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Article  |   April 2015
Direct encoding of orientation variance in the visual system
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Journal of Vision April 2015, Vol.15, 3. doi:10.1167/15.4.3
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      Liam J. Norman, Charles A. Heywood, Robert W. Kentridge; Direct encoding of orientation variance in the visual system. Journal of Vision 2015;15(4):3. doi: 10.1167/15.4.3.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Our perception of regional irregularity, an example of which is orientation variance, seems effortless when we view two patches of texture that differ in this attribute. Little is understood, however, of how the visual system encodes a regional statistic like orientation variance, but there is some evidence to suggest that it is directly encoded by populations of neurons tuned broadly to high or low levels. The present study shows that selective adaptation to low or high levels of variance results in a perceptual aftereffect that shifts the perceived level of variance of a subsequently viewed texture in the direction away from that of the adapting stimulus (Experiments 1 and 2). Importantly, the effect is durable across changes in mean orientation, suggesting that the encoding of orientation variance is independent of global first moment orientation statistics (i.e., mean orientation). In Experiment 3 it was shown that the variance-specific aftereffect did not show signs of being encoded in a spatiotopic reference frame, similar to the equivalent aftereffect of adaptation to the first moment orientation statistic (the tilt aftereffect), which is represented in the primary visual cortex and exists only in retinotopic coordinates. Experiment 4 shows that a neuropsychological patient with damage to ventral areas of the cortex but spared intact early areas retains sensitivity to orientation variance. Together these results suggest that orientation variance is encoded directly by the visual system and possibly at an early cortical stage.

Introduction
Summary statistics are computed by the visual system, presumably to be economical and to minimize computational effort when confronted with detailed environments (Ariely, 2001; Morgan, Mareschal, Chubb, & Solomon, 2012), and may play a role in many forms of region-based perception (e.g., texture perception). Summary statistics are available in many different forms, and human performance frequently correlates with predictions from models based on statistical summations. Ariely (2001) demonstrated that when a test circle was presented following a set of similar circles of varying radii, observers could determine whether or not the radius of the test circle was equal to that of the mean of the set despite not being able to reliably identify whether the test circle was actually contained in that set. This represents a dissociation between the perception of a summary representation that describes a set and the representations of the individual units within that set (Chong, Joo, Emmanouil, & Treisman, 2008; see also work on visual crowding: Parkes, Lund, Angelucci, Solomon, & Morgan, 2001; Solomon, 2010), suggesting the presence of a dedicated mechanism that extracts region-based information that is statistical in nature. The ability of the visual system to reliably encode statistical properties is apparent elsewhere; for instance, in estimating the mean direction among individual local motion paths (Williams & Sekuler, 1984) and in estimating the mean orientation among oriented line segments (Dakin, 2001; Dakin & Watt, 1997). 
More complex region-based characteristics require statistical estimation of a higher order. Orientation variance (a second moment statistic), for instance, is a regional property of which spatial gradients do not permit edge-based segmentation (Wolfson & Landy, 1998) but could inform object recognition by indicating surface irregularity. Orientation variance is of particular interest because the visual system may be intrinsically noisy, potentially perturbing the information that it receives. For example, estimations of a single orientation are consistent with a Gaussian distribution with a standard deviation centered on the actual orientation. Morgan and colleagues (Morgan et al., 2012; Morgan, Chubb, & Solomon, 2008) pointed out the apparent contradiction between this attribute of the visual system and our perception of homogenous texture: In a field of perfectly uniform elements we should see deviations from the mean, yet this is not the case. They theorize that in instances of textural analyses such as this, our perception is determined not only by our internal representation of individual orientations but also by a dedicated mechanism that directly estimates the variance. They provide evidence for this in finding a “dipper function” for discriminations based on orientation variance of the type that has also been documented in discriminations of blur (Watt & Morgan, 1983) and contrast (Nachmias & Sansbury, 1974). This threshold nonlinearity is thought to allow the visual system to discount its own imperfections (intrinsic noise) when conducting a statistical estimation, and only when the estimation of variance exceeds a certain criterion are the individual deviations apparent. 
Experiments 1 and 2 here explored whether orientation variance is encoded as a property of a texture using selective adaptation. The dominant theory of adaptation is that the perception of a given stimulus attribute is determined by the balance of activity between populations of neurons tuned to different levels of that attribute and that the neurons that are firing during exposure to the adapted stimulus become fatigued or inhibited (Krekelberg, Boynton, & Van Wezel, 2006), resulting in an imbalance that creates a misperception of subsequently perceived stimulus. 
Adaptation has previously been used as a tool to explore the fundamentals of region-based perception because it can reveal dedicated mechanisms specifically sensitive to statistical properties and the manner in which they encode the information. The visual system's representation of mean size (Corbett & Melcher, 2014; Corbett, Wurnitsch, Schwartz, & Whitney, 2012), luminance contrast (akin to extracting the variance of luminance information; Durgin, 2001), density (akin to extracting the same statistic from contrast itself; Durgin, 2001), and surface gloss (which is correlated with luminance skewness; Motoyoshi, Nishida, Sharan, & Adelson, 2007; although see Kentridge, Thomson, & Heywood, 2012; Kim & Anderson, 2010), for example, can be selectively adapted, revealing the role of populations of neurons tuned to low and high intensity levels of those attributes. Importantly, such effects are measurable on surfaces that resemble real materials and objects and are not restricted to abstract psychophysical displays (Durgin & Huk, 1997; Motoyoshi et al., 2007). 
In Experiment 1, observers were continually presented with two textures—one on the right and one on the left—during an adaptation phase. One of these textures was always constructed from a Gaussian distribution of a medium variance and the other was always constructed from a Gaussian distribution of either a relatively low or high variance. When presented with a similar pair of textures in the test phase, subjects were required to identify which texture (left or right) appeared to contain the most variance, and the point of subjective equality (PSE) was sought using an adaptive staircase method. Adapting to a low variance on one side should increase the perception of variance of the test texture on that side, and the opposite for adaptation to high variance. Importantly, mean orientations of the adapting and test stimuli were randomly determined for each presentation to negate low-level effects of orientation adaptation. 
Experiment 1: Orientation variance adaptation with randomized means
Method
Participants
Eight naïve observers (five females, three males; mean age = 21.8 years, SD = 1.83) took part in the study. Participants gave their written informed consent. 
Equipment and stimuli
The display monitor was viewed at a distance of 41 cm; subjects rested their head on a chin rest. Stimuli were presented on the uniform gray background (50 cdm−2) of a ViewSonic (Brea, CA) 17-in. (1254 × 877 pixels) color monitor driven by a Cambridge Research Systems (Kent, United Kingdom) VSG 2/5 Graphics System with a refresh rate of 100 Hz. 
The experimental stimuli used in both the adaptation and test sections consisted of a pair of textures, each comprising 9 × 9 Gabor patches. Each Gabor patch measured 0.6° in diameter and was separated from its neighbors by 0.3° with a small positional jitter (the Gabor patch was uniformly likely to fall on any point within a circular window of a radius of 0.1° at the specified location). Each texture, therefore, measured 7.8° in width and height. All Gabor patches had a spatial frequency of 4.2 cycles/degree, and each was assigned an individually randomly determined phase from the full 360° cycle. The Michelson contrast of each Gabor was 90%. The two textures were separated horizontally by 7.2°, with one appearing to the left and the other to the right of fixation for both the adaptation and test phases. 
Each texture's orientation statistics were determined by independently drawing each composite orientation value from a Gaussian distribution with a particular mean (μ) and standard deviation (σ). The value of μ was determined randomly for each patch on each presentation. The value of σ for each texture depended on several experimental parameters; during adaptation, one of the textures assumed a medium level (σ = 10) and the other assumed either a low (σ = 2) or a high (σ = 26) level. These values were chosen from a period of pilot testing on one of the participants as values that induced aftereffects that were comparable in magnitude to one another. Examples of the stimuli are shown in Figure 1
Figure 1
 
