The adjacent pixel nonlinearity: problems and solutions

Classification images for contrast discrimination

Contrast discrimination measures the smallest difference in contrast (the threshold) needed to successfully tell two stimuli apart. The contrast discrimination threshold typically increases with contrast. However, for low spatial frequency gratings the contrast threshold first increases, but then starts to decrease at contrasts above about 50%. This behaviour was originally observed in contrast discrimination experiments using dark spots as stimuli, suggesting that the contrast discrimination threshold for low spatial frequency gratings may be dominated by responses to the dark parts of the sinusoid. This study measures classification images for contrast discrimination experiments using a 1 cycle per degree sinusoidal grating at contrasts of 0, 25%, 50% and 75%. The classification images obtained clearly show that observers emphasize the darker parts of the sinusoidal grating (i.e. the troughs), and this emphasis increases with contrast. At 75% contrast, observers almost completely ignored the bright parts (peaks) of the sinusoid, and for some observers the emphasis on the troughs is already evident at contrasts as low as 25%. Analysis using a Hammerstein model suggests that the bias towards the dark parts of the stimulus is due to an early nonlinearity, perhaps similar to that proposed by Whittle.

Integration of contours defined by second-order contrast-modulation of texture

Boundaries in the visual world can be defined by changes in luminance and texture in the input image. A "contour integration" process joins together local changes into percepts of lines or edges. A previous study tested the integration of contours defined by second-order contrast-modulation. Their contours were placed in a background of random wavelets. Participants performed near chance. We re-visited second-order contour integration with a different task. Participants distinguished contours with "good continuation" from distractors. We measured thresholds in different amounts of external orientation or position noise. This gave two noise-masking functions. We also measured thresholds for contours with a baseline curvature to assess performance with more curvy targets. Our participants were able to discriminate the good continuation of second-order contours. Thresholds were higher than for first-order contours. In our modelling, we found this was due to multiple factors. There was a doubling of equivalent internal noise between first- and second-order contour integration. There was also a reduction in efficiency. The efficiency difference was only significant in our orientation noise condition. For both first- and second-order stimuli, participants were also able to perform our task with more curved contours. We conclude that humans can integrate second-order contours, even when they are curved. There is however reduced performance compared to first-order contours. We find both an impaired input to the integrating mechanism, and reduced efficiency seem responsible. Second-order contour integration may be more affected by the noise background used in the previous study. Difficulty segregating that background may explain their result.

Levelt's laws do not predict perception when luminance- and contrast-modulated stimuli compete during binocular rivalry

Incompatible patterns viewed by each of the two eyes can provoke binocular rivalry, a competition of perception. Levelt's first law predicts that a highly visible stimulus will predominate over a less visible stimulus during binocular rivalry. In a behavioural study, we made a counterintuitive observation: high visibility patterns do not always predominate over low visibility patterns. Our results show that none of Levelt's binocular rivalry laws hold when luminance-modulated (LM) patterns compete with contrast-modulated (CM) patterns. We discuss visual saliency, asymmetric feedback, and a combination of both as potential mechanisms to explain the CM versus LM findings. Competing orthogonal LM stimuli do follow Levelt's laws, whereas only the first two laws hold for competing CM stimuli. The current results provide strong psychophysical evidence for the existence of separate processing stages for LM and CM stimuli.

More superimposition for contrast-modulated than luminance-modulated stimuli during binocular rivalry

Luminance-modulated noise (LM) and contrast-modulated noise (CM) gratings were presented with interocularly correlated, uncorrelated and anti-correlated binary noise to investigate their contributions to mixed percepts, specifically piecemeal and superimposition, during binocular rivalry. Stimuli were sine-wave gratings of 2 c/deg presented within 2 deg circular apertures. The LM stimulus contrast was 0.1 and the CM stimulus modulation depth was 1.0, equating to approximately 5 and 7 times detection threshold, respectively. Twelve 45 s trials, per noise configuration, were carried out. Fifteen participants with normal vision indicated via button presses whether an exclusive, piecemeal or superimposed percept was seen. For all noise conditions LM stimuli generated more exclusive visibility, and lower proportions of superimposition. CM stimuli led to greater proportions and longer periods of superimposition. For both stimulus types, correlated interocular noise generated more superimposition than did anti- or uncorrelated interocular noise. No significant effect of stimulus type (LM vs CM) or noise configuration (correlated, uncorrelated, anti-correlated) on piecemeal perception was found. Exclusive visibility was greater in proportion, and perceptual changes more numerous, during binocular rivalry for CM stimuli when interocular noise was not correlated. This suggests that mutual inhibition, initiated by non-correlated noise CM gratings, occurs between neurons processing luminance noise (first-order component), as well as those processing gratings (second-order component). Therefore, first- and second-order components can contribute to overall binocular rivalry responses. We suggest the addition of a new well to the current energy landscape model for binocular rivalry that takes superimposition into account.

