Sensitivity to orientation modulation in micropattern-based textures

Impact of text contrast polarity on the retinal activity in myopes and emmetropes using modified pattern ERG

Environmental factors favoring myopia development are still being studied and there is accumulating evidence for a significant role of nearwork. Recently, reading standard black-on-white text was found to activate the retinal OFF pathway and induce choroidal thinning, which is associated with myopia onset. Contrarily, reading white-on-black text led to thicker choroids, being protective against myopia. Respective effects on retinal processing are yet unknown. Here, we exploratively assessed the impact of contrast polarity on the retinal activity and possible interactions with eccentricity and refractive error. We recorded pattern electroretinograms in myopic and emmetropic adults while presenting a dead leaves stimulus (DLS), overlaid by masks of different size in ring or circle shape, either filled with uniform gray or text of inverted or standard contrast. In myopes, retinal responses for DLS with standard and inverted contrast were larger when the perifovea was stimulated (6-12 deg), however, including the fovea resulted in smaller amplitudes for inverted contrast than in emmetropes. The retina of emmetropes was more sensitive to inverted contrast than to standard and gray within 12 deg, but most sensitive for gray in the perifovea. This demonstrates that the refractive error influences the sensitivity to text contrast polarity, with a special role of the peripheral retina, which is in line with previous studies about blur sensitivity. Defining whether the differences derive from retinal processing or anatomical features of a myopic eye requires further investigation. Our approach might be a first step to explain how nearwork promotes the eye's elongation.

Sensitivity to naturalistic texture relies primarily on high spatial frequencies

Natural images contain information at multiple spatial scales. Though we understand how early visual mechanisms split multiscale images into distinct spatial frequency channels, we do not know how the outputs of these channels are processed further by mid-level visual mechanisms. We have recently developed a texture discrimination task that uses synthetic, multi-scale, "naturalistic" textures to isolate these mid-level mechanisms. Here, we use three experimental manipulations (image blur, image rescaling, and eccentric viewing) to show that perceptual sensitivity to naturalistic structure is strongly dependent on features at high object spatial frequencies (measured in cycles/image). As a result, sensitivity depends on a texture acuity limit, a property of the visual system that sets the highest retinal spatial frequency (measured in cycles/degree) at which observers can detect naturalistic features. Analysis of the texture images using a model observer analysis shows that naturalistic image features at high object spatial frequencies carry more task-relevant information than those at low object spatial frequencies. That is, the dependence of sensitivity on high object spatial frequencies is a property of the texture images, rather than a property of the visual system. Accordingly, we find human observers' ability to extract naturalistic information (their efficiency) is similar for all object spatial frequencies. We conclude that the mid-level mechanisms that underlie perceptual sensitivity effectively extract information from all image features below the texture acuity limit, regardless of their retinal and object spatial frequency.

Second-order texture gratings produce overestimation of height in depictions of rectangles and steps

The horizontal-vertical illusion (HVI) has been proposed as a method to increase the perceived height of steps, increase toe clearance and prevent falls. High contrast vertical stripes are placed on the step riser abutting a horizontal edge-highlighter creating 'T' junctions which are thought to promote the illusion. Various configurations of the HVI were tested including luminance gratings (L) and second-order modulations of contrast (CM), spatial frequency (FM) and orientation (OM). Observers were asked to compare the apparent height of gratings with that of either filled, unmodulated rectangles or unfilled rectangles. Rectangles were presented alone or as part of a step with a highlighter. In some conditions highlighters matched the properties of the grating; in others or not. In one critical experiment, the HVI was compared for steps with highlighters that were separated from the riser by a thin line and those where the risers and highlighters were continuous. All gratings except FM appeared taller when presented in the step configuration with a continuous, matching highlighter. This effect was greatly reduced when a thin line separated the grating from the highlighter and abolished for mis-matched highlighters and risers. In the rectangle conditions, all cues appeared taller than blank rectangles and L and CM appeared taller than filled-unmodulated rectangles. In conclusion, second-order cues may be useful for inducing the HVI onto steps. However, the ability of vertical stripes and edge-highlighters to accentuate perceived step height may be due to aggregation of the highlighter into the grating rather than the normal horizontal-vertical illusion.

Second-order visual sensitivity in the aging population

Most visual and cognitive functions are affected by aging over the lifespan. In this study, our aim was to investigate the loss in sensitivity to different classes of second-order stimuli-a class of stimuli supposed to be mainly processed in extrastriate cortex-in the aging population. These stimuli will then allow one to identify specific cortical deficit independently of visibility losses in upstream parts of the visual pathway. For this purpose, we measured the sensitivity to first-order stimuli and second-order stimuli: orientation-modulated, motion-modulated or contrast-modulated as a function of spatial frequency in 50 aged participants. Overall, we observed a sensitivity loss for all classes of stimuli, but this loss differentially affects the three classes of second-order stimuli tested. It involves all modulation spatial frequencies in the case of motion modulation, but just high modulation spatial frequencies in the case of contrast- and orientation modulations. These observations imply that aging selectively affects the sensitivity to second-order stimuli depending on their type. Since there is evidence that these different second-order stimuli are processed in different regions of extrastriate cortex, this result may suggest that some visual cortical areas are more susceptible to aging effects than others.

Image segmentation driven by elements of form

While luminance, contrast, orientation, and terminators are well-established features that are extracted in early visual processing and support the parsing of an image into its component regions, the role of more complex features, such as closure and convexity, is less clear. A main barrier in understanding the roles of such features is that manipulating their occurrence typically entails changes in the occurrence of more elementary features as well. To address this problem, we developed a set of synthetic visual textures, constructed by replacing the binary coloring of standard maximum-entropy textures with tokens (tiles) containing curved or angled elements. The tokens were designed so that there were no discontinuities at their edges, and so that changing the correlation structure of the underlying binary texture changed the shapes that were produced. The resulting textures were then used in psychophysical studies, demonstrating that the resulting feature differences sufficed to drive segmentation. However, in contrast to previous findings for lower-level features, sensitivities to increases and decreases of feature occurrence were unequal. Moreover, the texture-segregation response depended on the kind of token (curved vs. angular, filled-in vs. outlined), and not just on the correlation structure. Analysis of this dependence indicated that simple closed contours and convex elements suffice to drive image segmentation, in the absence of changes in lower-level cues.

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.

