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Article  |   April 2011
Exploring expression space: Adaptation to orthogonal and anti-expressions
Author Affiliations
  • Richard Cook
    Cognitive, Perceptual and Brain Sciences Research Department, University College London, London, UKr.cook@ucl.ac.uk
  • Marana Matei
    Cognitive, Perceptual and Brain Sciences Research Department, University College London, London, UKmarananu@gmail.com
  • Alan Johnston
    Cognitive, Perceptual and Brain Sciences Research Department, University College London, London, UK
    Centre for Mathematics and Physics in the Life Sciences and Experimental Biology (CoMPLEX), University College London, London, UKa.johnston@ucl.ac.uk
Journal of Vision April 2011, Vol.11, 2. doi:10.1167/11.4.2
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      Richard Cook, Marana Matei, Alan Johnston; Exploring expression space: Adaptation to orthogonal and anti-expressions. Journal of Vision 2011;11(4):2. doi: 10.1167/11.4.2.

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Abstract

The present study sought to better understand the nature of the neural representation of expression. Specifically, we sought to compare the coding of naturally occurring expressions with the dimensional representation of facial identity (face space). Individual frames depicting the naturalistic facial expressions of a single individual were analyzed and used to estimate the mean posture and image texture of a dynamic sequence. The dimensionality present within the optic flow variation was extracted through the application of principal component analysis (PCA). Pairs of static anti-expressions were subsequently created by reconstructing postures corresponding to ±2.15 standard deviations along the axes defined by the first and second principal components comprising the computed “expression space.” Using an adaptation procedure, we show that adapting to an expression selectively biases perception of subsequently viewed stimuli in the direction of its anti-expression, analogous to similar findings with identity, but does not bias perception in the orthogonal direction. These findings suggest that the representation of naturally occurring expressions can be modeled using the same kind of multidimensional framework as has been proposed for identity.