Interactions between Orientation and Contrast Modulations Suggest Limited Cross-Cue Linkage

Recent studies of texture segmentation and second-order vision have proposed very similar models for the detection of orientation modulation and contrast modulation (OM and CM). From the similarity of the models it is tempting to assume that the two cues might be processed by a single generalised texture mechanism; however, recent results (Kingdom et al, 2003 Visual Neuroscience2 65–76) have suggested that these cues are detected independently, or at least in a mechanism that is able to maintain an apparent independence between the cues. We tested new combinations of OM and CM and found that CM at 0.4 cycle deg−1 facilitates the detection of OM at 0.2 cycle deg−1 when the peaks of contrast align with the extremes of orientation. There is also some evidence of weak facilitation of CM by OM under the same conditions. Further, this facilitation can be predicted by filter-rectify-filter channels optimised for the detection of each cue, adding weight to the argument that texture cues are processed in a single generalised mechanism that nonetheless achieves cue independence or near-independence in many circumstances. We also found that the amount of suprathreshold masking produced by an orientation cue depends on the overall percept formed by that cue.

The efficiency of second order orientation coherence detection

Neurons in early visual cortex respond to both luminance- (1st order) and contrast-modulated (2nd order) local features in the visual field. In later extra-striate areas neurons with larger receptive fields integrate information across the visual field. For example, local luminance-defined features can be integrated into contours and shapes. Evidence for the global integration of features defined by contrast-modulation is less well established. While good performance in some shape tasks has been demonstrated with 2nd order stimuli, the integration of contours fails with 2nd order elements. Recently we developed a global orientation coherence task that is more basic than contour integration, bearing similarity to the well-established global motion coherence task. Similar to our previous 1st order result for this task, we find 2nd order coherence detection to be scale-invariant. There was a small but significant threshold elevation for 2nd order relative to 1st order. We used a noise masking approach to compare the efficiency of orientation integration for the 1st and 2nd order. We find a significant deficit for 2nd order detection at both the local and global level, however the small size of this effect stands in stark contrast against previous results from contour-integration experiments, which are almost impossible with 2nd order stimuli.

Form-cue invariant second-order neuronal responses to contrast modulation in primate area V2

A fundamental task of the visual system is to extract figure-ground boundaries between images of objects, which in natural scenes are often defined not only by luminance differences but also by "second-order" contrast or texture differences. Responses to contrast modulation (CM) and other second-order stimuli have been extensively studied in human psychophysics, but the neuronal substrates of second-order responses in nonhuman primates remain poorly understood. In this study, we have recorded single neurons in area V2 of macaque monkeys, using both CM patterns as well as conventional luminance modulation (LM) gratings. CM stimuli were constructed from stationary sine wave grating carrier patterns, which were modulated by drifting envelope gratings of a lower spatial frequency. We found approximately one-third of visually responsive V2 neurons responded to CM stimuli with a pronounced selectivity to carrier spatial frequencies, and often orientations, that were clearly outside the neurons' passbands for LM gratings. These neurons were "form-cue invariant" in that their tuning to CM envelope spatial frequency and orientation was very similar to that for LM gratings. Neurons were tuned to carrier spatial frequencies that were typically 2-4 octaves higher than their optimal envelope spatial frequencies, similar to results from human psychophysics. These results are distinct from CM responses arising from surround suppression, but could be understood in terms of a filter-rectify-filter model. Such neurons could provide a functionally useful and explicit representation of segmentation boundaries as well as a plausible neural substrate for human perception of second-order boundaries.