Examples of the different levels of variance used during adaptation in the experiments. In panel a, both textures are of a medium variance. In panel b, the left texture (in this case, the adapting texture) is of a low variance and the right is of a medium variance. In panel c, the left texture (again, the adapting texture) is of a high variance and the right is again of a medium variance. Note that in this figure the two patches share the same mean orientation, but this was randomly determined separately for each patch on each presentation in the experiment.
Figure 1
 
Examples of the different levels of variance used during adaptation in the experiments. In panel a, both textures are of a medium variance. In panel b, the left texture (in this case, the adapting texture) is of a low variance and the right is of a medium variance. In panel c, the left texture (again, the adapting texture) is of a high variance and the right is again of a medium variance. Note that in this figure the two patches share the same mean orientation, but this was randomly determined separately for each patch on each presentation in the experiment.
Experimental conditions and design
Each subject completed two testing sessions, one for each level of adaptation (low and high). Half of the subjects received the adapting texture on the left of fixation and the other half received the texture on the right. Testing was conducted over a period of 2 days, with one session per day, and the order of the sessions was counterbalanced across subjects. 
Trial sequence
Subjects fixated a central cross. Each session began with a 60-s adaptation procedure consisting of 30 stimulus flashes, each lasting 1 s and separated by an interval of 1 s. In each flash both the medium-variance texture and the low- or high-variance texture were presented. For each adaptation flash, the textures were constructed de novo, with newly determined random mean orientations and each orientation drawn again from their relative distribution. Following adaptation, subjects received a warning tone and a pause of 750 ms before the test stimuli flashed onscreen for 500 ms. Subjects indicated which of the two textures in this flash appeared to contain the most orientation variance by pressing one of two keys, marking the end of one trial. Between trials, subjects were presented with a further top-up adaptation consisting of three flashes, and after every 25th trial they were presented with a prolonged top-up adaptation of 30 flashes. 
In each session, trials were presented using two randomly interleaved one-up one-down staircases that approximated the PSE. The variance of the test stimulus texture corresponding to the side of the low- or high-variance texture remained constant (at the medium level), and each staircase automatically adjusted the variance of the opposite texture until it reached an estimate of the subject's PSE (i.e., at which point they chose left/right in equal proportion). Two randomly interleaved staircases were used; in one staircase, this texture began the session with a variance that was higher (σ = 15) than that of the medium-variance texture, and in the second staircase the texture began with a variance that was lower (σ = 5). The variance was incrementally increased or decreased by a magnitude of 2° initially (first four trials per staircase) and from there on by a magnitude of 1° until a criterion of six reversals had been met. 
Results
The measured threshold levels correspond to the PSE (i.e., perceived level of variance of the test texture on the adapted side). This estimation was taken by averaging the final four reversal points of the two interleaved staircases for each condition. Data were averaged from all eight participants. 
For the high-adaptation condition, the PSE was 3.6° below the level of objective equality, whereas for the low-adaptation condition, the PSE was 3.2° above the level of objective equality (see Figure 2). Two one-sample t tests were carried out between these PSE estimates and zero (objective equality). Both were significant, with the measurement following high adaptation being significantly lower than the objective measurement, t(7) = 9.82, p < 0.001, and the measurement following low adaptation being significantly higher, t(7) = 4.92, p = 0.002. These results indicate that when observers adapted to a texture with low orientation variance, a subsequent texture appearing in the same location appeared to contain more variation than it actually did. The opposite was found following adaptation to high levels of variance. 
Figure 2
 
Results from Experiments 1 (random orientation of adapting textures) and 2 (constant orientation). Levels of PSE as a result of adapting to levels of low and high variance. A value of zero corresponds to the actual variance of the texture (objective equality), as shown by the horizontal axis. Thus, a value above this level indicates a shift in variance perception toward the higher end of the scale and a value below this level indicates a shift toward the lower end. Error bars show ±1 SEM.
Figure 2
 
