Discrimination of complex patterns: orientation information is integrated across spatial scale; spatial-frequency and contrast information are not

Transfer of visual perceptual learning over a task-irrelevant feature through feature-invariant representations: Behavioral experiments and model simulations

A large body of literature has examined specificity and transfer of perceptual learning, suggesting a complex picture. Here, we distinguish between transfer over variations in a "task-relevant" feature (e.g., transfer of a learned orientation task to a different reference orientation) and transfer over a "task-irrelevant" feature (e.g., transfer of a learned orientation task to a different retinal location or different spatial frequency), and we focus on the mechanism for the latter. Experimentally, we assessed whether learning a judgment of one feature (such as orientation) using one value of an irrelevant feature (e.g., spatial frequency) transfers to another value of the irrelevant feature. Experiment 1 examined whether learning in eight-alternative orientation identification with one or multiple spatial frequencies transfers to stimuli at five different spatial frequencies. Experiment 2 paralleled Experiment 1, examining whether learning in eight-alternative spatial-frequency identification at one or multiple orientations transfers to stimuli with five different orientations. Training the orientation task with a single spatial frequency transferred widely to all other spatial frequencies, with a tendency to specificity when training with the highest spatial frequency. Training the spatial frequency task fully transferred across all orientations. Computationally, we extended the identification integrated reweighting theory (I-IRT) to account for the transfer data (Dosher, Liu, & Lu, 2023; Liu, Dosher, & Lu, 2023). Just as location-invariant representations in the original IRT explain transfer over retinal locations, incorporating feature-invariant representations effectively accounted for the observed transfer. Taken together, we suggest that feature-invariant representations can account for transfer of learning over a "task-irrelevant" feature.

A comparison of contrast sensitivity and sweep visual evoked potential (sVEP) acuity estimates in normal humans

PURPOSE

Several previous studies have demonstrated that for normal adult subjects the optotype acuity measured with charts is better than the acuity determined with the sweep visual evoked potential (sVEP) using gratings or checks. However, there is no difference in psychophysical measures of acuity with optotype or grating charts. Thus, it is unclear whether the acuity discrepancy between optotype charts and the sVEP result from the stimulus design or other methodological differences. The purpose of this experiment is to determine the relationship between acuities extrapolated from a contrast sensitivity function (CSF) that uses optotypes and the sVEP.

METHODS

Normal subjects (N = 10) with acuity of 0.00 logMAR or better (ETDRS chart) were recruited for this study. Two commercially available systems were used to measure CSFs [i.e., the Beethoven System (Ryklin Software, NY) and the qCSF system (Adaptive Sensory Tech, CA)]. The stimuli for the Beethoven were sine wave gratings (0.75-18.50 cpd), and thresholds were determined with a 2-alternative forced choice (2-AFC) procedure combined with a staircase. The stimuli for the qCSF system were spatially filtered letters (10 possible letters, 10-AFC) with the letter sizes and contrasts determined by a Bayesian adaptive procedure. Visual acuity was determined by fitting the data with a double exponential equation and extrapolating the fit to a contrast sensitivity of one. The sVEP was obtained with the PowerDiva (Digital Instrumentation for Visual Assessment, version 3.5, CA). The stimuli were sine wave gratings (80% contrast, 3-36 cpd) counterphased at 7.5 Hz. The final acuity was the average of two estimates each derived from the average of 10 sweeps.

RESULTS

The average logMAR chart (acuity converted to cpd), sVEP, Beethoven, and qCSF acuities were 36.6 ± 4.62 cpd (mean ± SD), 31.2 ± 4.59 cpd, 27.3 ± 7.38 cpd, and 27.6 ± 6.36 cpd, respectively. The logMAR chart acuity was significantly different from the other acuity estimates (all p values < 0.05). The sVEP, Beethoven, and qCSF acuities were not different from one another (all p values > 0.05). The Beethoven and the qCSF acuities had a good intraclass correlation coefficient (ICC = 0.85).

CONCLUSIONS

Similar to previous publications, the sVEP acuity estimate was less than the optotype chart acuity. The acuity determined with the sVEP and the CSFs with letter and grating stimuli were not statistically different, suggesting that the difference in acuity with the sVEP and optotype charts does not result from stimulus differences. Other methodological differences must account for the discrepancy in sVEP and optotype chart acuity.

