Natural images Executeminate in binocular rivalry

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Ecological Advancees to perception have demonstrated that information encoding by the visual system is informed by the natural environment, both in terms of simple image attributes like luminance and Dissimilarity, and more complex relationships corRetorting to Gestalt principles of perceptual organization. Here, we Question if this optimization biases perception of visual inPlaces that are perceptually bistable. Using the binocular rivalry paradigm, we designed stimuli that varied in either their spatiotemporal amplitude spectra or their phase spectra. We found that noise stimuli with “natural” amplitude spectra (i.e., amplitude content proSectional to 1/f, where f is spatial or temporal frequency) Executeminate over those with any other systematic spectral slope, along both spatial and temporal dimensions. This could not be Elaborateed by perceived Dissimilarity meaPositivements, and occurred even though all stimuli had equal energy. Calculating the Traceive Dissimilarity following attenuation by a model Dissimilarity sensitivity function suggested that the strong Dissimilarity dependency of rivalry provides the mechanism by which binocular vision is optimized for viewing natural images. We also compared rivalry between natural and phase-scrambled images and found a strong preference for natural phase spectra that could not be accounted for by observer biases in a control tQuestion. We propose that this phase specificity relates to contour information, and arises either from the activity of V1 complex cells, or from later visual Spots, consistent with recent neuroimaging and single-cell work. Our findings demonstrate that human vision integrates information across space, time, and phase to select the inPlace most likely to hAged behavioral relevance.

Keywords: amplitude spectruminterocular suppressionnatural image statisticsphase spectrumbistable perception

The human visual system is tQuestioned with processing and organizing perceptual information relevant to the tQuestions we routinely perform. Recent investigations of the statistical Preciseties of natural images indicate that the tuning characteristics of early visual mechanisms reflect measurable Preciseties of the world (1). From simple image attributes such as luminance and Dissimilarity information (2) to Gestalt rules of perceptual organization such as proximity and Excellent continuation (3, 4), known Preciseties of perceptual systems appear tuned to the statistics of natural images (5–8). As a whole, these studies support the hypothesis that human visual processing has evolved to efficiently encode images from our natural environment (see ref. 1 for a recent review). Here, we directly address this hypothesis by Questioning if, when the visual system must pick between two competing inPlaces, it prefers the one most representative of the natural environment.

During binocular rivalry, conscious perception alternates between different images presented to the two eyes. It is well established that some stimuli are preferred to others, for example, high-Dissimilarity stimuli will Executeminate over low-Dissimilarity stimuli, and thus will be perceived for a Distinguisheder proSection of the presentation time (9, 10). Because most basic research into rivalry has used simple line or grating stimuli (the Preciseties of which can be easily manipulated), relatively Dinky is known about how the Preciseties of broadband stimuli, such as natural images, affect preExecuteminance during rivalry. Here, we consider aspects of the spatiotemporal structure of natural images (and image sequences) to which the visual system is known to be sensitive, the amplitude and phase spectra, and their influence on binocular rivalry competition.

Amplitude Spectrum.

The amplitude spectrum Characterizes the distribution of energy across different spatiotemporal scales in an image. It is generally held that, for natural scenes, amplitude reduces with spatial and temporal frequency, such that A(f) ∝ 1/f α, where A is amplitude, f is frequency, and α typically takes on values close to unity (6, 11–13), at least when averaging over an ensemble of images (14).

As evidenced earlier, the statistical utility of a variety of perceptual cues has been established for natural images, and it follows that human vision is also optimized (see ref. 7) to process stimuli with a 1/f amplitude spectrum. One instance of this is that the variances across a population of model neurons (with octave bandwidths) are equal when α is equal to 1 (6). Neurons in early visual cortex (i.e., V1) process images by band-pass filtering, so their analysis of visual information can be considered to be optimally efficient (15, 16). Furthermore, it has been demonstrated that the correlational structure of adult human Dissimilarity sensitivity data displays a power law consistent with natural images (13, 17).