Binocular combination of second-order stimuli

Phase information is a fundamental aspect of visual stimuli. However, the nature of the binocular combination of stimuli defined by modulations in contrast, so-called second-order stimuli, is presently not clear. To address this issue, we measured binocular combination for first- (luminance modulated) and second-order (contrast modulated) stimuli using a binocular phase combination paradigm in seven normal adults. We found that the binocular perceived phase of second-order gratings depends on the interocular signal ratio as has been previously shown for their first order counterparts; the interocular signal ratios when the two eyes were balanced was close to 1 in both first- and second-order phase combinations. However, second-order combination is more linear than previously found for first-order combination. Furthermore, binocular combination of second-order stimuli was similar regardless of whether the carriers in the two eyes were correlated, anti-correlated, or uncorrelated. This suggests that, in normal adults, the binocular phase combination of second-order stimuli occurs after the monocular extracting of the second-order modulations. The sensory balance associated with this second-order combination can be obtained from binocular phase combination measurements.

The three dimensions of human visual sensitivity to first-order contrast statistics

This work studies the preattentive discrimination of achromatic textures composed of mixtures of different (Weber) contrasts. These textures differ not at all in local spatial structure, but only in the relative proportions of different contrasts they comprise. It is shown that, like chromatic discrimination, preattentive discrimination of such textures is three-dimensional. The current results do not uniquely determine the characteristics of the three texture filters mediating human discrimination of these textures; they do, however, define the space of textures with 4th-order polynomial histograms to which human vision is sensitive. Three real-valued functions of contrast that collectively capture human sensitivity to the textures in this space are presented.

Separate first- and second-order processing is supported by spatial summation estimates at the fovea and eccentrically

We estimated spatial summation areas for the detection of luminance-modulated (LM) and contrast-modulated (CM) blobs at the fovea, 2.5, 5 and 10 deg eccentrically. Gaussian profiles were added or multiplied to binary white noise to create LM and CM blob stimuli and these were used to psychophysically estimate detection thresholds and spatial summation areas. The results reveal significantly larger summation areas for detecting CM than LM blobs across eccentricity. These differences are comparable to receptive field size estimates made in V1 and V2. They support the notion that separate spatial processing occurs for the detection of LM and CM stimuli.

Local luminance amplitude modulates the interpretation of shape-from-shading in textured surfaces

The pattern of illumination on an undulating surface can be used to infer its 3-D form (shape-from-shading). But the recovery of shape would be invalid if the luminance changes actually arose from changes in reflectance. So how does vision distinguish variation in illumination from variation in reflectance to avoid illusory depth? When a corrugated surface is painted with an albedo texture, the variation in local mean luminance (LM) due to shading is accompanied by a similar modulation in local luminance amplitude (AM). This is not so for reflectance variation, nor for roughly textured surfaces. We used depth mapping and paired comparison methods to show that modulations of local luminance amplitude play a role in the interpretation of shape-from-shading. The shape-from-shading percept was enhanced when LM and AM co-varied (in-phase) and was disrupted when they were out of phase or (to a lesser degree) when AM was absent. The perceptual differences between cue types (in-phase vs out-of-phase) were enhanced when the two cues were present at different orientations within a single image. Our results suggest that when LM and AM co-vary (in-phase) this indicates that the source of variation is illumination (caused by undulations of the surface), rather than surface reflectance. Hence, the congruence of LM and AM is a cue that supports a shape-from-shading interpretation.

The effects of amplitude-spectrum statistics on foveal and peripheral discrimination of changes in natural images, and a multi-resolution model

Psychophysical thresholds were measured for discriminating small changes in spatial features of naturalistic scenes (morph sequences), for foveal and peripheral vision, and under M-scaling. Sensitivity was greatest for scenes with near natural Fourier amplitude slope, perhaps implying that human vision is optimised for natural scene statistics. A low-level model calculated differences in local contrast between pairs of images within a few spatial frequency channels with bandwidth like neurons in V1. The model was "customised" to each observer's contrast sensitivity function for sinusoidal gratings, and it could replicate the "U-shaped" relationships between discrimination threshold and spectral slope, and many differences between picture sets and observers. A single-channel model and an ideal-observer analysis both failed to capture the U-shape.