Results from Experiments 1 (random orientation of adapting textures) and 2 (constant orientation). Levels of PSE as a result of adapting to levels of low and high variance. A value of zero corresponds to the actual variance of the texture (objective equality), as shown by the horizontal axis. Thus, a value above this level indicates a shift in variance perception toward the higher end of the scale and a value below this level indicates a shift toward the lower end. Error bars show ±1 SEM.
Interim discussion
Experiment 1 has shown that the perception of orientation variance can be selectively altered by adaptation-induced aftereffects. Importantly, as the mean orientation was randomly allocated for all adaptation and test textures, the effect is not an indirect aftereffect following adaptation to low-level orientation signals. Experiment 2 sought to replicate this finding but, instead of randomly assigning the mean orientation of the adapting textures, presented adapting textures with a mean orientation perpendicular (i.e., 90°, corresponding to horizontal) to that of the test textures (0°, corresponding to vertical) to ensure that the mean orientation of the test patch was not perceived at any time during the adaptation phases. The production of an aftereffect in this experiment would therefore strongly suggest that orientation variance is encoded in a manner that is not restricted specifically to a particular mean orientation. 
Experiment 2: Orientation variance adaptation across perpendicular means
Method
See the description of the method for Experiment 1. A new set of eight naïve observers (four females, four males; mean age = 22.8 years, SD = 2.71) took part in the study. 
Results
For the high-adaptation condition, the PSE was 4.3° below the level of objective equality, t(7) = 12.50, p < 0.001, whereas for the low-adaptation condition, the PSE was 3.6° above the level of objective equality, t(7) = 3.95, p = 0.006. These results (see Figure 2) thus replicate the findings from Experiment 1, but, importantly, this occurred despite the adaptation textures constantly having a mean orientation that was 90° in contrast to that of the test textures. To determine whether the magnitudes of the aftereffects were greater across experiments, the results of Experiments 1 and 2 were jointly analyzed in a 2 × 2 mixed model analysis of variance (ANOVA) with experiment number as a between-subjects factor and adaptation level as a within-subject factor. A main effect of adaptation level was found, F(1, 14) = 175.30, p < 0.001, but neither an effect of experiment number, F(1, 14) = 0.586, p = 0.457, nor an interaction was found, F(1, 14) = 0.801, p = 0.386. This indicates that the magnitude of the aftereffect is not affected by the adapting textures being random or perpendicular in their mean orientation. 
Interim discussion
Together, Experiments 1 and 2 established that the perception of orientation variance can be selectively altered by adaptation-induced aftereffects. Importantly, the effects could have emerged only if the variance was encoded at a level that was independent of mean orientation. This is highly suggestive of a dedicated mechanism within the visual system that extracts the statistical irregularity among orientation signals in a given texture, agreeing with work by Morgan et al. (2008, 2012) and other work more generally that has found evidence through adaptation aftereffects of statistical computations by the visual system (e.g., Corbett et al., 2012). 
Can the aftereffects be explained by low-level pattern adaptation? In Experiment 1 the presentation of randomly oriented adapting textures ensured that no single orientation was consistently adapted at any given retinal location. Pattern adaptation, therefore, cannot explain those results. In Experiment 2 the mean orientation of all adapting textures was purposefully set to be 90° throughout the presentation. Given the difference in variance of these two adapting textures, they will elicit differential levels of adaptation to an orientation of 90°, which may in turn underlie the observed aftereffect. Given that the magnitudes of the aftereffects in Experiments 1 and 2 are comparable, however, it seems unlikely that such local pattern adaptation effects played a role in the aftereffects in Experiment 2. Alternatively, it is possible that local pairwise statistics of neighboring orientations are encoded by the visual system and that this may confound an explanation of adaptation to the regional property of variance. If this were to explain the results, however, the representation of the pairwise correlation would have to be invariant to mean orientation. Further work on the representation of these orientation statistics is needed before this can be determined. 
Experiment 3 aimed to uncover the reference frame in which this variance aftereffect is based. The initial input into the visual system is based strictly on retinal coordinates, yet our visual experience is stable across eye movements, implying a spatiotopic representation of information coding. Such coding relies on retinotopic coding plus knowledge of changes in the self's viewpoint or position due to eye, head, or body movements. Early visual regions are retinotopically organized (Crespi et al., 2011; Gardner, Merriam, Movshon, & Heeger, 2008; Golomb, Nguyen-Phuc, Mazer, McCarthy, & Chun, 2010), whereas later visual regions show signs of spatiotopic coding (Zipser & Andersen, 1988). Neurons in parietal areas, for instance, show predictive coding of stimuli that will fall onto the receptive field once an eye movement has been made (Duhamel, Colby, & Goldberg, 1992). Additionally, many properties of mid- to high-level ventral stream processing (e.g., large receptive field sizes: MacEvoy & Epstein, 2007; position invariance: Grill-Spector & Malach, 2001) indicate spatiotopic coding. 
