial frequency tuning. In addition to an increased contrast sensitivity for iso-oriented visual-haptic gratings, we found a significant loss of sensitivity for orthogonally oriented visual-haptic gratings. We conclude that the tactile influence on vision is a result of a tactile input to orientation-tuned visual areas.     

Spatial frequency discrimination for sinewave gratings with random, bandpass frequency modulation: evidence for averaging in spatial acuity

Spatial frequency difference thresholds for vertical, high contrast sinewave gratings were estimated at 1.25, 2.5, 5.0 and 10.0 cyc deg-1. Within an experiment two independent manipulations of the stimulus were employed: (1) the number of cycles of the sinewave grating was varied over a range of 2.0 to 15.0 cycles; and (2) a stationary, random frequency modulation was imposed on the sinewave. The probability density function of the frequency modulation was a Gaussian whose dispersion coefficient was varied, in different experiments, in the range of 0 to 10% of the frequency of the parent sinewave. Both of these experimental variables were found to affect the precision with which spatial frequency discrimination could be performed. The Weber fraction increased both as the number of cycles present was decreased and as the dispersion coefficient of the modulating function was increased. These two effects were independent. The data support previous psychophysical findings that spatial frequency discrimination involves averaging over the total area of the stimulus and are compatible with spatial primitive models of spatial contrast vision. The data are not compatible with those of Hirsch and Hylton (J. opt. Soc. Am. 72, 1367-1374) which suggest that spatial interval discrimination occurs solely by operation of foveal mechanisms.     

Efficient Extraction of Fluorescence Emission Utilizing Multiple Surface Plasmon Modes from Gold Wire Gratings

We demonstrate directional enhanced fluorescence emission from fluorophores located above gold wire gratings. In contrast to previous studies on corrugated films, efficient coupling was recorded for multiple plasmon modes associated with both the active and substrate side of the wires. This difference is likely due to the subtle differences in how light interacts with corrugated films versus metal films with periodic subwavelength slots. For corrugated films, coupling between modes on opposite sides of the grating are out of phase, and therefore plasmon modes on the opposite side of the grating are only weakly excited. For wire gratings, transmission and reflection features have been modeled well with a dynamical diffraction model that includes surface plasmons, which allows for efficient coupling to surface plasmon modes on both sides of the grating. We also compared the two mechanisms for fluorescent enhancement, namely the intense electromagnetic field associated with surface plasmons and excited fluorophores radiating via surface plasmon modes. We found the latter mechanism clearly dominant.     

Stationary pattern adaptation and the early components in human visual evoked potentials

Pattern-onset visual evoked potentials were elicited from humans by sinusoidal gratings of 0.5, 1, 2 and 4 cpd (cycles/degree) following adaptation to a blank field or one of the gratings. The wave forms recorded after blank field adaptation showed an early positive component, P0, which decreased in amplitude with spatial frequency, whereas the immediately succeeding negative component, N1, increased in amplitude with spatial frequency. P0 and N1 components of comparable size were recorded at 1 cpd. Stationary pattern adaptation to a grating of the same spatial frequency as the test grating significantly reduced N1 amplitude at 4, 2 and 1 cpd. The N1 component elicited at 4 cpd was attenuated in log-linear fashion as the spatial frequency of the adaptation grating increased. P0, on the other hand, was unaffected by stationary pattern adaptation at all combinations of test and adapting spatial frequencies, although P0 amplitude is known to be attenuated by adaptation to a drifting grating. Since N1, but not P0, was significantly attenuated following adaptation and testing at 1 cpd, it was concluded that the neurons generating these components are functionally distinct. The use of a common adaptation grating discounted the possibility that N1, but not P0, was affected due to a difference in the rates of retinal image modulation caused by eye movements made while viewing adaptation gratings of different spatial frequencies. The neurons generating N1 were adapted at a lower rate of retinal image modulation than that apparently required for adaptation of the neurons generating P0, which suggests a difference between these neurons in the rate of stimulus modulation necessary for activation.