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

Contrast Sensitivity on 1/f Noise Is More Greatly Impacted by Older Age for the Fovea Than Parafovea

SIGNIFICANCE

Contrast sensitivity changes across the visual field with age and is often measured clinically with various forms of perimetry on plain backgrounds. In daily life, the visual scene is more complicated, and therefore, the standard clinical measures of contrast sensitivity may not predict a patient's visual experience in more natural environments.

PURPOSE

This study aims to determine whether contrast thresholds in older adults are different from younger adults when measured on a 1/f noise background (a nonuniform background whose spatial frequency content is similar to those present in the natural vision environments).

METHODS

Twenty younger (age range, 20 to 35 years) and 20 older adults (age range, 61 to 79 years) with normal ocular health were recruited. Contrast thresholds were measured for a Gabor patch of 6 cycles per degree (sine wave grating masked by a Gaussian envelope of standard deviation 0.17°) presented on 1/f noise background (root-mean-square contrast, 0.05 and 0.20) that subtended 15° diameter of the central visual field. The stimulus was presented at four eccentricities (0°, 2°, 4°, and 6°) along the 45° meridian in the noise background, and nine contrast levels were tested at each eccentricity. The proportion of correct responses for detecting the target at each eccentricity was obtained, and psychometric functions were fit to estimate the contrast threshold.

RESULTS

Older adults demonstrate increased contrast thresholds compared with younger adults. There was an eccentricity-dependent interaction with age, with the difference between groups being highest in the fovea compared with other eccentricities. Performance was similar for the two noise backgrounds tested.

CONCLUSIONS

Our results revealed a strong eccentricity dependence in performance between older and younger adults, highlighting age-related differences in the contrast detection mechanisms between fovea and parafovea for stimuli presented on nonuniform backgrounds.

Desenvolvimento e validação de medidas psicofísicas de sensibilidade ao contraste de segunda-ordem

A medida de sensibilidade ao contraste (SC) de primeira ordem é frequentemente utilizada para avaliação da percepção espacial. Nosso objetivo foi desenvolver e validar um teste de SC de segunda ordem para aplicação clínica. Modificações metodológicas foram realizadas na rotina psicofísica para redução do tempo de testagem e no primeiro experimento validamos a nova metodologia. Em um segundo experimento, dezesseis participantes foram testados nas mesmas condições do primeiro experimento. As medidas de consistência interna por alfa de Cronbach foram robustas para a medida de primeira ordem sendo α= 0,788, segunda ordem por ruído branco α= 0,668 e por ruído rosa α= 0,717. O desenvolvimento e validação deste novo experimento para medidas de SC de segunda ordem permitirá avançar nos estudos dos mecanismos básicos da percepção de espaço para estímulos complexos, assim como a aplicação clínica em diversas doenças.

Different luminance- and texture-defined contrast sensitivity profiles for school-aged children

Our current understanding of how the visual brain develops is based largely on the study of luminance-defined information processing. This approach, however, is somewhat limiting, since everyday scenes are composed of complex images, consisting of information characterized by physical attributes relating to both luminance and texture. Few studies have explored how contrast sensitivity to texture-defined information develops, particularly throughout the school-aged years. The current study investigated how contrast sensitivity to luminance- (luminance-modulated noise) and texture-defined (contrast-modulated noise) static gratings develops in school-aged children. Contrast sensitivity functions identified distinct profiles for luminance- and texture-defined gratings across spatial frequencies (SFs) and age. Sensitivity to luminance-defined gratings reached maturity in childhood by the ages of 9–10 years for all SFs (0.5, 1, 2, 4 and 8 cycles/degree or cpd). Sensitivity to texture-defined gratings reached maturity at 5–6 years for low SFs and 7–8 years for high SFs (i.e., 4 cpd). These results establish that the processing of luminance- and texture-defined information develop differently as a function of SF and age.