Methods of psychophysics offer a way to examine what information is remapped across a saccade onto a spatiotopic reference frame through investigating the transference of aftereffects following perceptual adaptation. There is some evidence from such methods that spatially detailed stimuli are encoded in spatiotopic coordinates, and the degree of this encoding correlates with stimulus complexity, suggesting an increasingly spatiotopic representation along the processing hierarchy of the visual system (Melcher, 2005; Melcher & Colby, 2008), which is supported by some neuroscientific studies (Merriam, Genovese, & Colby, 2007; Nakamura & Colby, 2002; although see Golomb & Kanwisher, 2012). Determining whether specific adaptation-induced aftereffects are retinotopic or spatiotopic, therefore, offers a way to explore how specific visual attributes are encoded with relation to the processing hierarchy of the visual system. The motion aftereffect, for instance, is known to be fixed in retinotopic coordinates (Knapen, Rolfs, & Cavanagh, 2009; Turi & Burr, 2012), reflecting its effect in early visual areas (possibly V1, the first cortical visual area), whereas the positional motion aftereffect (the apparent change in spatial position following motion adaptation) is spatiotopic (Turi & Burr, 2012). It was predicted in the present study that although aftereffects to mean orientation (i.e., the tilt aftereffect) are retinotopic, adaptation to orientation variance may reveal spatiotopic encoding. Although local orientation adaptation results in a retinotopic-specific tilt aftereffect (due to its operating in V1; Knapen, Rolfs, Wexler, & Cavanagh, 2010), the encoding of orientation variance is likely to require the large receptive field properties of later neurons, which are more likely to encode spatiotopically (Melcher, 2005; Melcher & Colby, 2008). 
In order to dissociate these reference frames, it is necessary to invoke an eye movement between the presentation of the adapting stimuli and the test stimuli. In Experiment 3, therefore, observers fixated either above or below the adapting stimuli and, when prompted, moved their gaze diagonally to either the left or the right of center before returning to either the original fixation position or the opposite fixation location (above or below). Finally, because attention is important for spatiotopic encoding of information (Crespi et al., 2011), subjects were encouraged to attend to the textures during the adaptation sections by carrying out a secondary task of indicating when one of the textures was presented with a relatively lower luminance contrast. 
Experiment 3: The reference frame of orientation variance adaptation
Method
Participants
Four observers (two females, two males; mean age = 22.5 years, SD = 1.73) took part in the study; three were naïve and one was one of the authors. Participants gave their written informed consent. 
Equipment and stimuli
See the description of the equipment and stimuli for Experiment 1. In this experiment, gaze fixation was recorded using an infrared video eye tracker (Cambridge Research Systems) with a sampling frequency of 250 Hz. 
During adaptation, the pair of textures was always presented in the center of the screen. In the test phase, the pair of textures was presented either in the center of the screen or in the upper or lower half (depending on the testing condition). 
Experimental conditions and design
Each subject completed four testing sessions. In each session, one of the adapting textures was of either a low or a high variance and was presented on either the left of fixation or the right of fixation. The order of the four sessions was counterbalanced across subjects: Half of the subjects fixated above the adapting stimuli and half fixated below. Testing was conducted over a period of 4 days, with one testing session per day. Each session consisted of four interleaved conditions in which the test stimuli were presented at different locations relative to the adapting stimuli. Thresholds acquired for these conditions were averaged across the left and right adaptation side conditions. Thus, individual threshold estimates were gathered for four conditions of test stimulus location for adaptation to low and high levels of variance. 
During adaptation, the fixation cross was presented 1.8° below the adapting stimuli (measured from bottom/top of textures) for half of the subjects and above for the remaining half. The test stimuli were presented after a period of adaptation. Four experimental conditions were included (see Figure 3) in which the retinotopic and spatiotopic positions of the test stimuli relative to the adapting stimuli were independently varied. Dissociating these conditions required subjects either to relocate their fixation to the opposite side of the adapting stimuli or to maintain fixation at the same location, and then to present the test stimuli either above or below the new fixation point. In order to equate for the number of eye movements across the four conditions, however, two eye movements were required to be made in each condition regardless of whether fixation changed for the testing period—a technique used previously by others (e.g., Corbett & Melcher, 2014; Knapen et al., 2009). Specifically, following adaptation, fixation moved diagonally to either the left or the right of center (equally likely) before relocating to the test position. The full aftereffect was measured when subjects relocated their fixation to its original position and the test stimuli were presented in the same location as the adapting stimuli. The retinotopic aftereffect was measured when subjects changed fixation to the opposite location and the test stimuli were presented on the opposite side of fixation to the adapting stimuli. The spatiotopic aftereffect was measured when subjects changed fixation to the opposite location and the test stimuli were presented in the same location on the screen as the adapting stimuli. The control (“none”) condition was measured when subjects relocated their fixation to its original position and the test stimuli were presented on the opposite side of fixation to the adapting stimuli. The purpose of this control condition was to correct for any retinotopic spreading of the adaptation effect that may explain any effect found in the spatiotopic condition that was not due to spatiotopic coding. To summarize, the test stimuli were presented to one of four locations relative to the position of the adapting stimuli: 
  1.  
    Same retinal, same spatial coordinates (full condition)
  2.  
    Same retinal, different spatial coordinates (retinotopic condition)
  3.  
    Different retinal, same spatial coordinates (spatiotopic condition)
  4.  
    Different retinal, different spatial coordinates (none condition)
Figure 3
 