Decisional separability, model identification, and statistical inference in the general recognition theory framework

Recent work in the general recognition theory (GRT) framework indicates that there are serious problems with some of the inferential machinery designed to detect perceptual and decisional interactions in multidimensional identification and categorization (Mack, Richler, Gauthier, & Palmeri, 2011). These problems are more extensive than previously recognized, as we show through new analytic and simulation-based results indicating that failure of decisional separability is not identifiable in the Gaussian GRT model with either of two common response selection models. We also describe previously unnoticed formal implicational relationships between seemingly distinct tests of perceptual and decisional interactions. Augmenting these formal results with further simulations, we show that tests based on marginal signal detection parameters produce unacceptably high rates of incorrect statistical significance. We conclude by discussing the scope of the implications of these results, and we offer a brief sketch of a new set of recommendations for testing relationships between dimensions in perception and response selection in the full-factorial identification paradigm.

Syllable structure and integration of voicing and manner of articulation information in labial consonant identification

Speech perception requires the integration of information from multiple phonetic and phonological dimensions. A sizable literature exists on the relationships between multiple phonetic dimensions and single phonological dimensions (e.g., spectral and temporal cues to stop consonant voicing). A much smaller body of work addresses relationships between phonological dimensions, and much of this has focused on sequences of phones. However, strong assumptions about the relevant set of acoustic cues and/or the (in)dependence between dimensions limit previous findings in important ways. Recent methodological developments in the general recognition theory framework enable tests of a number of these assumptions and provide a more complete model of distinct perceptual and decisional processes in speech sound identification. A hierarchical Bayesian Gaussian general recognition theory model was fit to data from two experiments investigating identification of English labial stop and fricative consonants in onset (syllable initial) and coda (syllable final) position. The results underscore the importance of distinguishing between conceptually distinct processing levels and indicate that, for individual subjects and at the group level, integration of phonological information is partially independent with respect to perception and that patterns of independence and interaction vary with syllable position.

Diagonal d' does not (always) diagnose failure of separability: An addendum to

Kingston, Diehl, Kirk, and Castleman (Journal of Phonetics, 2008) present a sophisticated experimental design and detection theoretic analysis of the internal auditory structure of phonological contrasts. However, a potentially important aspect of multidimensional detection theory - the covariance structure of assumed underlying multivariate Gaussian perceptual densities - was left unexplored. We discuss Kingston, et al.'s approach in the context of a general definition of multidimensional d' and present a description of two distinct configurations of perceptual densities requiring fundamentally different interpretations that account equally well for the "mean-shift integrality" results reported by Kingston, et al. We end with a brief discussion of approaches to distinguishing these underlying configurations empirically.

Anisotropic local contrast normalization: The role of stimulus orientation and spatial frequency bandwidths in the oblique and horizontal effect perceptual anisotropies

Visual ability for sine waves and other narrowband stimuli shows an oblique effect--worst performance at obliques, best at horizontal and vertical orientations. Recently, we have shown that with broadband stimuli (either 1/f(alpha) visual noise or natural scenes), performance for detecting oriented content is worst at horizontal, best at the obliques, and intermediate at vertical orientations (a "horizontal effect"). This horizontal effect has been explained by a cortical contrast normalization model that is both local (over orientation and spatial frequency) and anisotropic (due to a numerical bias of neurons with different preferred orientations). Here, the bandwidth of content at which an oblique effect or horizontal effect occurs was assessed in two suprathreshold matching experiments conducted with 1/f(alpha) noise stimuli filtered with a triangle increment function of varied bandwidth (16 levels of orientation and spatial frequency bandwidth). The results provided further support for the local anisotropic normalization model in that an oblique effect was observed when a fairly small range of orientations and high spatial frequencies were tested and the horizontal effect was observed for broadband increments > or = 20 degrees orientation bandwidth and > or = 1-octave in frequency. At intermediate spatial frequency and orientation increment bandwidths, a blend of the two anisotropies was observed.

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.