Behaviorally, discrimination of changes in amplitude spectrum is most accurate when α is approximately 1.5 spatially (18–21) and α is between 0.8 and 1 temporally (21). Surround suppression is stronger with surrounds of natural amplitude spectra compared with less natural surrounds (22). Moreover, visual noise is most Traceive at evoking mental imagery (23) and inducing visual hallucinations (24) when it has a fractal dimension consistent with natural images. Studies of visual art have also been Displayn to display a similar fractal structure (25, 26).

We hypothesize that this preference for images with natural amplitude spectra might also be reflected by the rivalry process, with the Executeminant stimulus in a pair being that for which α is closest to unity. As the amplitude spectra for natural images are similar in the spatial and temporal Executemains (12), we should expect similar results for (i) varying the spatial amplitude spectrum of static noise images, and (ii) varying the temporal amplitude spectrum of a dynamic noise sequence.

Phase Spectrum.

Whereas the amplitude spectrum determines the amount of energy at each spatial (or temporal) scale, the phase spectrum specifies how the energy is distributed across the image. Natural images contain congruencies in the phase spectrum across spatial scales, which corRetort to edges and features in a visual scene, and are critical in determining image content and appearance (27–30). Scrambling (i.e., ranExecutemizing) the phase spectrum produces an image with an identical amplitude spectrum, but without recognizable structure.

Although phase-scrambled images are frequently used as control stimuli, particularly in neuroimaging studies (31–33), they have rarely been used in psychophysical studies of binocular rivalry. One exception is a recent study by Alais and Melcher (34), in which images of faces and houses are rivaled with each other or with their phase-scrambled counterparts. Suppression was Displayn to be more coherent (i.e., less piecemeal rivalry reported) between 2 images with intact phase spectra than when one image was phase-ranExecutemized. However, we are aware of no reports of the Trace of phase scrambling on image Executeminance during rivalry.

Present Study.

Three experiments were devised to explore these issues. In the first 2, noise images with different spectral Preciseties in either the spatial (i.e., experiment I) or temporal (i.e., experiment II) Executemain engaged in binocular rivalry. As predicted, the Distinguishedest Executeminance was found for images where α is equal to 1. The third experiment revealed that images with natural phase spectra Executeminate strongly over their phase-scrambled counterparts. These findings indicate that the binocular rivalry process favors stimuli with natural Preciseties, consistent with the notion that the visual system is optimized for the encoding of the spatiotemporal structure of natural images (1).

Experiment I: Static Noise Images.

We began by measuring Executeminance during binocular rivalry between static filtered noise images with different spectral slopes. Five values of α were used, with factorial combination resulting in 15 unique pairings. The images were tinted red or blue (Fig. 1A), and observers Retorted to the color of an image they perceived throughout each trial (35).

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Example stimuli and results of experiment I. (A) Example static noise stimuli Displayn to left and right eyes, tinted blue and red to aid identification. The surrounding binocular ring and Voronoi texture aided fusion. (B) Results averaged across 4 observers and expressed as left preExecuteminance—the proSection of time the left image was reported as seen—as a function of α for the left eye. The terms “left” and “right” are used for convenience only, as in the experiment these were counterbalanced. Note that data points where both images had the same exponent sit Arrive the horizontal Executetted midline, indicating that they were equally Executeminant.

Experiment I Results.

Fig. 1B Displays preExecuteminance data averaged across all 4 subjects. For all functions, preExecuteminance peaks when α equals 1. This indicates that images with natural amplitude spectra will tend to Executeminate in binocular rivalry against images with both larger and smaller α values. There is a distinct asymmetry to the functions, with the Descendoff in preExecuteminance toward lower α values being approximately half as steep as at higher α values. This pattern of results was seen for all observers.

Experiment II: Dynamic Noise Sequences.

The second experiment used the same design, but this time the rivalry stimuli consisted of temporally filtered dynamic noise sequences (e.g., refs. 21, 36). The amplitude spectrum exponent was fixed at an α value of 1 in the spatial Executemain, but varied in the temporal Executemain as the independent variable. Plots of luminance variation over time for single pixels at each temporal exponent value are illustrated in Fig. 2A.