Pooling of first-order inputs in second-order vision

The processing of texture patterns has been characterized by a model that first filters the image to isolate one texture component, then applies a rectifying nonlinearity that converts texture variation into intensity variation, and finally processes the resulting pattern with mechanisms similar to those used in processing luminance-defined images (spatial-frequency- and orientation-tuned filters). This model, known as FRF for filter rectify filter, has the appeal of explaining sensitivity to second-order patterns in terms of mechanisms known to exist for processing first-order patterns. This model implies an unexpected interaction between the first and second stages of filtering; if the first-stage filter consists of narrowband mechanisms tuned to detect the carrier texture, then sensitivity to high-frequency texture modulations should be much lower than is observed in humans. We propose that the human visual system must pool over first-order channels tuned to a wide range of spatial frequencies and orientations to achieve texture demodulation, and provide psychophysical evidence for pooling in a cross-carrier adaptation experiment and in an experiment that measures modulation contrast sensitivity at very low first-order contrast.

Inconsistent channel bandwidth estimates suggest winner-take-all nonlinearity in second-order vision

The processing of texture patterns has been characterized by a model that postulates a first-stage linear filter to highlight a component texture, a pointwise rectification stage to convert contrast for the highlighted texture into mean response strength, followed by a second-stage linear filter to detect the texture-defined pattern. We estimated the spatial-frequency bandwidth of the second-stage filter mediating orientation discrimination of orientation-modulated second-order gratings by measuring threshold elevation in the presence of filtered noise added to the modulation signal. This experiment yielded no evidence for frequency tuning. A second experiment, in which subjects had to detect similar second-order gratings while judging their modulation frequency, produced bandwidth estimates of 1-1.5 octaves, similar to estimated bandwidths of first-order channels. We propose that an additional dominant-response-selection nonlinearity can account for these apparently contradictory results.

Orientation gradient detection exhibits variable coupling between first- and second-stage filtering mechanisms

We investigated sensitivity to orientation modulation using visual stimuli with bandpass filtered noise carriers. We characterized the relationship between the spatial parameters of the modulator and the carrier using a 2-AFC detection task. The relationship between these two parameters is potentially informative of the underlying coupling between first- and second-stage filtering mechanisms, which, in turn, may bear on the interrelationship between striate and extrastriate cortical processing. Our previous experiments on analogous motion stimuli found an optimum sensitivity when the ratio of the carrier and modulator spatial frequency parameters (r) was approximately ten. The current results do not exhibit an optimum sensitivity at a given value of the ratio r. Previous experiments involving second-order modulation sensitivity show an inconsistent range of estimates of optimum sensitivity at values of r between 5 and 50. Our results, using a complementary approach, confirm these discrepancies, demonstrating that the coupling between carrier and modulator frequency parameters depends on a number of stimulus-specific factors, such as contrast sensitivity, stimulus eccentricity, and absolute values of the carrier and modulator spatial frequency parameters. We show that these observations are true for a stimulus limited in eccentricity and that this orientation-modulated stimulus does not exhibit scale invariance. Such processing can not be modeled by a generic filter-rectify-filter model.

Human primary visual cortex (V1) is selective for second-order spatial frequency

A variety of cues can differentiate objects from their surrounds. These include "first-order" cues such as luminance modulations and "second-order" cues involving modulations of orientation and contrast. Human sensitivity to first-order modulations is well described by a computational model involving spatially localized filters that are selective for orientation and spatial frequency (SF). It is widely held that first-order modulations are represented by the firing rates of simple and complex cells ("first-order" neurons) in primary visual cortex (V1) that, likewise, have spatially localized receptive fields that are selective for orientation- and SF. Human sensitivity to second-order modulations is well described by a filter-rectify-filter (FRF) model, with first- and second-order filters selective for orientation and SF. However, little is known about how neuronal activity in visual cortex represents second-order modulations. We tested the FRF model by using an functional (f)MRI-adaptation protocol to characterize the selectivity of activity in visual cortex to second-order, orientation-defined gratings of two different SFs. fMRI responses throughout early visual cortex exhibited selective adaptation to these stimuli. The low-SF grating was a more effective adapter than the high-SF grating, incompatible with the FRF model. To explain the results, we extended the FRF model by incorporating normalization, yielding a filter-rectify-normalize-filter model, in which normalization enhances selectivity for second-order SF but only for low spatial frequencies. We conclude that neurons in human visual cortex are selective for second-order SF, that normalization (surround suppression) contributes to this selectivity, and that the selectivity in higher visual areas is simply fed forward from V1.

Exogenous attention enhances 2nd-order contrast sensitivity

Natural scenes contain a rich variety of contours that the visual system extracts to segregate the retinal image into perceptually coherent regions. Covert spatial attention helps extract contours by enhancing contrast sensitivity for 1st-order, luminance-defined patterns at attended locations, while reducing sensitivity at unattended locations, relative to neutral attention allocation. However, humans are also sensitive to 2nd-order patterns such as spatial variations of texture, which are predominant in natural scenes and cannot be detected by linear mechanisms. We assess whether and how exogenous attention--the involuntary and transient capture of spatial attention--affects the contrast sensitivity of channels sensitive to 2nd-order, texture-defined patterns. Using 2nd-order, texture-defined stimuli, we demonstrate that exogenous attention increases 2nd-order contrast sensitivity at the attended location, while decreasing it at unattended locations, relative to a neutral condition. By manipulating both 1st- and 2nd-order spatial frequency, we find that the effects of attention depend both on 2nd-order spatial frequency of the stimulus and the observer's 2nd-order spatial resolution at the target location. At parafoveal locations, attention enhances 2nd-order contrast sensitivity to high, but not to low 2nd-order spatial frequencies; at peripheral locations attention also enhances sensitivity to low 2nd-order spatial frequencies. Control experiments rule out the possibility that these effects might be due to an increase in contrast sensitivity at the 1st-order stage of visual processing. Thus, exogenous attention affects 2nd-order contrast sensitivity at both attended and unattended locations.

Scale dependence and channel switching in letter identification

Letters are broadband visual stimuli with information useful for discrimination over a wide range of spatial frequencies. Yet, recent evidence suggests that observers use only a single, fixed spatial-frequency channel to identify letters and that the scale of that channel, in units of letter size, is determined by the size of the letter (scale dependence). We report two letter-identification experiments using critical-band masking. With sufficiently high-amplitude, low- or high-pass masking noise, observers switched to a different range of spatial frequencies for the task. Thus, letter channels are not fixed for a given letter size. When an additional white-noise masker was added to the stimulus to flatten the contrast-sensitivity function, the letter channel used by the observer still depended on letter size, further supporting the hypothesis that letter identification is scale dependent.