Illustration of the conditions from Experiment 3. During adaptation, half of the subjects fixated above and half fixated below (shown here) the adapting stimuli. Adaptation to high variance is shown on the right and adaptation to medium variance is shown on the left. Following a period of adaptation, an eye movement was required to be made to either the left or the right (shown here) of center. Four stimulus conditions were interleaved in each block. In two of these conditions fixation returned to the original position for test, and in the remaining two conditions fixation moved to the opposite side of the adapting stimuli (either above or below) for test. The test stimuli then appeared either above or below the new fixation point. Thus, the combination of the fixation position and test stimuli location determined the reference frame (labeled in the figure).
Figure 3
 
Illustration of the conditions from Experiment 3. During adaptation, half of the subjects fixated above and half fixated below (shown here) the adapting stimuli. Adaptation to high variance is shown on the right and adaptation to medium variance is shown on the left. Following a period of adaptation, an eye movement was required to be made to either the left or the right (shown here) of center. Four stimulus conditions were interleaved in each block. In two of these conditions fixation returned to the original position for test, and in the remaining two conditions fixation moved to the opposite side of the adapting stimuli (either above or below) for test. The test stimuli then appeared either above or below the new fixation point. Thus, the combination of the fixation position and test stimuli location determined the reference frame (labeled in the figure).
Trial sequence
Subjects fixated a cross above or below the adaptation textures and pressed a button to begin a session. Each session began with a 60-s adaptation procedure consisting of 30 stimulus flashes, each lasting 1 s and separated by an interval of 1 s. Each flash contained the medium-variance texture and the low- or high-variance texture. For each adaptation flash, the textures were constructed de novo, with newly determined random mean orientations and each orientation drawn again from their relative distribution. Following adaptation, subjects were instructed by a warning tone to anticipate an eye movement. Following this (1 s), the fixation cross would move diagonally to 5.7° either to the left or to the right of the center of the monitor. The duration of this new fixation was 500 ms, after which the cross either returned to its original position above or below the location of the adapting stimuli or moved to the opposite position above or below the stimuli, depending on the testing condition. Following an additional period of 750 ms and a second warning tone, the test stimuli flashed onscreen for 500 ms either above or below the new fixation point, again depending on the testing condition. Subjects indicated which of the two textures appeared to contain the most orientation variance by pressing one of two keys, following which the fixation cross would relocate to its original position (if necessary), marking the end of one trial. Between trials, subjects were presented with a further top-up adaptation consisting of three flashes and, after every 25th trial, a prolonged top-up adaptation of 30 flashes. 
Trials were presented using eight randomly interleaved one-up one-down staircases; each of the four conditions was represented by two staircases per session. Each staircase progressed as in the previous experiments. 
Because attention is important for spatiotopic encoding of information (Crespi et al., 2011), subjects were encouraged to attend to the textures during the adaptation sections by carrying out a secondary task. This was to indicate, by pressing a button, if one of the textures was constructed of Gabor patches of a slightly lower contrast than normal (60% Michelson contrast). This occurred with a probability of 0.1 on each adaptation flash and was equally likely to be the left or the right texture. 
Additionally, eye tracking was carried out to ensure that subjects tracked the fixation cross during the intermittent relocation period following adaptation. If the eye tracker did not detect that the subject had fixated after 200 ms or that fixation subsequent to this was not within a 1° radius of the cross, then data from that trial were disregarded and the experiment continued without collecting data from that trial. Additionally, if fixation was not recorded to be within a radius of 1° of the cross during the time in which the test stimuli were onscreen, the trial was disregarded. 
Results
The online fixation monitoring ensured that trials were discarded if subjects moved their gaze away from the fixation cross. To ensure that subjects were nonetheless covertly attending to the adapting stimuli, their hit rates and false alarm rates in detecting the contrast decrement, which occurred, on average, once every 10 flashes, were compared. Hit rates (as a proportion) for each subject were 0.97, 0.97, 0.77, and 0.97, whereas no subject exceeded a false alarm rate of 0.01. These high performance rates suggest that the task was not difficult for three of the participants and may not have been that attentionally demanding. Spatiotopic encoding, however, requires only that spatial attention is not constrained by a secondary attentionally demanding task (Crespi et al., 2011). The task employed here ensures that the adapting stimuli are the participants' primary, and indeed only, stimuli to be attending. 
Thresholds collected from sessions in which the low or high adapting texture was present on the left or on the right were averaged to give a single threshold estimate for each testing condition, and this was done independently for adaptation to low and high variance. Thus, each threshold estimate is taken from an average of four staircases, and each threshold value represents the shift in variance (in degrees) that is required to obtain the PSE. These data are shown in Figure 4. A 2 × 2 repeated measures ANOVA was run separately for the high- and low-variance adaptation conditions, with the relative position of the adapting and test stimuli in retinotopic coordinates (same vs. different) and spatiotopic coordinates (same vs. different) as factors (full: same, same; retinotopic: same, different; spatiotopic: different, same; none: different, different). For low-variance adaptation, a significant main effect of retinotopic coordinates was found, F(1, 3) = 16.43, p = 0.027, with no main effect of spatiotopic coordinates, F(1, 3) = 0.74, p = 0.45, and no interaction, F(1, 3) = 0.32, p = 0.610. The same result was found for high-variance adaptation, with a significant main effect of retinotopic coordinates, F(1, 3) = 16.12, p = 0.028, but not spatiotopic coordinates, F(1, 3) = 2.07, p = 0.246, and no interaction, F(1, 3) = 0.33, p = 0.608. Importantly, through examining Figure 4 it is confirmed that following adaptation to either low or high variance, the perceived variance of the test texture is either increased or decreased, respectively (as shown by the positive and negative aftereffects shown in the figure). 
Figure 4
 
Results from Experiment 3. Each data point represents the average threshold across four observers. Results from low adaptation are shown in panel a; results from high adaptation are shown in panel b. The strength of the aftereffect measurement is determined by the increment or decrement in orientation variance required to null the adaptation effect (PSE). In both cases, the full and retinotopic PSEs are clearly larger than the spatiotopic and nonspecific effects. When the none PSE magnitude is subtracted from the other PSEs to account for retinotopic spreading (panels c and d), the spatiotopic effect is marginal, whereas the other two conditions still show substantial aftereffects. Error bars show ±1 SEM, with between-subjects variance removed.
Figure 4
 