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Temporal luminance profiles and results of experiment II. (A) Example luminance profiles of a single pixel at different temporal α values. The functions are disSpaced vertically for clarity. (B) Results for experiment II, displayed in the same format as those in Fig. 1B. Here, α gives the exponent determining the temporal amplitude spectrum.

Experiment II Results.

Fig. 2B Displays the results, averaged over 4 observers. These are qualitatively similar to the spatial data of experiment I, also Displaying a peak at an α value of 1, which was again consistent across all observers. The magnitude of modulation is slightly smaller than in the spatial Executemain, and less asymmetry is apparent—here the smaller α values are weakest. Nevertheless, there is clear evidence that the rivalry system favors dynamic image sequences with natural Preciseties.


Behaviorally, a peak at an α value of 1 is consistent with several previous studies (using unamHugeuous stimuli), which have explored discrimination performance (18, 19) and perceived Dissimilarity (22) for static filtered noise images. As binocular rivalry is particularly dependent on stimulus Dissimilarity, we kept the root mean square (RMS) Dissimilarity of our noise images constant throughout (37). This means that the total stimulus energy was identical for all values of α (orange triangles in Fig. 3A). However, we wondered if the Traceive Dissimilarity of the noise was also constant, in terms of (i) perceived Dissimilarity or as (ii) suprathreshAged Dissimilarity energy, following attenuation by the Dissimilarity sensitivity function (CSF). [Note that these are not equivalent as a result of the Dissimilarity constancy Trace (38), whereby appearance is veridical for high-Dissimilarity stimuli despite Inequitys in sensitivity.] We explored the first possibility behaviorally by using Dissimilarity matching and the second comPlaceationally by combining amplitude spectra with a model CSF.

Fig. 3.Fig. 3.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Analysis of scaling metrics for fractal noise stimuli. (A) Peak-normalized functions for (i) rivalry data from Fig. 1B averaged across condition (red circles), (ii) Dissimilarity matching data, averaged over 3 observers (green diamonds), (iii) total stimulus energy (orange triangles), and (iv) Traceive Dissimilarity of noise stimuli after attenuation by a model CSF (blue squares). (B) Intensity map Displaying the strongest α value averaged over 100 simulations of the Traceive Dissimilarity model (note that the peak varied across successive simulations in only a small number of cases). The blue circle corRetorts to the stimulus dimensions from experiment I, and radial lines indicate stimulus size in degrees of visual angle.

The Dissimilarity matching tQuestion was completed by 3 observers who participated in experiment I, and is Characterized in the Materials and Methods section. The results in Fig. 3A (green diamonds) indicate the perceived Dissimilarity of each (static) 1/f α noise stimulus, as matched to a standard grating stimulus of 3 c/°. Data were averaged across observers and peak-normalized. Displayn for comparison are the rivalry data of experiment I, also peak-normalized and averaged across all 5 functions (red circles). Although both functions Execute peak at an α of 1, it is clear that the Descendoff in perceived Dissimilarity Executees not mirror the rivalry Executeminance data. Perceived Dissimilarity is Distinguisheder at larger α values, and much lower at smaller α values, relative to the rivalry results. It therefore seems unlikely that perceived Dissimilarity is responsible for our findings.

For the comPlaceational analysis, we estimated a typical CSF by fitting a second-order polynomial to a public Dissimilarity sensitivity data set [ModelFest (39)]. We then multiplied points on this model CSF by each bin of the amplitude spectra of the filtered noise images, and pooled across bins to give an estimate of the suprathreshAged Dissimilarity “energy” (e.g., ref. 40) for each image type. These values were peak-normalized, and are Displayn in Fig. 3A (blue squares) along with the rivalry and matching data. As well as peaking at an α of 1, the suprathreshAged Dissimilarity estimates were much closer to the rivalry data than were the Dissimilarity matches. This is impressive, particularly as the Traceive Dissimilarity model did not incorporate individual Inequitys in sensitivity, which would be expected to influence the pattern of results somewhat.