Contextual effects on fine orientation discrimination tasks

We examined the influence of context on fine orientation discrimination performance using sinusoidal grating patterns. Discrimination performance was impaired in the presence of modulated surrounds of the same spatial frequency, orientation, and contrast as the center. When center and surround were out-of-phase, separated by a gap of mean luminance, or very different in spatial frequency, performance remained at control levels. When center and surround were in-phase but mismatched in mean luminance, suppression was reduced or eliminated and performance was equivalent to luminance-mismatched control conditions. We speculate that lateral interactions in fine orientation discrimination tasks do not occur between objects that are perceptually distinct.

The accessibility of spatial channels for stereo and motion

Using fractal noise images, we measured the dependence of D(min) on the spatial passband (spatial frequency and orientation) over which information was correlated either between the eyes for stereo or between sequential frames for motion. Without affecting the amplitude spectrum of the noise stimulus we used idealized filters to scramble the phase of components outside a pre-defined passband. Using a simple Gaussian model in which performance depends on the signal/noise within a restricted spatial region, we obtained estimates of the bandwidth of the narrowest underlying spatial frequency and orientation spectral region subserving these two comparable tasks. Spatial bandwidths varied with peak spatial frequency but were very broad approximating the spectrum of the stimulus itself. Orientation properties of the underlying mechanisms were isotropic. These results suggest that the independent activity of individual narrowband spatial channels is not perceptually accessible for these tasks.

A multiscale filtering explanation of gradient induction and remote brightness induction effects: a reply to Logvinenko (2003)

Grating induction is a brightness effect in which a counterphase spatial brightness variation (a grating) is induced in a homogeneous test strip that is surrounded by an inducing luminance grating (McCourt, 1982 Vision Research 22 119-134). Moulden and Kingdom (1991 Vision Research 31 1999-2008) introduced an interesting variant of grating induction (sometimes referred to as gradient induction) in which multiple strips of either a linear luminance ramp or a sine-wave grating were interlaced with strips of homogeneous luminance. We (Blakeslee and McCourt, 1999 Vision Research 39 4361-4377) demonstrated that a simple multiscale filtering explanation could account for grating induction. Recently, however, Logvinenko (2003 Perception 32 621-626) presented several arguments impugning the adequacy of spatial filtering approaches to understanding brightness induction in gradient induction stimuli. We propose that Logvinenko's arguments apply only to a limited class of filtering models, specifically those which employ only a single spatial filter. To test this hypothesis we modeled gradient induction stimuli as a function of inducing contrast, as well as Logvinenko's (2003) remote induction stimulus, using our multiscale oriented difference-of-Gaussians (ODOG) model (Blakeslee and McCourt 1999). The ODOG model successfully predicts the appearance of the inducing strips and the homogeneous test strips in the gradient induction stimuli and the appearance of the test patches in the remote induction stimuli. These results refute Logvinenko's (2003) claims, and we interpret them as providing strong evidence for a multiscale filtering approach to understanding both gradient induction and remote brightness induction effects.

Opponent-motion mechanisms are self-normalizing

In the ultimate stage of the Adelson-Bergen motion energy model [Adelson, E. H., & Bergen, J. (1985). Spatiotemporal energy models for the perception of motion. Journal of the Optical Society of America, 2, 284-299], motion is derived from the difference between directionally opponent energies E(L) and E(R). However, Georgeson and Scott-Samuel [Georgeson, M. A., & Scott-Samuel, N. E. (1999). Motion contrast: A new metric for direction discrimination. Vision Research, 39, 4393-4402] demonstrated that motion contrast-a metric that normalizes opponent motion energy (E(L)-E(R)) by flicker energy (E(L)+E(R))-is a better descriptor of human direction discrimination. In a previous study [Rainville, S. J. M., Makous, W. L., & Scott-Samuel, N. E. (2002). The spatial properties of opponent-motion normalization. Vision Research, 42, 1727-1738], we used a lateral masking paradigm to show that opponent-motion normalization is selective for flicker position, orientation, and spatial-frequency. In the present study, we used a superposition masking paradigm and compared results to lateral masking data, as the two masking types activate local and remote normalization mechanisms differentially. Although selectivity for flicker orientation and spatial frequency varied across observers, bandwidths were similar across lateral and superimposed masking conditions. Additional experiments demonstrated that normalization signals are pooled over a spatial region whose aspect ratio and size are consistent with those of local motion detectors. Together, results show no evidence of remote normalization signals predicted by broadband inhibitory models [(e.g.) Heeger, D. J. (1992). Normalization of cell responses in cat striate cortex. Visual Neuroscience, 9, 181-197; Foley, J. M. (1994). Human luminance pattern-vision mechanisms: Masking experiments require a new model. Journal of the Optical Society of America A-Optics and Image Science, 11, 1710-1719] but support a local normalization process whose spatial properties are inherited from low-level motion detectors.