Human cortical responses to contrast modulations of visual noise

We studied visual evoked potentials (VEPs) elicited by second-order contrast modulations of binary dynamic noise and first-order luminance modulations. Using a 3-point Laplacian operator centred on Oz, we found that contrast modulations of both low and higher spatial frequencies elicited a negative component whose latency was about 200 ms. The latency of this component was significantly longer than that of the early Laplacian components to first-order luminance modulations. These findings could be due to slower first-stage linear filters and additional processing stages of the second-order pathway. The topographical analysis of scalp recorded VEPs to central and half-field stimulation has suggested that the responses to second-order patterns are likely to be generated by neuronal structures within the primary visual cortex which may have inputs from extrastriate neurons via feedback connections.

The detection of motion in chromatic stimuli: first-order and second-order spatial structure

This study provides evidence for the existence of a low-level chromatic motion mechanism and further elucidates the conditions under which its operation becomes measurable in an experimental stimulus. Observers discriminated the direction of motion of amplitude modulated (AM) gratings that were defined by luminance or chromatic variation and masked with spatiotemporally broadband luminance or chromatic noise. The size and retinal location of the stimuli were varied and the effects of broadband noise and grating masks were both compared with the cohort of stimuli. Some significant disparities in the published literature were well explained by the results. In conclusion, evidence for a chromatically sensitive motion mechanism that evades the, detrimental effects of a luminance mask was found only at the fovea and only when the stimulus was small and centrally placed.

Interactions between luminance and contrast signals in global form detection

The human visual system is adept at detecting global structure, or form, within a scene. The initial stage of post-retinal processing for all aspects of vision is fed by On- and Off-centre cells sensitive to centred luminance increments and decrements respectively. These cells provide input to two parallel pathways that process variations in local luminance (first-order pathway) and local contrast (second-order pathway). Here, we investigate the contribution of luminance and contrast information to global form detection, a stage between the extraction of local orientation and the recognition of objects. The underlying processes involve two stages. We find that signals in the On-, Off- and second-order pathways are segregated at both stages of processing. Surprisingly, the non-linear stage in the second-order form pathway is different from that in motion processing: the second-order form detectors show an asymmetry in sensitivity to increments and decrements that is not apparent in motion. A functional architecture for global form detection is proposed along with its possible neural substrates.

Facilitation of contrast detection in near-peripheral vision

Foveal detection of a Gabor patch (target) is facilitated by collinear, displaced high-contrast flankers. Polat and Sagi reported that the same phenomenon occurred in the periphery, but no data were presented [Proc. Natl. Acad. Sci. 91 (1994) 1206]. Others have found no facilitation in a limited number of conditions tested. To resolve this apparent conflict, we measured lateral facilitation in the near-periphery using a range of stimulus parameters. We found facilitation for a range of target-flanker distances for peripheral eccentricities up to 6 degrees , but the magnitude of the effect was less than found in central vision. Facilitation varied across subjects and with spatial frequency. Flanker contrast had no effect over the range evaluated (10-80%). Equal facilitation was found for two global arrangements of the stimulus pattern. Facilitation was found using a temporal, but not a spatial two-alternative forced-choice paradigm, accounting for the different results among previous studies. This finding supports previous indications of the role of attention in altering such facilitation. The value of facilitation from lateral interactions for persons with central vision impairment, who have to shift their attention to a peripheral locus constantly, needs to be examined.

A visual mechanism tuned to black

Chubb et al. [Journal of the Optical Society of America A 11 (1994) 2350] investigated preattentive discrimination of achromatic textures comprising random mixtures of 17 Weber contrasts ranging linearly from -1 to 1. They showed that only a single mechanism B is used to discriminate between textures whose histograms are equated in mean and in variance. Although they provided a partial characterization of B, their methods did not allow them to measure the sensitivity of B to texture mean and variance. Here, additional measurements are performed to complete the functional characterization of B. The results reveal that B (i) is strongly activated by texture elements of the lowest contrast (near -1), (ii) is slightly activated by texture elements of contrast -0.875, and (iii) barely distinguishes the 15 contrasts ranging from -0.75 all the way up to 1. To reflect the sharpness of its tuning to very dark, sparse elements in a predominantly bright scene, we call B the blackshot mechanism.