Interocular ND filter suppression: Eccentricity and luminance polarity effects

The depth and extent of interocular suppression were measured in binocularly normal observers who unilaterally adapted to neutral density (ND) filters (0, 1.5, 2, and 3 ND). Suppression was measured by dichoptically matching sectors of a ring presented to the adapted eye to a fixed contrast contiguous ring presented to the non-adapted eye. Other rings of alternating polarity were viewed binocularly. Rings were defined by luminance (L), luminance with added dynamic binary luminance noise (LM), and contrast modulating the same noise (CM). Interocular suppression depth increased with increasing ND, nearing significance (p = 0.058) for 1.5 ND. For L and LM stimuli, suppression depth across eccentricity (±12° visual field) differed for luminance increment (white) versus luminance decrement (black) stimuli, potentially confounding eccentricity results. Suppression for increment-only (white) luminance stimuli was steeper centrally and extended across the visual field, but was deeper for L than for LM stimuli. Suppression for decrement-only (black) luminance stimuli revealed only central suppression. Suppression was deeper with CM than LM stimuli, suggesting that CM stimuli are extracted in areas receiving predominantly binocular input which may be more sensitive to binocular disruption. Increment (white) luminance stimuli demonstrate deeper interocular suppression in the periphery than decrement (black) stimuli, so they are more sensitive to changes in peripheral suppression. Asymmetry of suppression in the periphery for opposite polarity luminance stimuli may be due to interocular receptive field size mismatch as a result of dark adaptation separately affecting ON and OFF pathways. Clinically, measurement of suppression with CM stimuli may provide the best information about post-combination binocularity.

Modeling second-order boundary perception: A machine learning approach

Visual pattern detection and discrimination are essential first steps for scene analysis. Numerous human psychophysical studies have modeled visual pattern detection and discrimination by estimating linear templates for classifying noisy stimuli defined by spatial variations in pixel intensities. However, such methods are poorly suited to understanding sensory processing mechanisms for complex visual stimuli such as second-order boundaries defined by spatial differences in contrast or texture. We introduce a novel machine learning framework for modeling human perception of second-order visual stimuli, using image-computable hierarchical neural network models fit directly to psychophysical trial data. This framework is applied to modeling visual processing of boundaries defined by differences in the contrast of a carrier texture pattern, in two different psychophysical tasks: (1) boundary orientation identification, and (2) fine orientation discrimination. Cross-validation analysis is employed to optimize model hyper-parameters, and demonstrate that these models are able to accurately predict human performance on novel stimulus sets not used for fitting model parameters. We find that, like the ideal observer, human observers take a region-based approach to the orientation identification task, while taking an edge-based approach to the fine orientation discrimination task. How observers integrate contrast modulation across orientation channels is investigated by fitting psychophysical data with two models representing competing hypotheses, revealing a preference for a model which combines multiple orientations at the earliest possible stage. Our results suggest that this machine learning approach has much potential to advance the study of second-order visual processing, and we outline future steps towards generalizing the method to modeling visual segmentation of natural texture boundaries. This study demonstrates how machine learning methodology can be fruitfully applied to psychophysical studies of second-order visual processing.

Many naturally occurring visual boundaries are defined by spatial differences in features other than luminance, for example by differences in texture or contrast. Quantitative models of such “second-order” boundary perception cannot be estimated using the standard regression techniques (known as “classification images”) commonly applied to “first-order”, luminance-defined stimuli. Here we present a novel machine learning approach to modeling second-order boundary perception using hierarchical neural networks. In contrast to previous quantitative studies of second-order boundary perception, we directly estimate network model parameters using psychophysical trial data. We demonstrate that our method can reveal different spatial summation strategies that human observers utilize for different kinds of second-order boundary perception tasks, and can be used to compare competing hypotheses of how contrast modulation is integrated across orientation channels. We outline extensions of the methodology to other kinds of second-order boundaries, including those in natural images.

Apparent shift in long-range motion trajectory by local pattern orientation

The present study shows that the apparent direction of a moving pattern is systematically affected by its orientation. We found that the perceived direction of motion of a single Gabor grating changing position in discrete steps interleaved by blank inter-stimulus interval (ISI) is biased toward the orientation of the grating. This orientation-induced motion shift peaks for grating orientations ~±15 deg away from the physical motion trajectory and was profound for relatively short distances. Orientation adaptation revealed that the directional shift is determined by the apparent –not the physical –orientation of the grating, and a subsequent experiment demonstrated that directional shift is also influenced by the orientation of the contrast-defined stimulus envelope. Results provide further evidence that the apparent trajectory of a motion stimulus is determined by interactions between motion and pattern information at relatively high levels of visual processing.