Statistical model of natural stimuli predicts edge-like pooling of spatial frequency channels in V2

Background

It has been shown that the classical receptive fields of simple and complex cells in the primary visual cortex emerge from the statistical properties of natural images by forcing the cell responses to be maximally sparse or independent. We investigate how to learn features beyond the primary visual cortex from the statistical properties of modelled complex-cell outputs. In previous work, we showed that a new model, non-negative sparse coding, led to the emergence of features which code for contours of a given spatial frequency band.

Results

We applied ordinary independent component analysis to modelled outputs of complex cells that span different frequency bands. The analysis led to the emergence of features which pool spatially coherent across-frequency activity in the modelled primary visual cortex. Thus, the statistically optimal way of processing complex-cell outputs abandons separate frequency channels, while preserving and even enhancing orientation tuning and spatial localization. As a technical aside, we found that the non-negativity constraint is not necessary: ordinary independent component analysis produces essentially the same results as our previous work.

Conclusion

We propose that the pooling that emerges allows the features to code for realistic low-level image features related to step edges. Further, the results prove the viability of statistical modelling of natural images as a framework that produces quantitative predictions of visual processing.

A unified theory of brightness contrast and assimilation incorporating oriented multiscale spatial filtering and contrast normalization

Brightness induction includes both contrast and assimilations effects. Brightness contrast occurs when the brightness of a test region shifts away from the brightness of adjacent regions. Brightness assimilation refers to the opposite situation in which the brightness of the test region shifts toward that of the surrounding regions. Interestingly, in the White effect [Perception 8 (1979) 413] the direction of the induced brightness change does not correlate with the amount of black or white border in contact with the gray test patch. This has led some investigators to reject spatial filtering explanations not only for the White effect but for brightness perception in general. Instead, these investigators have offered explanations based on a variety of junction analyses and/or perceptual organization schemes. Here, these approaches are challenged with a critical set of new psychophysical measurements that determined the magnitude of the White effect, the shifted White effect [Perception 10 (1981) 215] and the checkerboard illusion [R.L. DeValois, K.K. DeValois, Spatial Vision, Oxford University Press, NY, 1988] as a function of inducing pattern spatial frequency and test patch height. The oriented difference-of-Gaussians (ODOG) computational model of Blakeslee and McCourt [Vision Res. 39 (1999) 4361] parsimoniously accounts for the psychophysical data, and illustrates that mechanisms based on junction analysis or perceptual inference are not required to explain them. According to the ODOG model, brightness induction results from linear spatial filtering with an incomplete basis set (the finite array of spatial filters in the human visual system). In addition, orientation selectivity of the filters and contrast normalization across orientation channels are critical for explaining some brightness effects, such as the White effect.

Contrast conservation in human vision

Visual experience, which is defined by brief saccadic sampling of complex scenes at high contrast, has typically been studied with static gratings at threshold contrast. To investigate how suprathreshold visual processing is related to threshold vision, we tested the temporal integration of contrast in the presence of large, sudden changes in the stimuli such occur during saccades under natural conditions. We observed completely different effects under threshold and suprathreshold viewing conditions. The threshold contrast of successively presented gratings that were either perpendicularly oriented or of inverted phase showed probability summation, implying no detectable interaction between independent visual detectors. However, at suprathreshold levels we found complete algebraic summation of contrast for stimuli longer than 53 ms. The same results were obtained during sudden changes between random noise patterns and between natural scenes. These results cannot be explained by traditional contrast gain-control mechanisms or the effect of contrast constancy. Rather, at suprathreshold levels, the visual system seems to conserve the contrast information from recently viewed images, perhaps for the efficient assessment of the contrast of the visual scene while the eye saccades from place to place.