The movement of motion-defined contours can bias perceived position

Illusory position shifts induced by motion suggest that motion processing can interfere with perceived position. This may be because accurate position representation is lost during successive visual processing steps. We found that complex motion patterns, which can only be extracted at a global level by pooling and segmenting local motion signals and integrating over time, can influence perceived position. We used motion-defined Gabor patterns containing motion-defined boundaries, which themselves moved over time. This 'motion-defined motion' induced position biases of up to 0.5 degrees , much larger than has been found with luminance-defined motion. The size of the shift correlated with how detectable the motion-defined motion direction was, suggesting that the amount of bias increased with the magnitude of this complex directional signal. However, positional shifts did occur even when participants were not aware of the direction of the motion-defined motion. The size of the perceptual position shift was greatly reduced when the position judgement was made relative to the location of a static luminance-defined square, but not eliminated. These results suggest that motion-induced position shifts are a result of general mechanisms matching dynamic object properties with spatial location.

Integration across Time Determines Path Deviation Discrimination for Moving Objects

BACKGROUND

Human vision is vital in determining our interaction with the outside world. In this study we characterize our ability to judge changes in the direction of motion of objects-a common task which can allow us either to intercept moving objects, or else avoid them if they pose a threat.

METHODOLOGY/PRINCIPAL FINDINGS

Observers were presented with objects which moved across a computer monitor on a linear path until the midline, at which point they changed their direction of motion, and observers were required to judge the direction of change. In keeping with the variety of objects we encounter in the real world, we varied characteristics of the moving stimuli such as velocity, extent of motion path and the object size. Furthermore, we compared performance for moving objects with the ability of observers to detect a deviation in a line which formed the static trace of the motion path, since it has been suggested that a form of static memory trace may form the basis for these types of judgment. The static line judgments were well described by a 'scale invariant' model in which any two stimuli which possess the same two-dimensional geometry (length/width) result in the same level of performance. Performance for the moving objects was entirely different. Irrespective of the path length, object size or velocity of motion, path deviation thresholds depended simply upon the duration of the motion path in seconds.

CONCLUSIONS/SIGNIFICANCE

Human vision has long been known to integrate information across space in order to solve spatial tasks such as judgment of orientation or position. Here we demonstrate an intriguing mechanism which integrates direction information across time in order to optimize the judgment of path deviation for moving objects.

On the flexibility of sustained attention and its effects on a texture segmentation task

Previously we have shown that transient attention--the more automatic, stimulus-driven component of spatial attention--enhances spatial resolution. Specifically, transient attention improves texture segmentation at the periphery, where spatial resolution is too low, but impairs performance at central locations, where spatial resolution is already too high for the task. In the present study we investigated whether sustained attention--the more controlled component of spatial attention-can also affect texture segmentation, and if so whether its effect will be similar to that of transient attention. To that end we combined central, symbolic cues with texture displays in which the target appears at several eccentricities. We found that sustained attention can also affect texture segmentation, but unlike transient attention, sustained attention improved performance at all eccentricities. Comparing the effect of pre-cues and post-cues indicated that the benefit brought about by sustained attention is significantly greater than the effect of location uncertainty reduction. These findings indicate that sustained attention is a more flexible mechanism that can optimize performance at all eccentricities in a task where performance is constrained by spatial resolution.

Scale-invariance of receptive field properties in primary visual cortex

Background

Our visual system enables us to recognize visual objects across a wide range of spatial scales. The neural mechanisms underlying these abilities are still poorly understood. Size- or scale-independent representation of visual objects might be supported by processing in primary visual cortex (V1). Neurons in V1 are selective for spatial frequency and thus represent visual information in specific spatial wavebands. We tested whether different receptive field properties of neurons in V1 scale with preferred spatial wavelength. Specifically, we investigated the size of the area that enhances responses, i.e., the grating summation field, the size of the inhibitory surround, and the distance dependence of signal coupling, i.e., the linking field.

Results

We found that the sizes of both grating summation field and inhibitory surround increase with preferred spatial wavelength. For the summation field this increase, however, is not strictly linear. No evidence was found that size of the linking field depends on preferred spatial wavelength.

Conclusion

Our data show that some receptive field properties are related to preferred spatial wavelength. This speaks in favor of the hypothesis that processing in V1 supports scale-invariant aspects of visual performance. However, not all properties of receptive fields in V1 scale with preferred spatial wavelength. Spatial-wavelength independence of the linking field implies a constant spatial range of signal coupling between neurons with different preferred spatial wavelengths. This might be important for encoding extended broad-band visual features such as edges.

Cue combination in a combined feature contrast detection and figure identification task

Target figures defined by feature contrast in spatial frequency, orientation or both cues had to be detected in Gabor random fields and their shape had to be identified in a dual task paradigm. Performance improved with increasing feature contrast and was strongly correlated among both tasks. Subjects performed significantly better with combined cues than with single cues. The improvement due to cue summation was stronger than predicted by the assumption of independent feature specific mechanisms, and increased with the performance level achieved with single cues until it was limited by ceiling effects. Further, cue summation was also strongly correlated among tasks: when there was benefit due to the additional cue in feature contrast detection, there was also benefit in figure identification. For the same performance level achieved with single cues, cue summation was generally larger in figure identification than in feature contrast detection, indicating more benefit when processes of shape and surface formation are involved. Our results suggest that cue combination improves spatial form completion and figure-ground segregation in noisy environments, and therefore leads to more stable object vision.

Visual saliency and texture segregation without feature gradient

A central notion in the study of texture segregation is that of feature gradient (or feature contrast). In orientation-based texture segregation, orientation gradients have indeed played a fundamental role in explaining behavioral results. Here, however, we show that general, smoothly varying, orientation-defined textures (ODTs) exhibit striking perceptual singularities that are completely unpredictable from orientation gradients. These singularities defy not only popular texture segregation theories but also virtually all computational segmentation methods, and they confound previous behavioral studies with smoothly varying ODTs. We provide psychophysical evidence that perceptual singularities in smooth ODTs are salient visual features consistent across observers and with significant effect on the perception and segregation of oriented textures. We further show that, although orientation gradients cannot predict them, perceptual singularities in smooth ODTs emerge directly from, and can be spatially localized by, two ODT curvatures. Given the traditional role of feature gradients in early vision, the significance of these findings extends well beyond orientation-based texture segregation to issues ranging from curve integration and fragment grouping, through the perception of 3D shape, to the functional organization of the primary visual cortex.