Results from Experiment 3. Each data point represents the average threshold across four observers. Results from low adaptation are shown in panel a; results from high adaptation are shown in panel b. The strength of the aftereffect measurement is determined by the increment or decrement in orientation variance required to null the adaptation effect (PSE). In both cases, the full and retinotopic PSEs are clearly larger than the spatiotopic and nonspecific effects. When the none PSE magnitude is subtracted from the other PSEs to account for retinotopic spreading (panels c and d), the spatiotopic effect is marginal, whereas the other two conditions still show substantial aftereffects. Error bars show ±1 SEM, with between-subjects variance removed.
Additionally, it is important to assess the role of retinotopic spreading, specifically in the spatiotopic condition, by subtracting the magnitude of the none PSE from all other PSEs. The result of this is shown in Figure 4. Clearly there is very little residual effect in the spatiotopic condition, whereas in the remaining retinotopic conditions it is still substantial. These results suggest that adaptation to orientation variance occurs in a strictly retinotopic reference frame. 
Interim discussion
Experiment 3 showed that the variance aftereffect is not encoded in spatiotopic coordinates. If this retinotopic specificity of the variance aftereffect indicates early cortical processing of orientation variance (Melcher, 2005; Melcher & Colby, 2008; Merriam et al., 2007; Nakamura & Colby, 2002), then a patient with damage to midlevel ventral areas but intact low-level areas should retain some sensitivity to the property of orientation variance. Patient MS was used in the following experiment to test this. MS is unable to make some region-based discriminations, including surface color and texture of objects (Cavina-Pratesi, Kentridge, Heywood, & Milner, 2010a, 2010b), which is most likely due to the bilateral damage to his medial occipitotemporal cortex, which has been shown in normal observers to correlate with the discrimination of such regional properties (Cavina-Pratesi et al., 2010a, 2010b). The early cortex in his left hemisphere, however, is spared, and the retinotopic organization of orientation-selective neurons may be sufficient to encode orientation variance. 
Experiment 4: Orientation variance discrimination in patient MS
Method
Participants
Patient MS has bilateral damage to his ventromedial occipitotemporal cortex, is profoundly achromatopsic and prosopagnosic, and has visual object agnosia. Damage to the left hemisphere includes the temporal pole, parahippocampal and fourth temporal gyri of the temporal lobe, the collateral sulcus, and the mesial occipitotemporal junction. His achromatopsia is most likely explained by the damage to the lingual gyrus and anterior collateral sulcus, typically associated with the human color area (see, e.g., Kentridge, Heywood, & Cowey, 2004). Damage in this vicinity is also likely to be the cause of his impairment in discriminating surface properties of objects more generally (Cavina-Pratesi et al., 2010a, 2010b). His ability to perceive object form remains intact, which is likely the result of his spared lateral occipital complex (Cavina-Pratesi et al., 2010a, 2010b). The damage in his right hemisphere is more extensive than that in the left, including the primary visual cortex resulting in a homonymous hemianopia with macular sparing, whereas his occipital lobe in his left hemisphere is largely intact. For a more extensive case description of MS, see Heywood, Cowey, and Newcombe (1994). Retinotopic mapping has not been successfully carried out in patient MS, so it is difficult to say with certainty which visual fields remain intact in his left hemisphere. It is clear that V1 is spared and possibly parts of V2 (second visual area), but given the extensive damage to his lingual gyrus, it is unlikely that V3 (third visual area) is intact and certain that V4 (fourth visual area) is not. Testing was conducted at the University of Durham's psychology department. MS was 63 years of age at the time of testing. Three control participants (all males; mean age = 25 years, SD = 2.00) took part in the same experiment as MS. 
Equipment and procedure
Equipment was the same as in the previous experiments. MS and control participants viewed the display monitor at a distance of roughly 80 cm and were not required to fixate or to use a chin rest. Fixation was not required because MS has great difficulty in maintaining fixation for an extended time period. To allow accurate comparison between MS and the controls, the controls were also allowed free viewing of the stimuli. 
Stimuli consisted of three separate textures of 10 × 10 Gabor patches. Each Gabor patch measured 0.45° in diameter and had a spatial frequency of 2.80 cycles/degree. Each was separated from its neighbors by 0.15°. Thus, each texture measured 5.85° in width and height. The phase of each Gabor was determined randomly from the full 360° cycle. The three textures were aligned vertically in the center of the display, with a distance of 0.40° separating each of the top and bottom textures from the middle. 
Each texture's orientation statistics were determined by independently drawing each composite orientation value from a Gaussian distribution with a particular mean (μ) and standard deviation (σ). The respective mean values of the three textures were determined by first assigning one of the textures a randomly determined value from the full 360° cycle. Of the two remaining textures, one was assigned this value +45° and the other +90°. Thus, each texture had a unique mean orientation with respect to the rest, and this was novel on each trial. The baseline σ was chosen to be 7, which was assigned to either one or two of the three textures, with the remaining texture(s) being assigned a value of 12 (high difficulty), 20 (middle difficulty), or 30 (low difficulty). Thus, one of the textures was odd with respect to the other two, but it was not simply the case that this odd texture always had the largest (or smallest) variance; it was equally likely on each trial that the odd texture would have more or less variance relative to the other textures. MS was instructed to indicate which texture—either the top or the bottom—appeared to be the odd one out. Because the middle texture was never the odd one out, this task was a two-alternative (and not a three-alternative) forced-choice discrimination task. Importantly, with this method, MS could not complete the task on the basis of local orientation comparisons or by analyzing only one of the textures. Figure 5 provides an illustration of the stimuli. 
Figure 5
 
Example stimuli used in Experiment 4. The task was to identify the odd texture (top or bottom) in terms of its variance (irregularity). The three difficulty levels are shown in panels a through c, with decreasing difficulty level left to right. Each texture had a unique mean orientation relative to the other two, which was randomly determined across trials, thus preventing scrutiny of the stimuli on a local scale.
Figure 5
 
Example stimuli used in Experiment 4. The task was to identify the odd texture (top or bottom) in terms of its variance (irregularity). The three difficulty levels are shown in panels a through c, with decreasing difficulty level left to right. Each texture had a unique mean orientation relative to the other two, which was randomly determined across trials, thus preventing scrutiny of the stimuli on a local scale.
The stimuli were presented onscreen until MS verbalized his response, at which point the experimenter pressed the appropriate response key. Five blocks were conducted, each containing 10 repetitions of each of the three discrimination levels, amounting to 30 trials per block. 
Results
For the high, middle, and low difficulty levels, respectively, MS produced the following accuracies: 30/50 (60%; p = 0.101), 37/50 (74%; p < 0.001), and 42/50 (84%; p < 0.001); these are shown as percentage scores in Figure 6. Normal observers (N = 3) on the same task did not produce errorless performances overall and showed the same rising trend in performance with decreasing task difficulty (90%, 97.3%, and 100%). These results suggest that although MS was clearly impaired relative to normal, non-age-matched controls, he shows some sensitivity to the property of orientation variance in the textures. 
Figure 6
 