The Effect of Spatial-Frequency Filtering on the Visual Processing of Global Structure

In three experiments we measured reaction times (RTs) and error rates in identifying the global structure of spatially filtered stimuli whose spatial-frequency content was selected by means of three types of 2-D isotropic filters (Butterworth of order 2, Butterworth of order 10, and a filters with total or partial Gaussian spectral profile). In each experiment, low-pass (LP), band-pass (BP), and high-pass (HP) filtered stimuli, with nine centre or cut-off spatial frequencies, were used. Irrespective of the type of filter, the experimental results showed that: (a) RTs to stimuli with low spatial frequencies were shorter than those to stimuli with medium or high spatial frequencies, (b) RTs to LP filtered stimuli were nearly constant, but they increased in a non-monotonic way with the filter centre spatial frequency in BP filtered stimuli and with the filter cut-off frequency in HP filtered stimuli, and (c) the identification of the global pattern occurred with all visible stimuli used, including BP and HP images without low spatial frequencies. To remove the possible influence of the energy, a fourth experiment was conducted with Gaussian filtered stimuli of equal contrast power ( crms = 0.065). Similar results to those described above were found for stimuli with spatial-frequency content higher than 2 cycles deg−1. A model of isotropic first-order visual channels collecting the stimulus spectral energy in all orientations explains the RT data. A subsequent second-order nonlinear amplitude demodulation process, applied to the output of the most energetic first-order channel, could explain the perception of global structure of each spatially filtered stimulus, including images lacking low spatial frequencies.

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.

Correlated and uncorrelated invisible temporal white noise alters mesopic rod signaling

We determined how rod signaling at mesopic light levels is altered by extrinsic temporal white noise that is correlated or uncorrelated with the activity of one (magnocellular, parvocellular, or koniocellular) postreceptoral pathway. Rod and cone photoreceptor excitations were independently controlled using a four-primary photostimulator. Psychometric (Weibull) functions were measured for incremental rod pulses (50 to 250 ms) in the presence (or absence; control) of perceptually invisible subthreshold extrinsic noise. Uncorrelated (rod) noise facilitates rod detection. Correlated postreceptoral pathway noise produces differential changes in rod detection thresholds and decreases the slope of the psychometric functions. We demonstrate that invisible extrinsic noise changes rod-signaling characteristics within the three retinogeniculate pathways at mesopic illumination depending on the temporal profile of the rod stimulus and the extrinsic noise type.

Broad bandwidth of perceptual learning in second-order contrast modulation detection

Comparing characteristics of learning in first- and second-order systems might inform us about different neural plasticity in the two systems. In the current study, we aim to determine the properties of perceptual learning in second-order contrast modulation detection in normal adults. We trained nine observers to detect second-order gratings at an envelope modulation spatial frequency of 8 cycles/° with their nondominant eyes. We found that, although training generated the largest improvements around the trained frequency, contrast sensitivity over a broad range of spatial frequencies also improved, with a 4.09-octave bandwidth of perceptual learning, exhibiting specificity to the trained spatial frequency as well as a relatively large degree of generalization. The improvements in the modulation sensitivity function (MSF) were not significantly different between the trained and untrained eyes. Furthermore, training did not significantly change subjects' ability in detecting first-order gratings. Our results suggest that perceptual learning in second-order detection might occur at the postchannel level in binocular neurons, possibly through reducing the internal noise of the visual system.

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.

Perceived contrast in complex images

To understand how different spatial frequencies contribute to the overall perceived contrast of complex, broadband photographic images, we adapted the classification image paradigm. Using natural images as stimuli, we randomly varied relative contrast amplitude at different spatial frequencies and had human subjects determine which images had higher contrast. Then, we determined how the random variations corresponded with the human judgments. We found that the overall contrast of an image is disproportionately determined by how much contrast is between 1 and 6 c/°, around the peak of the contrast sensitivity function (CSF). We then employed the basic components of contrast psychophysics modeling to show that the CSF alone is not enough to account for our results and that an increase in gain control strength toward low spatial frequencies is necessary. One important consequence of this is that contrast constancy, the apparent independence of suprathreshold perceived contrast and spatial frequency, will not hold during viewing of natural images. We also found that images with darker low-luminance regions tended to be judged as having higher overall contrast, which we interpret as the consequence of darker local backgrounds resulting in higher band-limited contrast response in the visual system.

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.

Foveal visual acuity is worse and shows stronger contour interaction effects for contrast-modulated than luminance-modulated Cs