Temporal properties of the visual responses to luminance and contrast modulated noise

Vision is sensitive to first-order luminance modulations and second-order modulations of carrier contrast. Our knowledge of the temporal properties of second-order vision is insufficient and contradictory. Using temporal summation and reaction time paradigms, we found that the type of visual noise (static or dynamic) determines the temporal properties of the responses to luminance and contrast modulations. In the presence of static noise, the temporal responses to both types of modulation of low and higher spatial frequencies were transient. When dynamic noise was used, the temporal responses to luminance and contrast modulations of higher spatial frequencies were sustained. At low spatial frequency, however, luminance modulations elicited transient responses, while contrast modulated dynamic noise produced sustained responses. The reaction times to near-threshold contrast modulations of low spatial frequency were slower than those to first-order patterns and they did not significantly differ at modulations of higher spatial frequency. The results suggest that the temporal characteristics of first-stage linear filters which feed the second-order pathway may determine the temporal responses to contrast modulated noise.

Sensitivity to contrast modulation: the spatial frequency dependence of second-order vision

We consider the overall shape of the second-order modulation sensitivity function (MSF). Because second-order modulations of local contrast or orientation require a carrier signal, it is necessary to evaluate modulation sensitivity against a variety of carriers before reaching a general conclusion about second-order sensitivity. Here we present second-order sensitivity functions for new carrier types (low pass (1/f) noise, and high pass noise) and demonstrate that, when first-order artefacts have been accounted for, the shape of the resulting MSFs are similar to one another and to those for white and broad band noise. They are all low pass with a likely upper frequency limit in the range 10-20 c/deg, suggesting that detection of second-order stimuli is relatively insensitive to the structure of the carrier signal. This result contrasts strongly with that found for (first-order) luminance modulations of the same noise types. Here the noise acts as mask and each noise type masks most those frequencies that are dominant in its spectrum. Thus the shape of second-order MSFs are largely independent of the spectrum of their noise carrier, but first-order CSFs depend on the spectrum of an additive noise mask. This provides further evidence for the separation of first- and second-order vision and characterises second-order vision as a low pass mechanism.

The effect of pixel nonlinearity on cathode-ray tube-based visual acuity tests

BACKGROUND

Pixel nonlinearity of a cathode-ray tube (CRT) display can cause differences between the actual image and the nominal image. One of the discrepancies, the anisotropy of interactions between neighboring pixels on the same raster line and between neighboring raster lines, may have an impact on the CRT-based visual acuity test where small horizontal and vertical gaps are used. We evaluated this impact.

METHOD

Two high-quality color CRT monitors were tested. The stimulus target was a black square ring on a white background. White gaps of one stroke width were opened in the middle of the straight sides of the square ring. In a gap width comparison study, the up and down gaps were flanked with a one-pixel band on the left and right side. The pixel value of the bands was varied to determine the luminance that made up and down gaps appear to have the same width as left and right gaps. The comparison was made at 1 and 2 m. In a visual acuity study, horizontal gap (left/right) acuity and vertical gap (up/down) acuity were measured separately at several distances between 8 and 11 m. Similar measurements were made when the monitor was rotated 90 degrees.

RESULTS

Gaps with edges that were parallel to raster lines (raster-parallel gaps) appeared wider than gaps with edges that were perpendicular to raster lines (raster-perpendicular gaps). To match the apparent width of the left and right gaps, the two one-pixel bands flanking the up and down gaps required a pixel value that corresponded approximately to a luminance of mid gray, indicating that the apparent width of a four-pixel left or right gap was similar to that of a five-pixel up or down gap. Raster-parallel gaps produced a higher percentage of correct responses than raster-perpendicular gaps in a visual acuity test. When nominal gap widths were equal, left and right gaps produced 10% or more correct responses than up and down gaps at some target sizes, which translated to a two-letter acuity difference. This acuity difference could not be accounted for by uncorrected astigmatism because the anisotropy persisted when the monitor was turned 90 degrees.

CONCLUSIONS

Pixel nonlinearity of a CRT-display results in an anisotropy of gap width that can be observed at and above visual acuity size. This anisotropy may introduce uncertainties in the results of CRT-based visual acuity tests where gaps of different orientations are used.