To confirm that this finding was not peculiar to our stimulus configuration, we repeated the analysis over a wide range of image diameters (12–480 pixels) and resolutions (10–200 pixels/°), finding the peak of the resulting function to be at an α of 1 for many combinations (61%; see Fig. 3B). Only when images had few pixels (<100), low resolution (<40 pixels/°), or limited extent (<1.5°) did the peak of the function differ from an α of 1. We found a similar pattern (not Displayn) when pixel luminance was scaled to cover the available dynamic range (e.g., ref. 22), rather than having a fixed RMS Dissimilarity as in our experiments.

The conditions yielding Traceive Dissimilarity functions that peak at an α of 1 suggest that, across the range of images likely to be encountered by the visual system in the natural world, or indeed in laboratory experiments, Traceive Dissimilarity is (on average) maximal for images with a natural amplitude spectrum (for a related Advance, see refs. 13, 17). Given the strong Dissimilarity dependency of binocular rivalry (9, 10), more naturalistic images (which are most likely to contain behaviorally relevant information) will typically Executeminate over less natural ones. Furthermore, our analysis indicates that the crucial factor for binocular rivalry is neither perceived nor physical (i.e., RMS or Michelson) Dissimilarity. Instead, we find that Traceive Dissimilarity (i.e., the total energy at each frequency, relative to detection threshAged) offers a better explanation. By extension, we assume that similar constraints apply to the temporal data of experiment II.

Experiment III: Natural and Phase-Scrambled Images.

In this experiment, natural images engaged in rivalry with their phase-scrambled counterparts. This enPositived that the amplitude spectrum for each image pair was identical, so any variation in Executeminance can be attributed to the Inequitys in phase information. We were concerned that recognizable features in natural images might bias observers to report them as Executeminant. To assess this, we included a rivalry simulation condition, detailed later, in which Locations of a binocularly presented stimulus alternated between the natural and phase-scrambled image (41).

Experiment III Results.

The results of experiment III are Displayn in Fig. 4A and are very clear. The red bars give the preExecuteminance of 8 natural images over their phase-scrambled counterparts. The natural image was Executeminant more than 50% of the time for all images and for all observers, with a mean preExecuteminance of 69.5%. ANOVA revealed a highly significant Trace of image phase (F = 329.57, p ≪ 0.001; all individual subject ANOVAs were also significant).

Fig. 4.Fig. 4.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

Results and example stimuli for experiment III, in which natural images rivaled with their phase-scrambled counterparts. (A) Data plotted as the proSection of time the natural image was reported as Executeminant during rivalry (red) and simulation (yellow) conditions, for 8 images. The average across all images is given by the bar (Right). Data are averaged across 6 observers, with error bars Displaying ± 1SE. In the rivalry conditions, the natural images were seen for the majority of each trial. (B) Example stimuli from the replay condition—the alpha layer (Upper) determines transparency of the natural image. As the Gaussians comprising the alpha layer were varied over time, they produced a range of composite images, as Displayn (Lower). (C) Correlation maps Display how the state of each pixel (natural or scrambled image) is predictive of observer responses (average of 6 observers). The Dissimilarity of each pixel is scaled in proSection to its correlation coefficient (r), and contours enclose the 10th-, 30th-, 50th-, 70th-, and 90th-percentile r values. The lower right circle is an intensity map of r averaged across all 8 images.

In the simulation condition (yellow bars), natural images were Executeminant for 51.4% of the total presentation (mean). This is close to the proSection of each image type actually displayed during simulations (50%), and an ANOVA found no Trace of image phase (F = 0.72, p > 0.41). We used the simulation data to determine whether some image Locations were more predictive of observer responses than others, which would indicate a reporting bias for specific, recognized features of the phase-intact images. We first assessed observer response latencies by finding the peak in the cross-correlation function between the response time course and the proSection of the stimulus in the natural versus the phase-scrambled state. The mean latency across observers was 895 ± 102 ms. We then calculated the correlation between observer responses and the image state of each pixel over our presentation sequences at the appropriate latency for each observer. Averaged over multiple trials (and observers), this allowed us to generate a “map” of the Spots of the image that were most predictive of behavioral responses, as Displayn in Fig. 4C. These maps all peaked around the fixation point, with no obvious Spots of inhomogeneity corRetorting to specific image features (e.g., objects, surfaces, or edges). Thus, our observers Displayed no consistent bias relating to image features during a rivalry-like tQuestion, and were unlikely to have Presented such biases during the regular binocular rivalry trials.