Neural mechanisms mediating responses to abutting gratings: luminance edges vs. illusory contours

The discontinuities of phase-shifted abutting line gratings give rise to perception of an "illusory contour" (IC) along the line terminations. Neuronal responses to such ICs have been interpreted as evidence for a specialized visual mechanism, since such responses cannot be predicted from conventional linear receptive fields. However, when the spatial scale of the component gratings (carriers) is large compared to the neuron's luminance passband, these IC responses might be evoked simply by the luminance edges at the line terminations. Thus by presenting abutting gratings at a series of carrier spatial scales to cat A18 neurons, we were able to distinguish genuine nonlinear responses from those due to luminance edges. Around half of the neurons (both simple and complex types) showed a bimodal response pattern to abutting gratings: one peak at a low carrier spatial frequency range that overlapped with the luminance passband, and a second distinct peak at much higher frequencies beyond the neuron's grating resolution. For those bimodally responding neurons, the low-frequency responses were sensitive to carrier phase, but the high-frequency responses were phase-invariant. Thus the responses at low carrier spatial frequencies could be understood via a linear model, while the higher frequency responses represented genuine nonlinear IC processing. IC responsive neurons also demonstrated somewhat lower spatial preference to the periodic contours (envelopes) compared to gratings, but the optimal orientation and motion direction for both were quite similar. The nonlinear responses to ICs could be explained by the same energy mechanism underlying responses to second-order stimuli such as contrast-modulated gratings. Similar neuronal preferences for ICs and for gratings may contribute to the form-cue invariant perception of moving contours.

Adaptive detection mechanisms in globally statistically nonstationary-oriented noise

Studies have shown that human observers can adapt their detection strategies on the basis of the statistical properties of noisy backgrounds. One common property of such studies is that the backgrounds studied are (or are assumed to be) statistically stationary. Less is known about how humans detect signals in the more complex setting of nonstationary backgrounds. We investigated detection performance in the presence of a globally nonstationary oriented noise background. We controlled for noise-correlation effects by considering a stationary background with a power spectrum matched to the average spectrum of the nonstationary process. Performance of a nonadaptive linear filter that was unable to make use of differences in local statistics yielded constant performance in both the stationary and the nonstationary backgrounds. In contrast, performance of an ideal observer that uses local noise statistics yielded substantially higher (140%) detectability with the nonstationary backgrounds than the stationary ones. Human observers showed significantly higher (33%) detection performance in the nonstationary backgrounds, suggesting that they can adapt their detection mechanisms to the local orientation properties.

Noise masking reveals channels for second-order letters

We investigate the channels underlying identification of second-order letters using a critical-band masking paradigm. We find that observers use a single 1-1.5 octave-wide channel for this task. This channel's best spatial frequency (c/letter) did not change across different noise conditions (indicating the inability of observers to switch channels to improve signal-to-noise ratio) or across different letter sizes (indicating scale invariance), for a fixed carrier frequency (c/letter). However, the channel's best spatial frequency does change with stimulus carrier frequency (both in c/letter); one is proportional to the other. Following Majaj et al. (Majaj, N. J., Pelli, D. G., Kurshan, P., & Palomares, M. (2002). The role of spatial frequency channels in letter identification. Vision Research, 42, 1165-1184), we define "stroke frequency" as the line frequency (strokes/deg) in the luminance image. That is, for luminance-defined letters, stroke frequency is the number of lines (strokes) across each letter divided by letter width. For second-order letters, letter texture stroke frequency is the number of carrier cycles (luminance lines) within the letter ink area divided by the letter width. Unlike the nonlinear dependence found for first-order letters (implying scale-dependent processing), for second-order letters the channel frequency is half the letter texture stroke frequency (suggesting scale-invariant processing).

Orientation-selective adaptation to first- and second-order patterns in human visual cortex

Second-order textures-patterns that cannot be detected by mechanisms sensitive only to luminance changes-are ubiquitous in visual scenes, but the neuronal mechanisms mediating perception of such stimuli are not well understood. We used an adaptation protocol to measure neural activity in the human brain selective for the orientation of second-order textures. Functional MRI (fMRI) responses were measured in three subjects to presentations of first- and second-order probe gratings after adapting to a high-contrast first- or second-order grating that was either parallel or orthogonal to the probe gratings. First-order (LM) stimuli were generated by modulating the stimulus luminance. Second-order stimuli were generated by modulating the contrast (CM) or orientation (OM) of a first-order carrier. We used four combinations of adapter and probe stimuli: LM:LM, CM:CM, OM:OM, and LM:OM. The fourth condition tested for cross-modal adaptation with first-order adapter and second-order probe stimuli. Attention was diverted from the stimulus by a demanding task at fixation. Both first- and second-order stimuli elicited orientation-selective adaptation in multiple cortical visual areas, including V1, V2, V3, V3A/B, a newly identified visual area anterior to dorsal V3 that we have termed LO1, hV4, and VO1. For first-order stimuli (condition LM:LM), the adaptation was no larger in extrastriate areas than in V1, implying that the orientation-selective first-order (luminance) adaptation originated in V1. For second-order stimuli (conditions CM:CM and OM:OM), the magnitude of adaptation, relative to the absolute response magnitude, was significantly larger in VO1 (and for condition CM:CM, also in V3A/B and LO1) than in V1, suggesting that second-order stimulus orientation was extracted by additional processing after V1. There was little difference in the amplitude of adaptation between the second-order conditions. No consistent effect of adaptation was found in the cross-modal condition LM:OM, in agreement with psychophysical evidence for weak interactions between first- and second-order stimuli and computational models of separate mechanisms for first- and second-order visual processing.

Is there opponent-orientation coding in the second-order channels of pattern vision?

Is there opponency between orientation-selective processes in pattern perception, analogous to opponency between color mechanisms? Here we concentrate on possible opponency in second-order channels. We compare several possible second-order structures: SIGN-opponent-only channels in which there is no opponency between orientations (also called complex channels or filter-rectify-filter mechanisms); three structures we group under the name ORIENTATION-opponent; and finally BOTH-opponent channels which combine features of both SIGN-opponent-only and ORIENTATION-opponent channels but lead to predictions that are distinct from either of theirs. We measured observers' ability to segregate textures composed of checkerboard and striped arrangements of vertical and horizontal Gabor grating patches. The observers' performance was compared to model predictions from the alternative opponent structures. The experimental results are consistent with SIGN-opponent-only channels. The results rule out the ORIENTATION-opponent and BOTH-opponent structures. Further, when the models were expanded to include a contrast gain-control (inhibition among channels in a normalization network) the SIGN-opponent-only model was also able to explain a contrast-dependent effect we found, thus providing another piece of evidence that such normalization is an important process in human texture perception.