Contrast-modulated (CM) stimuli are processed by spatial mechanisms that operate at larger spatial scales than those processing luminance-modulated (LM) stimuli and may be more prone to deficits in developing, amblyopic, and aging visual systems. Understanding neural mechanisms of contour interaction or crowding will help in detecting disorders of spatial vision. In this study, contour interaction effects on visual acuity for LM and CM C and bar stimuli are assessed in normal foveal vision. In Experiment 1, visual acuity is measured for all-LM and all-CM stimuli, at ~3.5× above their respective modulation thresholds. In Experiment 2, visual acuity is measured for Cs and bars of different type (LM C with CM bars and vice versa). Visual acuity is degraded for CM compared with LM Cs (0.46 ± 0.04 logMAR vs. 0.18 ± 0.04 logMAR). With nearby bars, CM acuity is degraded further (0.23 ± 0.01 logMAR or ~2 lines on an acuity chart), significantly more than LM acuity (0.11 ± 0.01 logMAR, ~1 line). Contour interaction for CM stimuli extends over greater distances (arcmin) than it does for LM stimuli, but extents are similar with respect to acuities (~3.5× the C gap width). Contour interaction is evident when the Cs and bars are defined differently: it is stronger when an LM C is flanked by CM bars (0.17 ± 0.03 logMAR) than when a CM C is flanked by LM bars (0.08 ± 0.02 logMAR). Our results suggest that contour interaction for foveally viewed acuity stimuli involves feature integration, such that the outputs of receptive fields representing Cs and bars are combined. Contour interaction operates at LM and CM representational stages, it can occur across stage, and it is enhanced at the CM stage. Greater contour interaction for CM Cs and bars could hold value for visual acuity testing and earlier diagnosis of conditions for which crowding is important, such as in amblyopia.

Power spectrum model of visual masking: simulations and empirical data

In the study of the spatial characteristics of the visual channels, the power spectrum model of visual masking is one of the most widely used. When the task is to detect a signal masked by visual noise, this classical model assumes that the signal and the noise are previously processed by a bank of linear channels and that the power of the signal at threshold is proportional to the power of the noise passing through the visual channel that mediates detection. The model also assumes that this visual channel will have the highest ratio of signal power to noise power at its output. According to this, there are masking conditions where the highest signal-to-noise ratio (SNR) occurs in a channel centered in a spatial frequency different from the spatial frequency of the signal (off-frequency looking). Under these conditions the channel mediating detection could vary with the type of noise used in the masking experiment and this could affect the estimation of the shape and the bandwidth of the visual channels. It is generally believed that notched noise, white noise and double bandpass noise prevent off-frequency looking, and high-pass, low-pass and bandpass noises can promote it independently of the channel's shape. In this study, by means of a procedure that finds the channel that maximizes the SNR at its output, we performed numerical simulations using the power spectrum model to study the characteristics of masking caused by six types of one-dimensional noise (white, high-pass, low-pass, bandpass, notched, and double bandpass) for two types of channel's shape (symmetric and asymmetric). Our simulations confirm that (1) high-pass, low-pass, and bandpass noises do not prevent the off-frequency looking, (2) white noise satisfactorily prevents the off-frequency looking independently of the shape and bandwidth of the visual channel, and interestingly we proved for the first time that (3) notched and double bandpass noises prevent off-frequency looking only when the noise cutoffs around the spatial frequency of the signal match the shape of the visual channel (symmetric or asymmetric) involved in the detection. In order to test the explanatory power of the model with empirical data, we performed six visual masking experiments. We show that this model, with only two free parameters, fits the empirical masking data with high precision. Finally, we provide equations of the power spectrum model for six masking noises used in the simulations and in the experiments.

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.

Perceptual learning of second order cues for layer decomposition

Luminance variations are ambiguous: they can signal changes in surface reflectance or changes in illumination. Layer decomposition-the process of distinguishing between reflectance and illumination changes-is supported by a range of secondary cues including colour and texture. For an illuminated corrugated, textured surface the shading pattern comprises modulations of luminance (first order, LM) and local luminance amplitude (second-order, AM). The phase relationship between these two signals enables layer decomposition, predicts the perception of reflectance and illumination changes, and has been modelled based on early, fast, feed-forward visual processing (Schofield et al., 2010). However, while inexperienced viewers appreciate this scission at long presentation times, they cannot do so for short presentation durations (250 ms). This might suggest the action of slower, higher-level mechanisms. Here we consider how training attenuates this delay, and whether the resultant learning occurs at a perceptual level. We trained observers to discriminate the components of plaid stimuli that mixed in-phase and anti-phase LM/AM signals over a period of 5 days. After training, the strength of the AM signal needed to differentiate the plaid components fell dramatically, indicating learning. We tested for transfer of learning using stimuli with different spatial frequencies, in-plane orientations, and acutely angled plaids. We report that learning transfers only partially when the stimuli are changed, suggesting that benefits accrue from tuning specific mechanisms, rather than general interpretative processes. We suggest that the mechanisms which support layer decomposition using second-order cues are relatively early, and not inherently slow.