Introduction
The skeleto-muscular structure of the human face has evolved in such a way as to enable us to produce a vast number of different facial poses and configurations. Being able to represent accurately these transient facial postures, hereafter “facial expressions,” is important as expressions contain a wealth of information highly relevant to social computation. The prototypical facial configurations associated with basic emotions (e.g., happiness, sadness, anger) are an important subset of facial expressions: Successful recognition of emotional expressions allows us to represent others' mental states, infer others' intentions, and predict behaviors, while impaired recognition of emotional expressions is often associated with social difficulties (Critchley et al., 2000; Hefter, Manoach, & Barton, 2005). However, basic emotional expressions represent only a small fraction of the facial expressions human adults are capable of. There are numerous expressions we encounter everyday, conveying, for example, confusion, boredom, or skepticism, which fall outside this classically defined set of prototypical emotions. Equally numerous subtle changes in facial posture mediate non-verbal communicative nuance. In addition, perceiving the postures of facial speech can support parallel auditory processing (McGurk & MacDonald, 1976). 
While there might be overlap between the neural substrates mediating identity and expression analysis (Calder & Young, 2005; Ganel, Valyear, Goshen-Gottstein, & Goodale, 2005), there also appears to be a degree of independence. Whereas processing of identity seems to be localized primarily in the inferior occipitotemporal cortex (Kanwisher, McDermott, & Chun, 1997), perception of emotional expressions (Winston, Henson, Fine-Goulden, & Dolan, 2004), mouth movements (Puce, Allison, Bentin, Gore, & McCarthy, 1998), and eye gaze (Hoffman & Haxby, 2000) seem to be mediated by lateral occipitotemporal regions. Certain emotional expressions may also recruit additional contributions from specific areas. The amygdala appears to be important for the perception of fear (Adolphs et al., 1999; Calder, Lawrence, & Young, 2001), whereas the right anterior insula has been implicated in the perception of disgust (Anderson, Christoff, Panitz, De Rosa, & Gabrieli, 2003). These dedicated mechanisms have been reflected in parallel routes for structure-based identity analysis and representation of transient facial expressions in influential cognitive (Bruce & Young, 1986) and neurocognitive (Haxby, Hoffman, & Gobbini, 2000) models of face perception. Dissociable substrates may reflect the fact that identity and expression represent largely independent sources of facial variation (Calder & Young, 2005). 
Recent work using adaptation paradigms suggests that this approach may yield useful insights into the representation of expression. Adaptation paradigms seek to bias the perception of a subsequently presented stimulus through prolonged exposure to an adapting stimulus. Traditionally, cortically based aftereffects have been attributed to differential fatigue in neuronal populations (Mollon, 1974; Sutherland, 1961). More recently, however, it has been argued that adaptation may serve a beneficial purpose, with aftereffects reflecting the ongoing process of perceptual calibration (Clifford & Rhodes, 2005; Rhodes, Watson, Jeffery, & Clifford, 2010). In either case, perceptual aftereffects imply the existence of specific neural mechanisms encoding the adapted dimension. 
The study of perceptual aftereffects has made a particularly striking contribution to our understanding of the dimensional representation of facial structure and to the development of the identity “face-space” framework. Adapting to a particular identity biases perception in a very specific direction, toward the corresponding anti-identity, i.e., in the diametrically opposite direction, across the mean of the dimensional space (Leopold, O'Toole, Vetter, & Blanz, 2001; Leopold, Rhodes, Muller, & Jeffery, 2005; Rhodes & Jeffery, 2006). In contrast, adapting to orthogonal identities does not bias systematically perception of subsequently viewed stimuli (Leopold et al., 2001, 2005; Rhodes & Jeffery, 2006). Consequently, a common view is that the representation of facial structure is achieved through opponent coding with structural attributes represented by the relative excitation of two opposing neuronal populations (Susilo, McKone, & Edwards, 2010). 
Previous studies on expression adaptation suggest that facial postures may also be subject to some form of dimensional coding, akin to that hypothesized for identity. Several authors have now shown that adapting to prototypical emotions serves to bias perception away from the adapting prototype (Benton et al., 2007; Ellamil, Susskind, & Anderson, 2008; Fox & Barton, 2007; Hsu & Young, 2004; Rutherford, Chattha, & Krysko, 2008; Webster, Kaping, Mizokami, & Duhamel, 2004). These aftereffects show view invariance with substantial effects reported when adapting and test stimuli are at different three-quarter orientations (Benton et al., 2007). Aftereffects also show identity invariance, with perceptual shifts observed when adapting and test stimuli depict different individuals (Fox & Barton, 2007). 
Nevertheless, our understanding of this “expression space” remains limited. One ambiguity relates to the direction of shift. Following adaptation to a particular facial identity, perception is biased toward the anti-identity (Leopold et al., 2001, 2005; Rhodes & Jeffery, 2006). However, while it is clear that adaptation shifts perception away from prototypical expressions, it is not clear whether perception is biased toward the corresponding anti-expression. This continuing uncertainty is attributable to the methodology employed previously. The most commonly used approach has been to measure aftereffects using morph continua derived from two prototypical expressions (Benton et al., 2007; Ellamil et al., 2008; Fox & Barton, 2007; Hsu & Young, 2004). However, this paradigm is limited insofar as one can conclude only that perception is being biased away from the adapting stimulus; the precise direction of shift remains ambiguous. An alternative approach was employed by Rutherford et al. (2008) who studied the effect of adapting to basic emotional expressions on self-reported perceptions of a supposedly neutral face. However, this method is also flawed insofar as it conflates a neutral expression with the mean expression. 
To date, the most informative investigation of the direction of emotional expression aftereffects is a recent study by Skinner and Benton (2010), reporting that adaptation to anti-emotional expressions biases perception toward the veridical emotion. However, the quality of anti-expression stimuli is inevitably constrained by the accuracy of the mean expression, as this point defines the direction of the anti-expression vector. The authors take as their mean expression the average shape and texture associated with just 7 postures comprising 6 basic emotions plus a “neutral” expression. Because it is unlikely that a composite of these exemplars corresponds closely to a true mean expression, anti-expressions derived by projecting into the opposite side of space will be biased by this sparsely sampled mean. The pattern of results reported may change if the mean was to include variation associated with facial speech, gaze changes, eye closures, and non-prototypical expressions. 
A second ambiguity relates to the dimensionality within expression space. Previous studies suggest that the dimensionality within expression space does not conform to the semantic dimensionality within human emotions (Ekman, 1992a, 1992b). For example, Rutherford et al. (2008) found that adapting to sad, fearful, angry, and disgusted expressions all biased perceptions toward happiness, whereas adapting to surprise increased perception of both anger and disgust. Similarly, Skinner and Benton (2010) report that adapting to anti-fear biases perception toward both fear and surprise; adapting to anti-anger biases perception toward both anger and disgust; and adapting to anti-disgust biases perception toward both disgust and anger. These findings suggest that while basic emotions may be regarded as semantically independent there might be considerable overlap in the neural representation of emotional facial expressions. It is thus unlikely that facial postures are represented by opposing pools of neurons responding maximally to prototypical emotional expressions. Rather, emotional expressions may be represented within a larger generic space that codes a much broader range of facial variation. 
The present study sought to investigate the dimensional coding of expressions in such a way as to facilitate comparison with the dimensional coding of identity. Specifically, we sought to determine whether adapting to a particular expression selectively biases perception in the direction of the corresponding anti-expression, in a manner comparable with identity coding (Leopold et al., 2001, 2005; Rhodes & Jeffery, 2006). Crucially however, we sought to adopt an entirely novel approach, by studying the natural variation observed in actors' facial expressions. This represents an important departure from the sparse sampling of emotional expressions that has prevented a fuller understanding of the dimensional coding of naturally occurring expressions. 
An actor was filmed while reciting question and answer jokes, and the variation in facial structure present within the sequence was subjected to principal component analysis (PCA; Berisha, Johnston, & McOwan, 2010; Cowe, 2003). Having determined the mean posture and dimensionality present within the sequence, two orthogonal pairs of anti-expressions were derived (A and B, C and D, Figure 1) as well as two orthogonal test continua (AB, CD). The experiment reported here compares the perceptual shifts following adaptation to postures either congruent or orthogonal to a continuum of test expressions. It was predicted that adapting to an expression would shift perception in the direction of the corresponding anti-expression but not systematically bias perception of the orthogonal test continuum. Consistent with the analogous effects with identity (Leopold et al., 2001, 2005; Rhodes & Jeffery, 2006), we find that adapting to an expression selectively biases perception toward its anti-expression. 
Figure 1
 