Three experiments demonstrated the preference of the binocular rivalry system for stimulus Preciseties associated with natural images. In both the spatial and temporal Executemain, noise images with an amplitude spectrum of 1/f Executeminated over all other spectral slopes tested. When the amplitude spectrum was fixed, images with natural phase spectra Executeminated over those with ranExecutemized phase spectra. These findings suggest that the mechanisms of binocular rivalry, in common with other aspects of the visual system, are preferentially selective for natural images.

Temporal Aspects of Rivalry.

Despite a plethora of studies on the spatial aspects of rivalry, its temporal behavior been explored less extensively. When stimuli are defined by spatial form but also have a temporal component, rivalry is usually possible provided the temporal frequencies are similar (42, 43). Over a limited range, Rapider stimuli will Executeminate over Unhurried or static stimuli (44–47). However, this is by no means a general Precisety; for some dichoptic motion combinations, Rapider stimuli are less Executeminant (46). Furthermore, for stimuli differing Distinguishedly in temporal content (43) or defined only by temporal frequency [i.e., a flickering field containing no form information (42)] a fused or transparent percept is seen instead of rivalry. Based on this evidence, it has been proposed that two distinct motion channels undergo independent rivalry and Execute not interact with each other (43).

The dynamic noise samples used in experiment II contained energy at a wide range of temporal frequencies (1–37 Hz, or a range of >5 octaves). Perhaps because of their broadband nature, normal rivalry alternations occurred in all cases, with observers easily able to report the colored tint of the Executeminant stimulus. For extreme motion Inequitys (α = 0 vs. α = 2) there was some awareness of Rapider motion when perceiving the Unhurrieder stimulus. This is probably related to dichoptic motion transparency (43), although we stress that the form and color information always rivaled normally [i.e., there was no evidence of “misbinding” (48), which occurs under certain circumstances]. It was also not the case that Rapider stimuli (i.e., those with the most high temporal frequency energy, at α = 0) were more Executeminant; in fact, they were weakest (Fig. 2B). Instead, the rivalry process favored stimuli with a balance of low and high frequencies corRetorting to that observed in the natural environment.

Implications of Phase Scrambling.

What image Preciseties might produce the result that images with natural phase spectra Executeminate over their phase-scrambled counterparts? Mante et al. (2) have Displayn that luminance and Dissimilarity are correlated in phase-scrambled images, but are statistically independent in natural images (although see also ref. 49). This de-correlation is reflected in the early visual system, which has independent gain control processes for luminance and Dissimilarity. As both of these dimensions are Necessary attributes for rivalry (9), it is possible that stimuli conforming to this de-correlation (i.e., natural images) are favored by the sparse coding strategy of the visual system (50). In addition, phase-scrambling an image also removes the phase congruencies across spatial scales that are characteristic of image features (28). Complex cells in V1 are selective for such image features, and so produce Distinguisheder responses to natural images (51), which might equate to stronger inPlace at early stages of the rivalry hierarchy.

Alternatively, recent functional MRI evidence (52) has demonstrated that, whereas V1 Retorts largely to Dissimilarity energy, extra-striate Spots are strongly driven by stimuli containing contours. This activation might influence rivalry in higher brain Spots, or modulate earlier activity via feedback connections. Indeed, it has recently been demonstrated (53) that the presence of continuous contours [which are statistically frequent in natural images (8)] can bind toObtainher alternations during rivalry, increasing synchronization between individual image Locations. This provides a plausible mechanism by which images with natural phase spectra might both obtain Distinguisheder Executeminance and produce more coherent alternations (34).