Cross-orientation summation in texture segregation

Human texture vision has been modeled as a filter-rectify-filter (FRF) process, in which '2nd-order' filters detect changes in the rectified outputs of luminance-based '1st-order' filters. This study tested the validity of the two basic assumptions of the standard FRF model, namely (a) that the 2nd-order filters are sensitive to spatial modulations in both contrast and orientation, and (b) that the 2nd-order filters are tuned to different 1st-order orientations. In the first experiment, we tested subthreshold summation between two orthogonal carrier orientations in detection of a texture region, which was defined by contrast modulations across regions in the two carrier orientations, while systematically varying the relative change magnitudes between the two orientations. The results showed that the detection thresholds were determined by spatial difference in the contrast integrated over the two orientations. Orientation difference did act as a segregation cue, but only when there was no differences in carrier contrast. This suggests that two mechanisms are involved in texture segregation; one that detects changes in luminance contrast and another that detects changes in orientation. To further analyze the latter mechanism, a second experiment measured cross-orientation summation in the detection of purely orientation-defined textures, using stimuli that were density modulations of two orientations presented among randomly-orientated distractors. Again, the relative modulation magnitudes between the two orientations was systematically varied. The results are consistent with the notions that (a) the dominant orientation is extracted from the 1st-order outputs before the 2nd-order process, and that (b) the 2nd-order, spatial comparison process integrates those dominant signals over different orientations.

The role of local grouping and global orientation contrast in perception of orientation-modulated textures

We explored the contribution to perception of orientation-modulated textures of visual processes selective either for orientation contrast or orientation grouping. To distinguish between these two processes we manipulated the axis of local grouping of texture elements independently of the direction of global orientation modulation. The general question posed was whether visibility of texture structure (measured as threshold for discriminating spatial-frequency of texture structure) is dependent on the magnitude of orientation contrast, strength and direction of local grouping, or some combination of the two. We demonstrated that the factor of primary importance is the amplitude of global orientation contrast rather than the presence of local grouping content. Using orientation-interleaved textures (containing two superimposed textures modulated around orthogonal orientations), we further showed that orientation single-opponent processes are a more likely candidate for detecting orientation contrast than double-opponent processes.

Orientation opponency in human vision revealed by energy-frequency analysis

Studies of second-order visual processing have primarily been concerned with understanding the mechanisms for detecting spatiotemporal variations in such attributes as contrast, orientation, spatial frequency, etc. Here, we have examined the orientation characteristics of second-order processes using bandpass noise whose Fourier energy is sinusoidally modulated across orientation, rather than across space or time. Sensitivity for detecting orientation-energy modulations was measured as a function of modulation frequency. The sensitivity function was bandpass, with a pronounced peak at an orientation frequency of 4 cycles/pi. An inverse Fourier transform of the sensitivity function revealed a filter profile displaying a centre-surround antagonism across orientation, with an excitatory centre within 6-9 deg and inhibitory lobes at 15-20 deg from the filter's centre. The degree of centre-surround antagonism increased with stimulus size far beyond the spatial range of the first-order filters (more than 64 times the dominant spatial wavelength of the noise carrier). These results suggest that second-order processing involves 'orientation-opponent' channels that extract differences in first-order outputs across orientation over a wide area of the visual field.

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.

Spatiotemporal interactions in detection of texture orientation modulations

Previous studies have revealed spatial and temporal characteristics of texture orientation modulation detection. This study examined spatiotemporal interactions. We measured threshold amplitudes for detecting orientation modulations in various waveforms. The orientation modulations were presented in a dynamic texture display in which the spatial arrangement and mean orientation of elements were randomly updated at a given frame duration (17-900 ms). The results of three experiments all indicated significant spatiotemporal interactions. As the frame duration was decreased, the detection sensitivity declined more steeply for the sinusoidal orientation modulations than for the square and missing-fundamental waveforms (Expt 1), declined more steeply for low spatial-frequency sinusoidal modulations than for high frequency ones (Expt 2), and declined more steeply for sparse textures than for dense textures (Expt 3). These results indicate that the visual system loses its sensitivity more profoundly for long-range orientation modulations than for short-range modulations as the rate of orientation change increases, suggesting that the mechanism for detecting orientation modulation reduces its effective spatial range for rapid input changes.

Properties of second-order spatial frequency channels

The segregation of texture patterns may be carried out by a set of linear spatial filters (to enhance one of the constituent textures), a nonlinearity (to convert the higher contrast of response to that constituent to a higher mean response), and finally subsequent ("second-order") linear spatial filters (to provide a strong response to the texture-defined edge itself). In this paper, the properties of such second-order filters are characterized. Observers were required to detect or discriminate textures that were modulated between predominantly horizontally oriented and predominantly vertically oriented noise patterns. Spatial summation for these patterns reached asymptote for a stimulus size of 15 x 15 deg. Modulation contrast sensitivity was nearly flat over a five-octave range of spatial frequency, but was bandpass when stated as efficiency (relative to an idealized observer confronted with the same task). Increment threshold showed the improved performance with a sub-threshold pedestal seen in the "dipper effect", but the typical Weber's law behavior at higher pedestal contrasts was not observed at the highest pedestal modulation contrasts achievable with our stimuli. Sub-threshold summation experiments indicate that second-order filters have a moderate bandwidth.

Texture-orientation mechanisms pool colour and luminance contrast

Do texture-sensitive mechanisms operate separately on, or pool, luminance and colour contrast information? We addressed this question by measuring threshold-versus-amplitude functions for orientation-modulated (OM) gratings comprised of gabor elements defined by either colour or luminance contrast. In both the uncrossed (all elements in test and mask defined by either colour or luminance contrast) and crossed (equal mixtures of luminance and colour contrast in both test and mask) conditions, evidence of sub-threshold facilitation between test and mask was obtained. The sub-threshold facilitation in the crossed condition could not be accounted for by luminance artifacts in the ostensibly isoluminant gabors. The results are consistent with a single visual mechanism sensitive to OM textures that pools information from both the luminance and chromatic post-receptoral mechanisms.