Lateral interactions: size does matter

Usually a high-contrast, co-local mask increases contrast threshold (inhibition). Interestingly, a laterally displaced mask (flanker) can facilitate contrast detection (Vision Research 33 (1993) 993; 34 (1994) 73). When spatial scaling of these flanker effects was implied, stimulus bandwidth was confounded with spatial frequency (lambda(-1)). Under conditions where at lower spatial frequencies, the size (standard deviation, sigma) of the Gabor patch was smaller (sigma<lambda) than higher spatial frequencies (sigma=lambda), the effect appeared scale invariant. We replicated the original results for all conditions. However, when Gabor size was fixed (sigma=lambda), facilitation changed with spatial frequency (range 2--13 cycles/deg). When Gabor size was varied (sigma=0.5-2 lambda), usually the combination of larger patch sizes and lower spatial frequencies caused inhibition. We were unable to find any conditions that demonstrated spatial scaling. The size, both lambda and sigma, of both stimulus and flankers, influenced contrast threshold. Also, facilitation reduced as contrast of the flankers was reduced to detection threshold. Some facilitation was apparent with sub-threshold flankers. These results need to be reconciled with current models of lateral interactions.

Are corresponding points fixed?

Several investigators have claimed that the retinal coordinates of corresponding points shift with vergence eye movements. Two kinds of shifts have been reported. First, global shifts that increase with retinal eccentricity; such shifts would cause a flattening of the horopter at all viewing distances and would facilitate fusion of flat surfaces. Second, local shifts that are centered on the fovea; such shifts would cause a dimple in the horopter near fixation and would facilitate fusion of points fixated at extreme viewing distances. Nearly all of the empirical evidence supporting shifts of corresponding points comes from horopter measurements and from comparisons of subjective and objective fixation disparity. In both cases, the experimenter must infer the retinal coordinates of corresponding points from external measurements. We describe four factors that could affect this inference: (1) changes in the projection from object to image points that accompany eye rotation and accommodation, (2) fixation errors during the experimental measurements, (3) non-uniform retinal stretching, and (4) changes in the perceived direction of a monocular point when presented adjacent to a binocular point. We conducted two experiments that eliminated or compensated for these potential errors. In the first experiment, observers aligned dichoptic test lines using an apparatus and procedure that eliminated all but the third error. In the second experiment, observers judged the alignment of dichoptic afterimages, and this technique eliminates all the errors. The results from both experiments show that the retinal coordinates of corresponding points do not change with vergence eye movements. We conclude that corresponding points are in fixed retinal positions for observers with normal retinal correspondence.

Interaction between first- and second-order orientation channels revealed by the tilt illusion: psychophysics and computational modelling

This paper examines the interaction between first- and second-order contours in the orientation domain. Using the simultaneous tilt illusion (TI), we show that the apparent rotation of a vertical test grating away from that of a surrounding inducing grating (repulsion effect) occurs when both the inducing and test grating are either first- or second-order. Furthermore, a significant repulsion effect is obtained when a first-order inducing grating surrounds a second-order test. If lateral inhibitory interactions between populations of orientation selective neurons provides a plausible explanation for orientation repulsion effects [Blakemore, C. B. Carpenter, R. H. S. & Georgeson, M. A. (1970) Nature, 228, 37-39], it is likely that the cue-invariant mechanisms that encodes the orientation of first- and second-order contours also exhibit inhibitory interactions. A two-channel computational model of orientation encoding is presented where one channel encodes only first-order stimuli while the second channel encodes both first- and second-order contours. In addition to predicting the orientation repulsion effects we observed, the model also provides a functional account of orientation attraction effects in terms of the responses of populations of orientation-tuned neurons.