Visual chimaeras obtained with the Riesz transform

Similar to an auditory chimaera (Smith et al, 2002 Nature 416 87-90), a visual chimaera can be defined as a synthetic image which has the fine spatial structure of one natural image and the envelope of another image in each spatial frequency band. Visual chimaeras constructed in this way could be useful to vision scientists interested in the study of interactions between first-order and second-order visual processing. Although it is almost trivial to generate 1-D chimaeras by means of the Hilbert transform and the analytic signal, problems arise in multidimensional signals like images given that the partial directional Hilbert transform and current 2-D demodulation algorithms are anisotropic or orientation-variant procedures. Here, we present a computational procedure to synthesise visual chimaeras by means of the Riesz transform--an isotropic generalisation of the Hilbert transform for multidimensional signals--and the associated monogenic signal--the vector-valued function counterpart of the analytic signal in which the Riesz transform replaces the Hilbert transform. Examples of visual chimaeras are shown for same/different category images.

Increasing stimulus size impairs first- but not second-order motion perception

As stimulus size increases, the direction of high-contrast moving stimuli becomes increasingly difficult to perceive. This counterintuitive effect, termed spatial suppression, is believed to reflect antagonistic center-surround interactions--mechanisms that play key roles in tasks requiring sensitivity to relative motion. It is unknown, however, whether second-order motion also exhibits spatial suppression. To test this hypothesis, we measured direction discrimination thresholds for first- and second-order stimuli of varying sizes. The results revealed increasing thresholds with increasing size for first-order stimuli but demonstrated no spatial suppression of second-order motion. This selective impairment of first-order motion predicts increasing predominance of second-order cues as stimulus size increases. We confirmed this prediction by utilizing compound stimuli that contain first- and second-order information moving in opposite directions. Specifically, we found that for large stimuli, motion perception becomes increasingly determined by the direction of second-order cues. Overall, our findings show a lack of spatial suppression for second-order stimuli, suggesting that the second-order system may have distinct functional roles, roles that do not require high sensitivity to relative motion.

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.

The Riesz transform and simultaneous representations of phase, energy and orientation in spatial vision

To represent the local orientation and energy of a 1-D image signal, many models of early visual processing employ bandpass quadrature filters, formed by combining the original signal with its Hilbert transform. However, representations capable of estimating an image signal's 2-D phase have been largely ignored. Here, we consider 2-D phase representations using a method based upon the Riesz transform. For spatial images there exist two Riesz transformed signals and one original signal from which orientation, phase and energy may be represented as a vector in 3-D signal space. We show that these image properties may be represented by a Singular Value Decomposition (SVD) of the higher-order derivatives of the original and the Riesz transformed signals. We further show that the expected responses of even and odd symmetric filters from the Riesz transform may be represented by a single signal autocorrelation function, which is beneficial in simplifying Bayesian computations for spatial orientation. Importantly, the Riesz transform allows one to weight linearly across orientation using both symmetric and asymmetric filters to account for some perceptual phase distortions observed in image signals - notably one's perception of edge structure within plaid patterns whose component gratings are either equal or unequal in contrast. Finally, exploiting the benefits that arise from the Riesz definition of local energy as a scalar quantity, we demonstrate the utility of Riesz signal representations in estimating the spatial orientation of second-order image signals. We conclude that the Riesz transform may be employed as a general tool for 2-D visual pattern recognition by its virtue of representing phase, orientation and energy as orthogonal signal quantities.

Spatial summation of first-order and second-order motion in human vision

This study assessed spatial summation of first-order (luminance-defined) and second-order (contrast-defined) motion. Thresholds were measured for identifying the drift direction of 1c/deg., luminance-modulated and contrast-modulated dynamic noise drifting at temporal frequencies of 0.5, 2 and 8Hz. Image size varied from 0.125 degrees to 16 degrees . The effects of increasing image size on thresholds for luminance-modulated noise were also compared to those for luminance-defined gratings. In all cases, performance improved as image size increased. The rate at which performance improved with increasing image size was similar for all stimuli employed although the slopes corresponding to the initial improvement were steeper for first-order compared to second-order motion. The image sizes at which performance for first-order motion asymptote were larger than for second-order motion. In addition, findings showed that the minimum image size required to support reliable identification of the direction of moving stimuli is greater for second-order than first-order motion. Thus, although first-order and second-order motion processing have a number of properties in common, the visual system's sensitivity to each type of motion as a function of image size is quite different.