Results from Experiment 4: MS's variance discrimination task. MS performed significantly greater than chance in the medium- and low-difficulty levels and with progressively more accuracy with increasing variance difference between the discriminanda. This suggests that he may retain an ability to perform the second moment regional estimations that allow the encoding of variance.
Figure 6
 
Results from Experiment 4: MS's variance discrimination task. MS performed significantly greater than chance in the medium- and low-difficulty levels and with progressively more accuracy with increasing variance difference between the discriminanda. This suggests that he may retain an ability to perform the second moment regional estimations that allow the encoding of variance.
General discussion
The effect of variance adaptation is clearly demonstrated in Experiments 1, 2, and 3. The results suggest that what has been adapted is a specific mechanism that is selective to orientation variance, a second moment statistic of regional orientation information. Importantly, the effect cannot be explained on the basis of an undesired effect of adaptation to local orientation (i.e., the tilt aftereffect) due to the random mean orientations used in Experiments 1 and 3 and the perpendicular means used in Experiment 2. This echoes results found following adaptation to other statistical properties (Corbett et al., 2012; Durgin, 2001; Durgin & Huk, 1997; Motoyoshi et al., 2007) and findings that regional information of a set, or texture, is encoded independently of individual local components (Ariely, 2001; Corbett et al., 2012). This result is particularly in line with that recently obtained by Ouhnana, Bell, Solomon, and Kingdom (2013), who demonstrated a perceptual aftereffect for the property of positional regularity, although in that study adaptation only caused textures to appear less regular. In the present set of experiments, we showed that adaptational aftereffects for orientation variance are bidirectional. Such a finding, along with the work of Morgan et al. (2008), points to a mechanism within the visual system that directly encodes the variance of a set of oriented lines in a manner in which the neural representation of variance is determined at least by two channels: one tuned broadly for low variance and one for high variance. Alternatively, multiple narrowly tuned channels, much like those that determine sensitivity to the property of spatial frequency, may yet be revealed to underlie the perception of orientation variance. 
The adaptation aftereffect, however, as shown in Experiment 3, is limited to a retinotopic reference frame. This is also true of the tilt aftereffect, which follows adaptation to a single orientation (Knapen et al., 2010). Knapen et al. (2010) argued that finding spatiotopic aftereffects of orientation adaptation would be unlikely due to it being carried out in V1; remapping of the adaptation would require that the adapted state of neurons be transmitted horizontally through the cortex, requiring a dense connectivity between neurons that isn't found in the early cortex. It was hypothesized in the present study, however, that aftereffects specific to variance adaptation may reveal spatiotopic encoding due to the large receptive fields that may be required to achieve such large-scale estimations. These large-scale receptive fields are to be found downstream from the primary visual cortex in areas that display progressively more signs of spatiotopy (Merriam et al., 2007). In the present study, however, no evidence for a spatiotopic aftereffect was found. This may indicate that variance perception is achieved and represented at a much earlier level in the visual system than previously expected. Alternatively, the aftereffect may be represented in visual processing areas in the parietal cortex, which exhibit retinotopic organization (Schluppeck, Glimcher, & Heeger, 2005; Silver, Ress, & Heeger, 2005). Processing in the parietal cortex, however, is more typically involved in the preparation and coordination of visually guided movements than in the perception of region-based image properties. 
An aftereffect's retinotopic specificity is not sufficient to imply early cortical processing, however, because there is some contention about whether mid- to high cortical areas indeed show an increased sensitivity to spatiotopic encoding. Some evidence from neuroimaging suggests that the vast majority of processing in low- and high-level areas is strictly retinotopic (Gardner et al., 2008). These findings, however, may only reflect differences in the stimuli used and the lack of directed spatial attention toward the stimuli. In Gardner et al.'s (2008) study, for instance, the stimuli were presented parafoveally while subjects performed an attentionally demanding task at fixation. It is now known that selective spatial attention toward a stimulus is a crucial factor in determining its spatiotopic encoding in mid- to high-level areas (Crespi et al., 2011). The failure to find spatiotopic aftereffects in the present study cannot be explained by the claim that subjects were not attending to the adapting stimuli because they performed very well in a secondary task that required them to make judgements of the Gabor patches' contrast. Note, however, that a number of recent studies have also failed to demonstrate spatiotopic aftereffects despite including a secondary attention task (Afraz & Cavanagh, 2008, 2009; Knapen et al., 2009; although see Corbett & Melcher, 2014, for evidence of spatiotopic encoding of mean size using methods similar to those used in the present study). 
The results from Experiment 4 do support the possibility that orientation variance is encoded relatively early in the visual system, as it was shown that patient MS is sensitive to the level of orientation variance in the textures. Patient MS's damage includes midlevel ventral visual areas but not low-level areas. Although MS performed poorly relative to young control participants, he performed significantly above chance in the two least-difficult conditions. The possibility remains, however, that it is in fact MS's intact parietal, and not occipital, cortex that supports the integration orientation signals in a manner that supports variance perception. If this were the case, however, activity in such areas would likely be found in tasks involving region-based discriminations, but this is not the case (e.g., Cavina-Pratesi et al., 2010a, 2010b). In light of recent evidence, it may not be entirely surprising that early visual areas are capable of encoding a region-based visual statistic such as variance. The results of Freeman, Ziemba, Heeger, Simoncelli, and Movshon (2013), for instance, suggest that texture statistics are represented first in V2, and Joo, Boynton, and Murray (2012) have even shown that effects of long-range orientation pattern modulation are present in as early as V1. These areas, which are spared in patient MS, may underlie his ability to discriminate variance. 
Acknowledgments
This work was supported by a doctoral fellowship from the Durham University Biophysical Sciences Institute. 
Commercial relationships: none. 
Corresponding author: Liam J. Norman. 
Email: liam.norman@dur.ac.uk. 
Address: Department of Psychology, Durham University, Durham, United Kingdom. 
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Figure 1
 