Dual nonlinearities regulate contrast sensitivity in pattern discrimination tasks

Many current psychophysical models propose that visual processing in cortex is hierarchical, with nonlinearities sandwiched between linear stages of processing. In earlier publications, we proposed a model of this type to account for masking effects found with spatial frequency and orientation discriminations. Our model includes two nonlinear mechanisms that regulate contrast sensitivity in early cortical mechanisms. The first is a local within-pathway nonlinearity that accelerates at low contrasts but is compressive at high. The second is a pooled nonlinear gain control process that operates over a broad range of neurons with different tuning characteristics. Here, we test predictions of the model for spatial frequency discriminations. The model predicts that at low contrasts, adding a grating mask oriented parallel to test gratings will improve discrimination performance via operation of the within-pathway nonlinearity, analogous to the "dipper effect" found with contrast discriminations. Adding an orthogonally oriented mask is predicted to have no effect at low contrasts, where pooled gain control processes contribute little to performance. At high contrasts, the model predicts that performance will asymptote and become independent of contrast with either parallel or orthogonal masks. The results confirm model predictions.

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.

Recognizing spatial patterns: a noisy exemplar approach

Models of categorization typically rely on the use of stimuli composed of well-defined dimensions (e.g., Ashby & Maddox (1998) in Choice, decision, and measurement: Essays in honor of R. Duncan Luce, p. 251-301, Mahwah, NJ: Erlbaum). We apply a similar approach to the analysis of recognition memory. Using a version of short-term recognition paradigm (Sternberg, Science 153 (1966) 652), we asked whether NEMO Sternberg's, a noisy exemplar summed-similarity model, could account for variation in mean performance on individual trials. NEMO provided a very good overall fit to recognition data from three experiments. However, its failure to fit data for certain lists of stimuli suggested a revision of the summed-similarity assumption. Our model-based analysis showed that subjects used interitem similarity, in addition to probe-item similarity, as the basis for their decisions. This represents a major departure from existing recognition models that assume subjects' judgments depend exclusively on the summed similarity of the probe to the study items.

Orientation-selective summing mechanisms revealed in visual search

We investigated properties of the neural mechanisms that mediate detection of complex grating targets in an orientation-based visual search task. Targets and distractors were composed of small patches of compound sinusoidal gratings. Components were chosen to differ enough in spatial frequency to stimulate separate and independent mechanisms at the primary cortical layer of processing. The orientations of the components were both vertical in distractor patches. In the uncrossed condition, both components of the target tilted either 3 degrees left or right. In the crossed condition, one component of the target tilted left and the other tilted right. Search was faster and more accurate in the uncrossed condition, ruling out mediation either by V1-like tuned mechanisms or by a higher-level mechanism that signals differences in orientation. Results were consistent with two classes of mid-level summing mechanisms. We argue that mid-level mechanisms such as these may be the neural substrate for conceptual orientation feature maps.

The role of spatial frequency channels in letter identification

How we see is today explained by physical optics and retinal transduction, followed by feature detection, in the cortex, by a bank of parallel independent spatial-frequency-selective channels. It is assumed that the observer uses whichever channels are best for the task at hand. Our current results demand a revision of this framework: Observers are not free to choose which channels they use. We used critical-band masking to characterize the channels mediating identification of broadband signals: letters in a wide range of fonts (Sloan, Bookman, Künstler, Yung), alphabets (Roman and Chinese), and sizes (0.1-55 degrees ). We also tested sinewave and squarewave gratings. Masking always revealed a single channel, 1.6+/-0.7 octaves wide, with a center frequency that depends on letter size and alphabet. We define an alphabet's stroke frequency as the average number of lines crossed by a slice through a letter, divided by the letter width. For sharp-edged (i.e. broadband) signals, we find that stroke frequency completely determines channel frequency, independent of alphabet, font, and size. Moreover, even though observers have multiple channels, they always use the same channel for the same signals, even after hundreds of trials, regardless of whether the noise is low-pass, high-pass, or all-pass. This shows that observers identify letters through a single channel that is selected bottom-up, by the signal, not top-down by the observer. We thought shape would be processed similarly at all sizes. Bandlimited signals conform more to this expectation than do broadband signals. Here, we characterize processing by channel frequency. For sinewave gratings, as expected, channel frequency equals sinewave frequency f(channel)=f. For bandpass-filtered letters, channel frequency is proportional to center frequency f(channel) proportional, variantf(center) (log-log slope 1) when size is varied and the band (c/letter) is fixed, but channel frequency is less than proportional to center frequency f(channel) proportional, variantf(center)(2/3) (log-log slope 2/3) when the band is varied and size is fixed. Finally, our main result, for sharp-edged (i.e. broadband) letters and squarewaves, channel frequency depends solely on stroke frequency, f(channel)/10c/deg=(2/3), with a log-log slope of 2/3. Thus, large letters (and coarse squarewaves) are identified by their edges; small letters (and fine squarewaves) are identified by their gross strokes.