Application of Riesz transforms to the isotropic AM-PM decomposition of geometrical-optical illusion images

The existence of a special second-order mechanism in the human visual system, able to demodulate the envelope of visual stimuli, suggests that spatial information contained in the image envelope may be perceptually relevant. The Riesz transform, a natural isotropic extension of the Hilbert transform to multidimensional signals, was used here to demodulate band-pass filtered images of well-known visual illusions of length, size, direction, and shape. We show that the local amplitude of the monogenic signal or envelope of each illusion image conveys second-order information related to image holistic spatial structure, whereas the local phase component conveys information about the spatial features. Further low-pass filtering of the illusion image envelopes creates physical distortions that correspond to the subjective distortions perceived in the illusory images. Therefore the envelope seems to be the image component that physically carries the spatial information about these illusions. This result contradicts the popular belief that the relevant spatial information to perceive geometrical-optical illusions is conveyed only by the lower spatial frequencies present in their Fourier spectrum.

Visual Processing in Amblyopia: Human Studies

Within the last five years, there have been a number of exciting new advances in our knowledge and understanding of amblyopia. This article reviews recent psychophysical studies of naturally occurring amblyopia in humans. These studies suggest that: 1) There are significant differences in the patterns of visual loss among the clinically defined categories of amblyopes. A key factor in determining the nature of the loss is the presence or absence of binocularity. 2) Dysfunction within the amblyopic visual system first occurs in area V1, and the effects of amblyopia may be amplified downstream. 3) There appears to be substantial neural plasticity in the amblyopic brain beyond the "critical period."

The detection of the motion of contrast modulation: a parametric study

Despite a long and productive history as a focus of research interest, the details of how humans detect motion in an image remain controversial. This debate has not been helped by the lack of a clear parametric description of motion discrimination for some of the more simple visual stimuli employed in the literature to date. With this in mind, in the present work, we examined a peculiarity observed in the perception of the motion of second-order (contrast-modulated) stimuli: Under certain stimulus conditions, there is a reversal in the perceived direction of motion of the pattern. The aim was to quantify this phenomenon, relate the reversal to forward (veridical) and ambiguous motion, and place the behavioral data in the context of the window of visibility model of spatiotemporal contrast sensitivity. The direction of motion of contrast-modulated patterns was measured as a function of temporal frequency and carrier contrast, under different critical stimulus conditions. The stimulus properties manipulated were spatial frequency, spatial-phase relationship of carrier and sidebands, color, duration, and, most critically, the retinal location of the stimulus. On a purely empirical basis, the data reconciled several conflicts in the recent literature. From a theoretical standpoint, the data were well explained by the window of visibility approach in the majority of conditions and were partially explained in the remaining conditions. The results raise some interesting questions about underlying motion detection mechanisms and the assumptions embodied in our approach to motion modeling and the visual system in general. Supplemental materials for this article may be downloaded from app.psychonomic-journals.org/content/supplemental.

Conjunction benefits and costs reveal decision priming for first-order and second-order features

Across two experiments, decision priming was examined for conjunctions composed of first-order or first- and second-order stimulus features. Observers indicated the presence or absence of one or two features in a Gabor stimulus. When a pair of stimulus features differed in their speed of discrimination, responses indicating the presence of a conjunction were faster than those for the single feature for which discrimination was slowest (conjunction benefits). Also, responses indicating the absence of a conjunction were delayed if one of the features was present (conjunction costs). These results show that first- and second-order features can prime decisions about the presence of a conjunction and suggest that the two kinds of signals can be combined at a decision stage after the discrimination of stimulus properties has begun for each system.

Single-band amplitude demodulation of Müller-Lyer illusion images

The perception of the Müller-Lyer illusion has previously been explained as a result of visual low band-pass spatial filtering, although, in fact, the illusion persists in band-pass and high-pass filtered images without visible low-spatial frequencies. A new theoretical framework suggests that our perceptual experience about the global spatial structure of an image corresponds to the amplitude modulation (AM) component (or its magnitude, also called envelope) of its AM-FM (alternatively, AM-PM) decomposition. Because demodulation is an ill-posed problem with a non-unique solution, two different AM-FM demodulation algorithms were applied here to estimate the envelope of images of Müller-Lyer illusion: the global and exact Daugman and Downing (1995) AMPM algorithm and the local and quasi-invertible Maragos and Bovik (1995) DESA. The images used in our analysis include the classic configuration of illusion in a variety of spatial and spatial frequency content conditions. In all cases, including those of images for which visual low-pass spatial filtering would be ineffective, the envelope estimated by single-band amplitude demodulation has physical distortions in the direction of perceived illusion. It is not plausible that either algorithm could be implemented by the human visual system. It is shown that the proposed second order visual model of pre-attentive segregation of textures (or "back-pocket" model) could recover the image envelope and, thus, explain the perception of this illusion even in Müller-Lyer images lacking low spatial frequencies.