Scale invariance is driven by stimulus density

Scale invariance refers to aspects of visual perception that remain constant with changes in viewing distance. Previously, Dakin and Herbert [Proc. Roy. Soc. B. 265 (1397) (1998) 659] reported that the spatial integration region (IR) for mirror symmetry in bandpass noise is scale invariant because its dimensions scale with the inverse of peak spatial frequency. In bandpass noise, however, peak spatial frequency covaries with stimulus numerosity (i.e. the total number of information samples) and density (i.e. the total number of information samples per unit area). In this study, we report four experiments that decoupled properties of the retinal image affected by viewing distance--spatial frequency, numerosity, size, and density--and measured their effect on IR size. Stimuli consisted of bandpass microelements with vertically mirror-symmetric but otherwise random positions, and we measured observer resistance to random jitter imposed on microelement position. Results show that jitter resistance and IR size vary with the inverse of stimulus density but are unaffected by changes in stimulus spatial frequency, numerosity, or size. We found the IR has a 2:1 height-to-width aspect ratio and integrates information from approximately 18 microelements regardless of their spatial separation. Our results reveal that stimulus density plays a central role in the visual system's implementation of scale invariance. Using an ideal-observer, we demonstrate that scale invariance reflects genuine neural scale selection rather than a physical limitation on the stimulus' information content. Our findings that jitter resistance and IR size vary with the inverse of density challenge current models of spatial vision but can be reconciled with a model that compares the output of bandpass non-Fourier mechanisms to select spatial scales that match stimulus density.

Discriminating isotrigon textures [corrected]

Higher order spatial correlations can capture edge and object relationships. Isotrigon textures are useful for studying our sensitivity to these correlations. We determined human discrimination performance for 18 isotrigon texture types and compared it with outputs from statistical discriminant models. Some of the models employed versions of the Allan Variance in receptive field outputs. Physiologically plausible mechanisms for such calculations are presented. Two discriminant models emulated human performance well, one based upon a global variance measure, and the other based upon a localised variance with an orientation bias. The 18 texture types were also shown to contain characteristic mini-textures.

Ideal cue combination for localizing texture-defined edges

Many visual tasks can be carried out by using several sources of information. The most accurate estimates of scene properties require the observer to utilize all available information and to combine the information sources in an optimal manner. Two experiments are described that required the observers to judge the relative locations of two texture-defined edges (a vernier task). The edges were signaled by a change across the edge of two texture properties [either frequency and orientation (Experiment 1) or contrast and orientation (Experiment 2)]. The reliability of each cue was controlled by varying the distance over which the change (in frequency, orientation, or contrast) occurred-a kind of "texture blur." In some conditions, the position of the edge signaled by one cue was shifted relative to the other ("perturbation analysis"). An ideal-observer model, previously used in studies of depth perception and color constancy, was fitted to the data. Although the fit can be rejected relative to some more elaborate models, especially given the large quantity of data, this model does account for most trends in the data. A second, suboptimal model that switches between the available cues from trial to trial does a poor job of accounting for the data.

A note about preferred orientations at the first and second stages of complex (second-order) texture channels

Complex (second-order) channels have been useful in explaining many of the phenomena of perceived texture segregation. These channels contain two stages of linear filtering with an intermediate pointwise nonlinearity. One unanswered question about these hypothetical channels is that of the relationship between the preferred orientations of the two stages of filtering. Is a particular orientation at the second stage equally likely to occur with all orientations at the first stage, or is there a bias in the "mapping" between the two stages' preferred orientations? In this study we consider two possible mappings: that where the orientations at the two stages are identical (called "consistent" here) and that where the orientations at the two stages are perpendicular ("inconsistent"). We explore these mappings using a texture-segregation task with textures composed of arrangements of grating-patch elements. The results imply that, to explain perceived texture segregation, complex channels with a consistent orientation mapping must be either somewhat more prevalent or more effective than those with an inconsistent mapping.

Visual response saturation to orientation contrast in the perception of texture boundary

We analyzed how the visual response to orientation modulation in texture patterns varied as a function of the magnitude of orientation contrast. Using a contrast-discrimination technique, we measured threshold increments of orientation contrast (the orientation contrast required for discriminating between two textures) at various pedestal-orientation contrasts. The orientation-contrast-response function estimated for a step-orientation contrast, which produces a vivid percept of surface boundaries, saturated at approximately 30 degrees (experiment 1). The saturation was still evident even when the strength of the step-orientation contrast was reduced by orientation noise (experiment 2), but no strong saturation was found for textures that did not produce a vivid percept of surface boundaries (experiment 3). These results are consistent with the notion that orientation-based texture segregation involves the generation of a neural representation of the surface boundary whose strength is nearly independent of the magnitude of orientation contrast.

Temporal resolution of orientation-based texture segregation

We analysed the temporal-frequency characteristics of two functional processes involved in orientation-based texture segregation: local orientation coding and subsequent orientation-contrast coding. Two texture images, in which each micropattern was rotated by 90 degrees, were alternated at various temporal frequencies. A micropattern was a second-derivative (D2) of a Gaussian that loses orientation information when temporally fused with the orthogonal D2 pattern. We measured the upper temporal-frequency limits for localising the target region whose mean orientation differed from the background by 90 degrees or by 45 degrees. If the temporal limit of the texture perception is determined by the most sluggish processing stage, the temporal limit for the 90 degrees texture should be determined by local orientation coding or by orientation-contrast coding, depending on which stage has the lower temporal precision. On the other hand, the 45 degrees texture should always be segregated below the temporal limit of local orientation coding regardless of the temporal limit of orientation-contrast coding. We found that the temporal limit for the 90 degrees texture was slightly higher than that for the 45 degrees texture under spatial conditions appropriate for texture segregation. Moreover, an orientation-noise analysis of segregation performance for a wide range of temporal frequencies revealed that the temporal-frequency sensitivities for the two textures were nearly identical. These results imply that the temporal limit for orientation-based texture segregation depends only on that of local orientation coding. This conclusion further suggests that the potential temporal resolution of orientation-contrast coding is not lower than that of local orientation coding, which would imply that the orientation-contrast coding is unlikely to be mediated by sluggish neural processes.

What does second-order vision see in an image?