The temporal properties of first- and second-order vision

Vision is sensitive to first-order modulations of luminance and second-order modulations of image contrast. There is now a body of evidence that the two types of modulation are detected by separate mechanisms. Some previous experiments on motion detection have suggested that the second-order system is quite sluggish compared to the first-order system. Here we derive temporal properties of first- and second-order vision at threshold from studies of temporal integration and two-pulse summation. Three types of modulation were tested: luminance gratings alone, luminance modulations added to dynamic visual noise, and contrast modulations of dynamic noise. Data from the two-pulse summation experiment were used to derive impulse response functions for the three types of stimulus. These were then used to predict performance in the temporal integration experiment. Temporal frequency response functions were obtained as the Fourier transform of impulse responses derived from data averaged across two observers. The response to noise-free luminance gratings of 2 c/deg was bi-phasic and transient in the time domain, and bandpass in the frequency domain. The addition of dynamic noise caused the response to become mono-phasic, sustained and low-pass. The response to contrast modulated noise (second-order) was also mono-phasic, sustained and low-pass, with only a slightly longer integration time than in the first-order case. The ultimate roll-off at high frequencies was about the same as for the first-order case. We conclude that second-order vision may not be as sluggish as previously thought.

Use of an early nonlinearity to measure optical and receptor resolution in the human infant

We measured the resolution of the optics and receptoral processes in human infants. To do so, we recorded visual-evoked potentials (VEPs) to sampled sinewave gratings, stimuli that generate highly visible distortion products at a nonlinearity early in the retina. We varied the spatial frequency content of the stimulus to determine the frequencies that can be transmitted through the optics and receptors and thereby generate distortion products. Data were collected from adults and 2- to 7-month-old infants. The results indicated that the resolution of the infants' optical/receptoral processes was within a factor of two of adults' even at the earliest ages tested. These first stages of processing, therefore, do not explain infants' poor performance in many visual tasks, or restrict the types of visual stimuli affecting more central mechanisms that undergo experience-dependent development.

Sensitivity to modulations of luminance and contrast in visual white noise: separate mechanisms with similar behaviour

Human vision can detect spatiotemporal information conveyed by first-order modulations of luminance and by second-order, non-Fourier modulations of image contrast. Models for second-order motion have suggested two filtering stages separated by a rectifying nonlinearity. We explore here the encoding of stationary first-order and second-order gratings, and their interaction. Stimuli consisted of 2-D binary, broad-band, static, visual noise sinusoidally modulated in luminance (LM, first-order) or contrast (CM, second-order). Modulation thresholds were measured in a two-interval forced-choice staircase procedure. Sensitivity curves for LM and CM had similar shape as a function of spatial frequency, and as a function of the size of a circular Gaussian blob of modulation. Weak background gratings present in both intervals produced order-specific facilitation: LM background facilitated LM detection (the dipper function) and CM facilitated CM detection. LM did not facilitate CM, nor vice-versa, neither in-phase nor out-of-phase, and this is strong evidence that LM and CM are detected via separate mechanisms. This conclusion was further supported by an experiment on the detection of LM/CM mixtures. From a general mathematical model and a specific computer simulation we conclude that a single mechanism sensitive to both LM and CM cannot predict the pattern of results for mixtures, while a model containing separate pathways for LM and CM, followed by energy summation, does so successfully and is quantitatively consistent with the finding of order-specific facilitation.

Horizontal and vertical disparity, eye position, and stereoscopic slant perception

The slant of a stereoscopically defined surface cannot be determined solely from horizontal disparities or from derived quantities such as horizontal size ratio (HSR). There are four other signals that, in combination with horizontal disparity, could in principle allow an unambiguous estimate of slant: the vergence and version of the eyes, the vertical size ratio (VSR), and the horizontal gradient of VSR. Another useful signal is provided by perspective slant cues. The determination of perceived slant can be modeled as a weighted combination of three estimates based on those signals: a perspective estimate, a stereoscopic estimate based on HSR and VSR, and a stereoscopic estimate based on HSR and sensed eye position. In a series of experiments, we examined human observers' use of the two stereoscopic means of estimation. Perspective cues were rendered uninformative. We found that VSR and sensed eye position are both used to interpret the measured horizontal disparities. When the two are placed in conflict, the visual system usually gives more weight to VSR. However, when VSR is made difficult to measure by using short stimuli or stimuli composed of vertical lines, the visual system relies on sensed eye position. A model in which the observer's slant estimate is a weighted average of the slant estimate based on HSR and VSR and the one based on HSR and eye position accounted well for the data. The weights varied across viewing conditions because the informativeness of the signals they employ vary from one situation to another.