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.

The effect of white-noise mask level on sinewave contrast detection thresholds and the critical-band-masking model

It is known that visual noise added to sinusoidal gratings changes the typical U-shaped threshold curve which becomes flat in log-log scale for frequencies below 10c/deg when gratings are masked with white noise of high power spectral density level. These results have been explained using the critical-band-masking (CBM) model by supposing a visual filter-bank of constant relative bandwidth. However, some psychophysical and biological data support the idea of variable octave bandwidth. The CBM model has been used here to explain the progressive change of threshold curves with the noise mask level and to estimate the bandwidth of visual filters. Bayesian staircases were used in a 2IFC paradigm to measure contrast thresholds of horizontal sinusoidal gratings (0.25-8 c/deg) within a fixed Gaussian window and masked with one-dimensional, static, broadband white noise with each of five power density levels. Raw data showed that the contrast threshold curve progressively shifts upward and flattens out as the mask noise level increases. Theoretical thresholds from the CBM model were fitted simultaneously to the data at all five noise levels using visual filters with log-Gaussian gain functions. If we assume a fixed-channel detection model, the best fit was obtained when the octave bandwidth of visual filters decreases as a function of peak spatial frequency.

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.

Identification of contrast-defined letters benefits from perceptual learning in adults with amblyopia

Amblyopes show specific deficits in processing second-order spatial information (e.g. Wong, Levi, & McGraw (2001). Is second-order spatial loss in amblyopia explained by the loss of first-order spatial input? Vision Research, 41, 2951-2960). Recent work suggests there is a significant degree of plasticity in the visual pathway that processes first-order spatial information in adults with amblyopia. In this study, we asked whether or not there is similar plasticity in the ability to process second-order spatial information in adults with amblyopia. Ten adult observers with amblyopia (five strabismic, four anisometropic and one mixed) were trained to identify contrast-defined (second-order) letters using their amblyopic eyes. Before and after training, we determined observers' contrast thresholds for identifying luminance-defined (first-order) and contrast-defined letters, separately for the non-amblyopic and amblyopic eyes. Following training, eight of the 10 observers showed a significant reduction in contrast thresholds for identifying contrast-defined letters with the amblyopic eye. Five of these observers also showed a partial transfer of improvement to their fellow untrained non-amblyopic eye for identifying contrast-defined letters. There was a small but statistically significant transfer to the untrained task of identifying luminance-defined letters in the same trained eye. Similar to first-order spatial tasks, adults with amblyopia benefit from perceptual learning for identifying contrast-defined letters in their amblyopic eyes, suggesting a sizeable degree of plasticity in the visual pathway for processing second-order spatial information.

Spatial interactions reveal inhibitory cortical networks in human amblyopia

Humans with amblyopia have a well-documented loss of sensitivity for first-order, or luminance defined, visual information. Recent studies show that they also display a specific loss of sensitivity for second-order, or contrast defined, visual information; a type of image structure encoded by neurons found predominantly in visual area A18/V2. In the present study, we investigate whether amblyopia disrupts the normal architecture of spatial interactions in V2 by determining the contrast detection threshold of a second-order target in the presence of second-order flanking stimuli. Adjacent flanks facilitated second-order detectability in normal observers. However, in marked contrast, they suppressed detection in each eye of the majority of amblyopic observers. Furthermore, strabismic observers with no loss of visual acuity show a similar pattern of detection suppression. We speculate that amblyopia results in predominantly inhibitory cortical interactions between second-order neurons.

Second-order spatial summation in amblyopia

Amblyopes show bilateral loss of sensitivity for second-order (contrast defined) stimuli that can be further suppressed by flanking second-order stimuli (whereas flanks facilitate sensitivity in normal observers). The suppressive flank effect in amblyopes might be explained by abnormal pooling of second-order contrast across visual space. In this study, we investigate whether amblyopes show abnormal second-order spatial summation by measuring contrast detection thresholds for 1c/deg modulations of random noise (stimuli 1-12 cycles) in amblyopic observers, strabismic observers with no visual acuity loss, and normal (control) observers. Non-control observers showed substantial bilateral loss of sensitivity relative to the control observers, as expected. However, all observers showed essentially equal second-order spatial summation: contrast detection threshold decreased with approximately the square root of the number of cycles, and then became independent of size at 6-8 cycles (similar asymptotes). We conclude that the pooling of second-order contrast across visual space is unaffected by amblyopia.