Spatial phase sensitivity of mechanisms mediating discrimination of small orientation differences

Experiments with spatially superimposed gratings have defined mechanisms that sum signals across spatial frequency bands while mediating discriminations of small differences in orientation. In the present experiments, localized stimuli (Gaussian bars and derivatives of Gaussian bars) occupying different spatial frequency bands were superimposed in different phase and location relationships to assess the sensitivity of the summing mechanisms to these differences. Masking (loss of accuracy when a second component is added as a mask) was unaffected by differences in either phase or location (15 min separation). Summation (increase in accuracy when both components vary together) occurs for all phase relationships but is reduced by spatial separation.

Perceptual learning for a pattern discrimination task

Our goal was to differentiate low and mid level perceptual learning. We used a complex grating discrimination task that required observers to combine information across wide ranges of spatial frequency and orientation. Stimuli were 'wicker'-like textures containing two orthogonal signal components of 3 and 9 c/deg. Observers discriminated a 15% spatial frequency shift in these components. Stimuli also contained four noise components, separated from the signal components by at least 45 degrees of orientation or approximately 2 octaves in spatial frequency. In Experiment 1 naive observers were trained for eight sessions with a four-alternative same-different forced choice judgment with feedback. Observers showed significant learning, thresholds dropped to approximately 1/3 of their original value. In Experiment 2 we found that observers showed far less learning when the noise components were not present. Experiment 3 found, unlike many other studies, almost complete transfer of learning across orientation. The results of Experiments 2 and 3 suggest that, unlike many other perceptual learning studies, most learning in Experiment 1 occurs at mid to high levels of processing rather than within low level analyzers tuned for spatial frequency and orientation. Experiment 4 found that performance was more severely impaired by spatial frequency shifts in noise components of the same spatial frequency or orientation as the signal components (though there was significant variability between observers). This suggests that after training observers based their responses on mechanisms tuned for selective regions of Fourier space. Experiment 5 examined transfer of learning from a same-sign task (the two signal components both increased/decreased in spatial frequency) to an opposite-sign task (signal components shifted in opposite directions in frequency space). Transfer of learning from same-sign to opposite-sign tasks and vice versa was complete suggesting that observers combined information from the two signal components independently.

What limits simultaneous discrimination accuracy?

Discrimination accuracy decreases when viewers simultaneously monitor two perceptually distinct stimulus components for changes in a common property, e.g. contrast [Magnussen & Greenlee (1997). Journal of Experimental Psychology: Human Perception and Performance, 23, 1603-1616; Olzak & Wickens (1997). Perception, 26, 1101-1120]. We ask whether the limitation is in monitoring two components or in making dual decisions about a single property. Using the same uncertainty paradigm as Magnussen and Greenlee, we find no evidence of a processing limitation when viewers simultaneously monitor one component (1.25 c/d) for a possible change in contrast and a second component (5 c/d) for a possible change in spatial frequency, regardless of whether the components are spatially separated or superimposed. The limitation is in making dual decisions about a single property.

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.