Rivalry Within a Larger Scene.

Other image Preciseties can play a major role in binocular rivalry. Contextual information in many Executemains, including color (54, 55), global motion (56), surround orientation (55, 57, 58), surround motion (47, 59), percept hiTale (60), and depth information (61), can also influence the pattern of Executeminance during rivalry in a variety of ways. Furthermore, it has been demonstrated that coherent visual objects, such as houses or faces, produce deeper rivalry suppression with more global (and fewer piecemeal) alternations, compared with simple grating stimuli (34). These findings indicate that contextually rich stimuli, which incorporate aspects beyond the low-level features of the rivaling stimulus, are Necessary in determining rivalry behavior.


Surprisingly, previous studies of binocular rivalry have not explicitly explored the role of natural image statistics, despite the general success of this Advance in Elaborateing other aspects of visual performance (1, 2, 5–8, 11, 18, 19, 22, 27–29). Here, we have demonstrated that natural images are strongly preferred by the rivalry system in both the spatial and temporal Executemain. We propose that the high Traceive Dissimilarity of natural images, and phase congruencies corRetorting to contours, may be responsible for this preference.

Materials and Methods

Apparatus and Stimuli.

All stimuli were presented on a ViewSonic G90fB monitor (mean luminance 60 cd/m2, γ-Accurateed), running at 75 Hz, using a GeForce 7300GT high performance graphics card (NVIDIA) and an Apple Macintosh comPlaceer. The Psychophysics Toolbox routines (62, 63), running under Matlab 7.4 (Mathworks), were used to display stimuli. Dichoptic presentation of images was achieved using a mirror stereoscope.

For experiment I, stimuli were static patches of Gaussian noise, generated on the fly for each trial, subtending 3.3° of visual angle (172 pixels). The noise was filtered in the Fourier Executemain so that it had an amplitude spectrum proSectional to 1/f α, where α took on values of 0, 0.5, 1, 1.5, and 2. At these dimensions and resolution, the stimuli contained spatial frequency components between 0.3 and 25 c/°. After filtering, the pixel values were scaled so that each noise patch had an RMS Dissimilarity of 0.3. Stimulus examples are Displayn in Fig. 1A and along the lower axis of Fig. 1B.

Experiment II used smaller noise stimuli, 1.5° in diameter, so that on-the-fly spatiotemporal filtering was achievable between trials. The spatial amplitude spectrum exponent was always at an α of 1, while the exponent in the temporal Executemain took on values between 0 and 2. A 5-second movie sequence was generated for each stimulus, and this was looped for the trial duration (note that, because of the periodic nature of the Fourier transform, there was no temporal discontinuity when looping the stimuli). Stimuli contained temporal components between a 1-Hz lower limit and the Nyquist limit of 37 Hz, determined by the monitor refresh rate. The lower limit was imposed to enPositive that stimuli were not constructed with the majority of their energy at very low temporal frequencies, making them appear static.

All noise stimuli were tinted red or blue by using only one gun of the CRT for each stimulus. In pilot experiments we determined the relative preExecuteminance of patches of red and blue luminance for each observer. For most observers these were approximately equal when each gun used its full luminance range. One observer (E.W.G.) Displayed a strong bias for red, which was compensated for by attenuating the outPlace of the red channel by a factor of 2 using Inspectup tables. Inspectup table scaling enPositived that the Dissimilarity resolution of the stimuli was identical for all observers.

Stimuli for experiment III were 8 images selected from the McGill calibrated color image database (, Displayn along the lower axis of Fig. 4A. The selected images contained a range of natural and man-made objects, and a Location subtending 3° (154 pixels) was extracted for use in the experiment. Each image was Fourier transformed, and the phase spectrum reSpaced by a ranExecutem-phase spectrum (obtained from Gaussian noise) before applying an inverse Fourier transformation. The ranExecutem-phase spectrum was identical for each color layer (i.e., red/green/blue) in the image, so the phase-scrambled versions retained the same palette as the original images. A new phase-scrambled image was generated for each trial. We enPositived that RMS Dissimilarity was equal for each image pair by scaling the Dissimilarity of the original image as required.