Examples of the different levels of variance used during adaptation in the experiments. In panel a, both textures are of a medium variance. In panel b, the left texture (in this case, the adapting texture) is of a low variance and the right is of a medium variance. In panel c, the left texture (again, the adapting texture) is of a high variance and the right is again of a medium variance. Note that in this figure the two patches share the same mean orientation, but this was randomly determined separately for each patch on each presentation in the experiment.
Figure 1
 
Examples of the different levels of variance used during adaptation in the experiments. In panel a, both textures are of a medium variance. In panel b, the left texture (in this case, the adapting texture) is of a low variance and the right is of a medium variance. In panel c, the left texture (again, the adapting texture) is of a high variance and the right is again of a medium variance. Note that in this figure the two patches share the same mean orientation, but this was randomly determined separately for each patch on each presentation in the experiment.
Figure 2
 
Results from Experiments 1 (random orientation of adapting textures) and 2 (constant orientation). Levels of PSE as a result of adapting to levels of low and high variance. A value of zero corresponds to the actual variance of the texture (objective equality), as shown by the horizontal axis. Thus, a value above this level indicates a shift in variance perception toward the higher end of the scale and a value below this level indicates a shift toward the lower end. Error bars show ±1 SEM.
Figure 2
 
Results from Experiments 1 (random orientation of adapting textures) and 2 (constant orientation). Levels of PSE as a result of adapting to levels of low and high variance. A value of zero corresponds to the actual variance of the texture (objective equality), as shown by the horizontal axis. Thus, a value above this level indicates a shift in variance perception toward the higher end of the scale and a value below this level indicates a shift toward the lower end. Error bars show ±1 SEM.
Figure 3
 
Illustration of the conditions from Experiment 3. During adaptation, half of the subjects fixated above and half fixated below (shown here) the adapting stimuli. Adaptation to high variance is shown on the right and adaptation to medium variance is shown on the left. Following a period of adaptation, an eye movement was required to be made to either the left or the right (shown here) of center. Four stimulus conditions were interleaved in each block. In two of these conditions fixation returned to the original position for test, and in the remaining two conditions fixation moved to the opposite side of the adapting stimuli (either above or below) for test. The test stimuli then appeared either above or below the new fixation point. Thus, the combination of the fixation position and test stimuli location determined the reference frame (labeled in the figure).
Figure 3
 
Illustration of the conditions from Experiment 3. During adaptation, half of the subjects fixated above and half fixated below (shown here) the adapting stimuli. Adaptation to high variance is shown on the right and adaptation to medium variance is shown on the left. Following a period of adaptation, an eye movement was required to be made to either the left or the right (shown here) of center. Four stimulus conditions were interleaved in each block. In two of these conditions fixation returned to the original position for test, and in the remaining two conditions fixation moved to the opposite side of the adapting stimuli (either above or below) for test. The test stimuli then appeared either above or below the new fixation point. Thus, the combination of the fixation position and test stimuli location determined the reference frame (labeled in the figure).
Figure 4
 
Results from Experiment 3. Each data point represents the average threshold across four observers. Results from low adaptation are shown in panel a; results from high adaptation are shown in panel b. The strength of the aftereffect measurement is determined by the increment or decrement in orientation variance required to null the adaptation effect (PSE). In both cases, the full and retinotopic PSEs are clearly larger than the spatiotopic and nonspecific effects. When the none PSE magnitude is subtracted from the other PSEs to account for retinotopic spreading (panels c and d), the spatiotopic effect is marginal, whereas the other two conditions still show substantial aftereffects. Error bars show ±1 SEM, with between-subjects variance removed.
Figure 4
 
Results from Experiment 3. Each data point represents the average threshold across four observers. Results from low adaptation are shown in panel a; results from high adaptation are shown in panel b. The strength of the aftereffect measurement is determined by the increment or decrement in orientation variance required to null the adaptation effect (PSE). In both cases, the full and retinotopic PSEs are clearly larger than the spatiotopic and nonspecific effects. When the none PSE magnitude is subtracted from the other PSEs to account for retinotopic spreading (panels c and d), the spatiotopic effect is marginal, whereas the other two conditions still show substantial aftereffects. Error bars show ±1 SEM, with between-subjects variance removed.
Figure 5
 
Example stimuli used in Experiment 4. The task was to identify the odd texture (top or bottom) in terms of its variance (irregularity). The three difficulty levels are shown in panels a through c, with decreasing difficulty level left to right. Each texture had a unique mean orientation relative to the other two, which was randomly determined across trials, thus preventing scrutiny of the stimuli on a local scale.
Figure 5
 
Example stimuli used in Experiment 4. The task was to identify the odd texture (top or bottom) in terms of its variance (irregularity). The three difficulty levels are shown in panels a through c, with decreasing difficulty level left to right. Each texture had a unique mean orientation relative to the other two, which was randomly determined across trials, thus preventing scrutiny of the stimuli on a local scale.
Figure 6
 
Results from Experiment 4: MS's variance discrimination task. MS performed significantly greater than chance in the medium- and low-difficulty levels and with progressively more accuracy with increasing variance difference between the discriminanda. This suggests that he may retain an ability to perform the second moment regional estimations that allow the encoding of variance.
Figure 6
 
Results from Experiment 4: MS's variance discrimination task. MS performed significantly greater than chance in the medium- and low-difficulty levels and with progressively more accuracy with increasing variance difference between the discriminanda. This suggests that he may retain an ability to perform the second moment regional estimations that allow the encoding of variance.
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