Paradigm shifts: new techniques to answer new questions

The advent of a multiple-channels approach to spatial vision 20 years ago raised important questions that were difficult to approach empirically, given the technology and analytic tools of the time. These questions concerned the interaction or combination of different components of a stimulus--questions that have recently resurfaced in more complex form. Classical psychophysical methods for assessing whether two stimulus aspects are coded independently (e.g., masking, adaptation, and cue-summation) provide only limited information about the nature of whatever interactions are discovered. In both older work in detection and recent work in complex pattern discrimination, we have used a double-judgment paradigm in which the observer rates two aspects of a stimulus simultaneously. The paradigm provides a rich source of information about the codes underlying each psychophysical decision and which are unique in permitting us to psychophysically investigate effects resulting from neural noise in the system. Our analyses draw on theories of dimensional interaction in signal detection theory and in information theory, and on methods from several branches of statistics, including categorical data analysis and structural equation modeling. We review the theoretical, technological, methodological, and personal influences that led us to develop this approach.

Constancy scaling and conflict when the Zöllner illusion is seen in three dimensions

If a standard Zöllner illusion is seen as a staircase in depth, pairs of long lines flanking convex stair edges appear to diverge as usual, but divergence in pairs flanking concave edges can appear reduced. If the stair is reversed perceptually in the manner of the Schröder staircase, convex and concave shapes exchange and the extent of apparent divergence in the long line pairs exchanges with them. The effect is enhanced if explicit stair edges are added, and reduced if the standard Zöllner pattern is replaced by one in which segments of the long lines are offset in the direction of the usual illusory effect. The observations suggest that the three-dimensional potential of the pattern cannot be excluded from explanations of the illusion, and are compatible with the view of Gregory and Harris that inappropriate constancy scaling is its primary cause, triggered 'bottom-up' by pattern properties or 'top-down' by cognitive inference. However, these two mechanisms would have to be acting in conflict to generate suppression of divergence in the concave steps. Pattern processing for properties, such as orientation, that are not associated with the potential of the Zöllner illusion as a three-dimensional configuration, but that have been suggested as sources of the illusion in recent studies, could also be acting in opposition to hypothesis scaling in the concave steps.

Neural recoding in human pattern vision: model and mechanisms

We describe a model of neural recoding in spatial vision that specifies how the outputs of selected units akin to VI cells are normalized and combined to signal information about particular stimulus attributes. The recoding portion of the model is linked to psychophysical behavior via a two-stage signal-detection decision module that specifies how the outputs of the combining mechanisms are used in making fine spatial discriminations. We describe how masking and cue summation experiments isolate each of the processing stages, how earlier results from such studies guided development of the model, and we demonstrate how these procedures permit empirical estimates of model parameters as well as tests of alternative formulations. An important part of our work describes the characteristics of two complementary types of higher-level mechanisms isolated from previously published discrimination data. One sums normalized primary-level responses over disparate frequencies to signal precise information about the orientation of a stimulus; the other sums over all orientations to signal the spatial grain of texture-like patterns. We demonstrate how the model accounts for a large body of previously published discrimination data, and present the results of a new quantitative test of model predictions.

Evolving concepts of spatial channels in vision: from independence to nonlinear interactions

By the 1960s it was evident from neuroanatomy that there were extensive recurrent interactions, both excitatory and inhibitory, among visual cortical neurons. Nevertheless, the psychophysical discovery of 'spatial-frequency channels' gave rise to a decade in which parallel, independent channels were thought to subserve early spatial vision. Recent work, however, has clearly demonstrated that early visual channels do not perform a Fourier or wavelet decomposition of the image. Instead, they interact through a variety of nonlinear pooling mechanisms. Such nonlinear interactions perform important computations in texture perception, stereopsis, and motion and form vision.

The combination of filters in early spatial vision: a retrospective analysis of the MIRAGE model

Since the discovery of spatial-frequency-tuned channels in the visual system, most theories attempting to account for pattern encoding have assumed that the filters can be independently accessed and flexibly combined. We review here an alternative model, 'MIRAGE', in which the filters are inflexibly combined before pattern analysis. In the MIRAGE model the half-wave rectified outputs of all spatial-frequency channels are combined before locating spatial zero-bounded regions in the neural image, which serve as the spatial primitives for pattern analysis. We describe the evidence that led to this model, and review recent evidence on the rules of filter combination.