The human visual system is sensitive to both first-order variations in luminance and second-order variations in local contrast and texture. Although there is some debate about the nature of second-order vision and its relationship to first-order processing, there is now a body of results showing that they are processed separately. However, the amount, and nature, of second-order structure present in the natural environment is unclear. This is an important question because, if natural scenes contain little second-order structure in addition to first-order signals, the notion of a separate second-order system would lack ecological validity. Two models of second-order vision were applied to a number of well-calibrated natural images. Both models consisted of a first stage of oriented spatial filters followed by a rectifying nonlinearity and then a second set of filters. The models differed in terms of the connectivity between first-stage and second-stage filters. Output images taken from the models indicate that natural images do contain useful second-order structure. Specifically, the models reveal variations in texture and features defined by such variations. Areas of high contrast (but not necessarily high luminance) are also highlighted by the models. Second-order structure--as revealed by the models--did not correlate with the first-order profile of the images, suggesting that the two types of image 'content' may be statistically independent.

Salience from feature contrast: variations with texture density

The salience of popout targets was measured in regular line arrays as a function of texture density. Test targets (singletons with orientation, motion, or luminance contrast) presented at different raster widths were compared with reference lines (lines brighter than surrounding lines) presented at fixed raster width. The luminance at which the reference target appeared as salient as the particular test target was taken as a measure of the relative salience of the test target. For orientation or motion contrast, targets at medium to small raster widths were far more salient than targets in sparse or very dense line arrangements. For targets defined by luminance contrast, salience variations with texture density were less pronounced. Some subjects also reported salience for lines in sparse arrangements even when these did not display feature contrast. When such non-specific saliency effects were subtracted from the actual measurements, salience curves for orientation or motion contrast revealed peaks of increased sensitivity at line spacings below 2-3 deg and flat curves at larger grid sizes. In an additional experiment, saliency effects from orientation contrast were measured using texture lines of different size. Salience variations were commonly observed. However, the curves were not found to scale with the different sizes of texture elements but were constantly related to the free space between neighbouring lines. This suggests that peaks in the salience profiles reflect the limited spatial extent of the underlying neural mechanisms.

Alignment of orientation-modulated textures

We conducted a Vernier acuity experiment using orientation-modulated (OM) textures in which the overall shape (skewness) of the modulations was manipulated independently of their orientation content. Misalignments between OMs were consistent with the application of global positional tags, but not on the basis of a single cue (e.g. centroid, peak, or zero-crossing). Instead, modelling of our results in terms of orientation-opponent spatial filters not only led to an excellent fit, but also to estimates of the size and shape of these filters that correspond closely to those made by other researchers using a different task and different stimulus parameters and configurations.

Orientation integration in detection and discrimination of contrast-modulated patterns

Orientation detection and discrimination thresholds were measured for Gabor 'envelopes' formed from contrast-modulation of luminance 'carriers'. Consistent with previous research differences between carrier and envelope orientation had no effect on sensitivity to envelopes. Using plaid carriers in which the proportion of contrast modulation 'carried' by each plaid component was systematically manipulated, it was shown that this tolerance to carrier-envelope orientation difference reflects linear summation across orientation indicative of a single second-stage channel coding for contrast-defined structure. That contrast envelopes did not exhibit linear summation across spatial-frequency, nor across combinations of orientation and spatial-frequency differences, suggests that these second-order channels operate only within certain spatial scales. Using arrays of Gabor micropatterns as carriers in which the orientation distribution of the carriers was manipulated independently of the difference between envelope orientation and mean carrier orientation, it was further demonstrated that the locus of orientation integration must occur prior to envelope detection. In the context of two-stage models that incorporate a non-linearity between the stages, the pattern of results obtained is consistent with the operation of an orientation pooling process between first-stage and second-stage channels, analogous to having all filters of the first-stage feed into all filters of the second-stage within the same spatial-frequency band.

Luminance spatial frequency differences facilitate the segmentation of superimposed textures

Do superimposed textures segregate on the basis of a difference in their luminance spatial frequency? We addressed this question using orientation-gratings, which consist of dense arrays of Gabor micropatterns whose orientations vary sinusoidally across space. Two orientation gratings of the same texture spatial frequency were combined in anti-phase, to produce a 'dual-modulation' orientation grating. Thresholds for detecting the dual-modulation gratings were measured as a function of the difference in Gabor spatial frequency between the two grating components. When the two components were made from the same Gabors, thresholds were relatively high. However a one octave difference in Gabor spatial frequency between the components caused thresholds to fall close to those of single-modulation orientation gratings. The fall in threshold was accompanied by a change in appearance of the stimulus; to that of two transparent, interwoven, flow patterns. We show that these results are incompatible with current Filter-Rectify-Filter models of 'second-order' pattern detection. Rather, they favour the idea that feature analysis precedes texture analysis, with the visual system encoding local orientation content prior to the texture stage.

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.

On the mechanism for scale invariance in orientation-defined textures

Texture perception is generally found to be scale invariant, that is, the perceived properties of textures do not change with viewing distance. Previously, Kingdom, F. A. A., Keeble, D. R. T., & Moulden, B. (Vision Research, 1995, 35, 79-91) showed that the orientation modulation function (OMF), which describes sensitivity to sinusoidal modulations of micropattern orientation as a function of modulation spatial frequency, was scale invariant--peak sensitivity occurred at a modulation spatial frequency which was invariant with viewing distance when modulation frequency was plotted in object units, e.g. cycles cm-1. We have attempted to determine the mechanism underlying the scale invariant properties of the OMF. We first confirmed that the OMF was scale invariant using Gabor-micropattern textures. We then measured OMFs at a number of viewing distances, while holding constant various stimulus features in the retinal image. The question was which stimulus feature(s) disrupted scale invariance when manipulated in this way. We found that the scale (size) of the micropatterns was a critical factor and that the most important scale parameter was the micropatterns' carrier spatial frequency. Micropattern length and density were shown to have a small influence on scale invariance, while micropattern width had no influence at all. These results are consistent with the idea that scale invariance in orientation-defined textures is a consequence of 'second-stage' texture-sensitive mechanisms being tied in spatial scale selectivity to their 'first-stage' luminance-contrast-sensitive inputs.