The influence of spatial and temporal noise on the detection of first-order and second-order orientation and motion direction

Thresholds for identifying the direction of second-order motion (contrast-modulated dynamic noise) are consistently higher than those for identifying spatial orientation, unlike first-order gratings for which the two thresholds are typically the same. Two explanations of this phenomenon have been proposed: either first-order and second-order patterns are encoded by separate mechanisms with different properties, or dynamic noise selectively impairs ("masks") sensitivity to second-order motion direction but not orientation. The former predicts the two thresholds should remain distinct for second-order patterns, irrespective of the temporal structure (static vs. dynamic) of the noise carrier. The latter predicts direction thresholds should be higher than orientation thresholds, for both second-order and first-order motion patterns, when dynamic (but not static) noise is present. To resolve this issue we measured direction and orientation thresholds for first-order (luminance) and second-order (contrast or polarity) modulations of static or dynamic noise. Results were decisive: The two thresholds were invariably the same for first-order stimuli but markedly different (direction thresholds approximately 50% higher) for second-order stimuli, regardless of the temporal properties (static or dynamic) and the overall contrast of the noise, or the drift temporal frequency of the envelope. This suggests that first-order and second-order motion are encoded separately and that the mechanisms encoding second-order stimuli cannot determine direction at the absolute threshold for spatial form.

Sensitivity to spatial and temporal modulations of first-order and second-order motion

This study characterises the spatiotemporal "window of visibility" for first-order motion (luminance-modulated noise) and three varieties of second-order motion (contrast-modulated, polarity-modulated and spatial length-modulated noise). Direction-identification thresholds (minimum modulation depth producing 79.4% correct) were measured for each motion pattern (acuity permitting) over a five octave range of spatial and temporal frequencies (0.5-16 c/deg and 0.5-16 Hz respectively). Thresholds were converted into modulation sensitivity (1/threshold). For first-order motion patterns, sensitivity functions were generally bandpass. However, for second-order motion patterns, functions were predominantly lowpass in nature. In particular, the functions corresponding to contrast-modulated and polarity-modulated noise were virtually identical in terms of shape and sensitivity. However, sensitivity to modulations of spatial length was extremely poor and more lowpass, suggesting that additional strategies, perhaps a feature-based system, may be required for encoding motion of images of this type.

Visually distinct patterns with matching subband statistics

A commonly used representation of a visual pattern is a statistical distribution measured from the output of a bank of filters (Gaussian, Laplacian, Gabor, etc.). Both marginal and joint distributions of filter responses have been advocated and effectively used for a variety of vision tasks, including texture classification, texture synthesis, object detection, and image retrieval. This paper examines the ability of these representations to discriminate between an arbitrary pair of visual stimuli. Examples of patterns are derived that provably possess the same marginal and joint statistical properties, yet are "visually distinct." This is accomplished by showing sufficient conditions for matching the first k moments of the marginal distributions of a pair of images. Then, given a set of filters, we show how to match the marginal statistics of the subband images formed through convolution with the filter set. Next, joint statistics are examined and images with similar joint distributions of subband responses are shown. Finally, distinct periodic patterns are derived that possess approximately the same subband statistics for any arbitrary filter set.

Spatial frequency selective masking of first-order and second-order motion in the absence of off-frequency 'looking'

Converging evidence suggests that, at least initially, first-order (luminance defined) and second-order (e.g. contrast defined) motion are processed independently in human vision. However, adaptation studies suggest that second-order motion, like first-order motion, may be encoded by spatial frequency selective mechanisms each operating over a limited range of scales. Nonetheless, the precise properties of these mechanisms are indeterminate since the spatial frequency selectivity of adaptation aftereffects may not necessarily represent the frequency tuning of the underlying units [Vision Research 37 (1997) 2685]. To address this issue we used visual masking to investigate the spatial-frequency tuning of the mechanisms that encode motion. A dual-masking paradigm was employed to derive estimates of the spatial tuning of motion sensors, in the absence of off-frequency 'looking'. Modulation-depth thresholds for identifying the direction of a sinusoidal test pattern were measured over a 4-octave range (0.125-2 c/deg) in both the absence and presence of two counterphasing masks, simultaneously positioned above and below the test frequency. For second-order motion, the resulting masking functions were spatially bandpass in character and remained relatively invariant with changes in test spatial frequency, masking pattern modulation depth and the temporal properties of the noise carrier. As expected, bandpass spatial frequency tuning was also found for first-order motion. This provides compelling evidence that the mechanisms responsible for encoding each variety of motion exhibit spatial frequency selectivity. Thus, although first-order and second-order motion may be encoded independently, they must utilise similar computational principles.