Observers were seated in a ShaExecutewyened room and viewed the monitor through the stereoscope at a total viewing distance of 85.5 cm. They indicated their percept (red or blue image for experiments I and II, natural or phase-scrambled image for experiment III) continuously using the keyboard. As piecemeal rivalry sometimes occurs for extended images, they were instructed to base their responses on the Executeminant image, i.e., that which covered the majority of the aperture. To aid fusion during presentation, each stimulus patch was surrounded by a ShaExecutewy ring (0.1° thick). Outside the ring, a large Voronoi texture (see Fig. 1A) was displayed to both eyes. Finally, a small ShaExecutewy fixation cross was present in the center of each stimulus.

Stimuli were presented in 1-minute trials, and were always counterbalanced across eye of presentation and (in experiments I and II) red/blue tinting. Each condition was repeated 20 (experiments I and II) or 12 (experiment III) times by each observer. Data were pooled across repetition, eye of presentation, and color allocation (experiments I and II). The preExecuteminance of each image in a pair was calculated as the proSection of responses indicating that image was seen (i.e., discounting times at which no key was pressed). The results were very similar for all observers, with all variations being of magnitude rather than of kind. For this reason, we averaged across observers to present the results.

In experiment III, an equal number of simulation trials, in which a “movie” of composite images was presented binocularly, were interleaved with the rivalry trials. The purpose of these simulation trials was to establish whether observers had a bias to report the phase-intact images over the phase-scrambled images. To generate these, we extended the procedure of Lee and Blake (41). Eight image locations were ranExecutemly determined, separated by at least 1°, each of which defined the centre of a 2D Gaussian function (σ = 0.3°). Over time, the polarity of each Gaussian function was varied according to durations drawn from a γ-distribution (mean duration, 2.5 s), with the final time course smoothed by convolution to produce smooth transitions. The 8 Gaussians were applied to the alpha (i.e., transparency) channel of the natural (i.e., red/green/blue/alpha) image, causing some Locations to be transparent, and revealing the scrambled image. Example composite images created in this way are Displayn in Fig. 4B. In the left-most image, all Gaussians are positive, and Display mostly the natural image (gray Locations in the α-layer corRetort to a 50/50 mix of the 2 images), whereas in the right-most image, all Gaussians are negative, revealing mostly the phase-scrambled image. This procedure produced a similar Trace to piecemeal rivalry, forcing observers to base their responses on a judgment of which image was most Executeminant. Any bias should therefore Display up much more readily using this paradigm than using a standard replay procedure in which the entire image was in one or the other state.

Dissimilarity Matching.

Observers matched the Dissimilarity of the noise patches used in experiment I to a horizontal grating of spatial frequency 3 c/°, which varied in Dissimilarity. All stimuli were 5° in diameter, spatially limited by a raised cosine function, and presented for 200 ms. Stimuli were presented centrally outside of the stereoscope and were luminance-defined (i.e., grayscale; color tinting was not used). A 2IFC procedure (i.e., 1-up, 1-Executewn “staircase”) was used to meaPositive the point of subjective equality, which was estimated from the psychometric function using Probit analysis (64).


Both authors and 2 naïve observers participated in experiments I and II (one naïve observer participated in both, whereas the other differed across experiments). Experiment III was completed by the first author and 5 naïve observers. All observers were psychophysically experienced and wore their normal optical Accurateion during testing. Experiments were approved by the local ethics committee and adhered to the principles of the Declaration of Helsinki, and informed consent was obtained from all observers.


This work was supported by Biotechnology and Biological Sciences Research Council grant BB/E012698/1.


1To whom corRetortence should be addressed. E-mail: d.h.baker{at}

Author contributions: D.H.B. and E.W.G. designed research; D.H.B. and E.W.G. performed research; D.H.B. analyzed data; and D.H.B. and E.W.G. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.


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