Orientation-based texture segmentation in strabismic amblyopia

Texture segmentation of 'target' Gabors from an array of 'background' Gabors was measured in terms of the difference in orientation between the two regions, as well as the difference in orientation within each region. Segmentation was shown to occur on the basis of local orientation differences at the boundary between the target and background regions (Nothdurft, H.C. (1992). Feature analysis and the role of similarity in preattentive vision. Perception and Psychophysics, 52, 355-375.). We obtained similar results for both the amblyopic and non-amblyopic eye of three strabismic amblyopes, and showed also that the effects of texture undersampling and positional jitter were similar for the two eyes. This pattern of results is consistent with intact mechanisms of texture perception in amblyopic cortex, and suggests also that any amblyopic deficits in first-order cortical units (undersampling and/or positional uncertainty) do not limit higher-order texture segmentation processes. Therefore, first- and second-order processes involved in perceptual grouping of oriented elements (that appear to be abnormal in amblyopic cortex; Kovács, I., Polat, U., Norcia, A.M. (1996). Breakdown of binding mechanisms in amblyopia. Association for Research in Vision and Ophthalmology Abstracts; Mussap, A.J., Levi, D.M. (1995). Amblyopic deficits in perception of second-order orientation. Investigative Ophthalmology and Visual Science (Supplement), 36, S634; Mussap, A.J., Levi, D.M. (1998). Amblyopic deficits in perceptual grouping. Vision Research, submitted) do not contribute to texture perception based on orientation contrast.

Spatial frequency discrimination and detection characteristics for gratings defined by orientation texture

We describe evidence consistent with the proposal that the visual system contains a parallel array of size-tuned mechanisms sensitive to orientation texture-defined (OTD) form, and propose that the relative activity of these mechanisms determines spatial frequency discrimination threshold for OTD gratings. Using a pattern of short lines we measured spatial frequency discrimination thresholds for OTD gratings and luminance-defined (LD) gratings. For OTD gratings, the orientation of texture lines varied sinusoidally across the bars of the gratings, but line luminance was constant. For LD gratings, line orientation was constant, but line luminance varied sinusoidally across the bars of the grating. When the number of texture lines (i.e. spatial samples) per grating cycle was below about six, spatial sampling strongly affected both the spatial frequency discrimination and grating detection thresholds for OTD and LD gratings. However, when the number of spatial samples per grating cycle exceeded about six, plots of both discrimination threshold and detection threshold were different for OTD and LD gratings. For an OTD grating of any given spatial frequency, spatial frequency discrimination threshold fell as the number of samples per grating cycle was increased while holding texture line length constant: the lower limit was reached at six to ten samples per cycle. When we progressively increased the viewing distance (keeping the cycles per degree (cpd) constant), spatial frequency discrimination threshold reached a lower limit and increased thereafter. We propose that this minimum threshold represents a balance between opposing effects of the number of samples per grating cycle and the length of texture lines, and approaches the absolute physiological lower limit for OTD gratings. Spatial frequency discrimination was possible up to at least 7 cpd. Grating acuity for an OTD grating was considerably lower than the physiological limit for LD gratings, presumably because detectors of OTD form include a spatial integration stage following the processing of individual lines. For an LD grating, discrimination threshold fell as the number of samples per grating cycle was increased and asymptoted at six to ten samples per cycle. Spatial frequency discrimination thresholds for OTD and LD gratings were similar at low spatial frequencies (up to 3-4 cpd), but increased more steeply for OTD gratings at high spatial frequencies. For both OTD and LD gratings, discrimination threshold fell steeply as the number of grating cycles was increased from 0.5 to ca. 2.5 cycles, and thereafter decreased more slowly or not at all suggesting that, for both OTD and LD gratings, spatial frequency discrimination can be regarded as a special case of line interval or bar width discrimination. As orientation contrast was progressively increased, discrimination threshold for an OTD grating fell steeply up to about four to five times grating detection threshold, then saturated. This parallels the effect of luminance contrast on discrimination threshold for an LD grating.

Spatial summation in simple (Fourier) and complex (non-Fourier) texture channels

Complex (non-Fourier, second-order) channels have been proposed to explain aspects of texture-based region segregation and related perceptual tasks. Complex channels contain two stages of linear filtering with an intermediate pointwise nonlinearity. The intermediate nonlinearity is crucial. Without it, a complex channel is equivalent to a single linear filter (a simple channel). Here we asked whether the intermediate nonlinearity is piecewise-linear (an ordinary rectifier), or compressive, or expansive. We measured the perceptual segregation between element-arrangement textures where the contrast and area of the individual elements were systematically varied. For solid-square elements, the tradeoff between contrast and area was approximately linear, consistent with simple linear channels. For Gabor-patch elements, however, the tradeoff was highly nonlinear, consistent with complex channels in which the intermediate nonlinearity is expansive (with an exponent somewhat higher than 2). Also, substantial individual differences in certain details were explainable by differential intrusion from "off-frequency" complex channels. Lastly, the results reported here (in conjunction with those of other studies) suggest that the strongly compressive intensive nonlinearity previously known to act in texture segregation cannot be attributed to a compressive nonlinearity acting locally and relatively early (before the spatial-frequency and orientation-selective channels) but could result from inhibition among the channels (as in a normalization network).

The computation of orientation statistics from visual texture

This paper examines how observers estimate the overall orientation of spatially disorganised textures containing variable orientation. Experiments used asymmetrical distributions of orientations to separate the predictions from different models of average orientation estimation. Stimuli were composed of two spatially intermingled sets of oriented patches, each set having Gaussian distributed element orientation. The threshold separation of the means of the two sets was determined for a variety of tasks. Discrimination of these textures from a reference composed of two sets with the same mean orientation was well predicted by discrimination of orientation variability. A single interval judgement of which set contained more elements required a greater separation of the set orientations and suggested that the sets must be resolved in the orientation domain for independent representation of their properties. That resolution is required to perform this task further suggests that orientational skew is not coded. Threshold offsets for judgement of average orientation were re-expressed as shifts of four candidate features for coding the central tendency of texel orientations. Comparison with similar thresholds for single distributions of orientations indicated that average orientation is assigned to the centroid of a set of orientation measures.

A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures

Two distinct paradigms have characterized most previous studies of texture perception: one has dealt with texture segregation, the other with the processing of texture gradients. Typically, studies of texture segregation have used stimuli with abrupt textural variations, whereas studies of texture gradient processing have used stimuli with smooth textural variations. In this study we have asked whether the mechanisms which process abrupt and smooth textural variations are the same, by considering whether a simple linear model can account for the detection of orientation modulation in micropattern-based textures with three types of modulation: sine-wave (SN), square-wave (SQ) and missing fundamental (MF). The MF waveform was constructed by removing the fundamental harmonic from a square-wave. We found a clear overall ordering of sensitivity: SQ > SN > MF. We found that sensitivity to the SQ and MF stimuli could be predicted very well from the SN data if one assumed that the r.m.s. output of a single linear channel underlay the detection of the orientation modulation. This suggests that the detection of both abrupt and smooth changes in orientation-defined textures is subserved by a common mechanism which mimics the operation of a single linear channel.