(Left) Schematic representation of principal component analysis. PCA identifies a set of dimensions that allow the most efficient description of the natural variation. Crucially, the resulting axes are orthogonal, that is to say there is no correlation in the variance of the morphable model for each expression described by the dimensions. (Right) Representation of the expression space. A and B anti-expressions correspond to points equidistant from the mean on the first principal component, while C and D anti-expressions are points equidistant from the mean on the second principal component. It was predicted that adapting to an expression should bias perception in the direction of its anti-expression, but adapting to an orthogonal expression should have little effect.
Figure 1
 
(Left) Schematic representation of principal component analysis. PCA identifies a set of dimensions that allow the most efficient description of the natural variation. Crucially, the resulting axes are orthogonal, that is to say there is no correlation in the variance of the morphable model for each expression described by the dimensions. (Right) Representation of the expression space. A and B anti-expressions correspond to points equidistant from the mean on the first principal component, while C and D anti-expressions are points equidistant from the mean on the second principal component. It was predicted that adapting to an expression should bias perception in the direction of its anti-expression, but adapting to an orthogonal expression should have little effect.
Methods
Participants
Sixteen healthy adults (5 males) with a mean age of 22.0 years served as participants in the experiment. All had normal or corrected-to-normal vision and were naive to the purpose of the experiment. The study was approved by the University College London Ethics Committee and performed in accordance with the ethical standards set out in the 1964 Declaration of Helsinki. 
Stimuli
The stimuli used were derived using PCA performed on a sequence of 500 color bitmap images depicting a female actor recalling and reciting question and answer jokes. The original sequence was filmed at a rate of 25 frames/s using a JVC GR-DVL9600 digital camera. A 20-s sequence was then chosen containing minimal rigid head motion but which was nevertheless rich in non-rigid motion. This sequence was then separated into 500 bitmap images. 
The images were first described in terms of their posture deviations from the sequence average, as well as their texture characteristics, using a biologically plausible optic flow algorithm (Berisha et al., 2010; Cowe, 2003; Johnston, McOwan, & Benton, 1999; Johnston, McOwan, & Buxton, 1992). A single frame was chosen to act as the reference. For the remaining n − 1 frames, flow fields that warped the facial features back to their position in the reference image, on a pixel-by-pixel basis, were calculated. By averaging these flow fields, the mean warp was calculated, which in turn was applied to the reference frame to derive the mean face shape. The flow fields were then adjusted so that they registered to the mean face shape rather than the original reference. The resulting fields describe the variation in face shape present within the sequence. 
However, “texture deviations” reflecting changes in lighting or shadow, or iconic changes whereby a feature (e.g., teeth) is present in the target, but not in the mean face, or vice versa, are not described within the flow-field variance. In order to represent the texture deviations, it was necessary to feature align all frames. Because the flow fields had been adjusted to register to the warp mean rather than the original reference, they could be used to warp each frame such that the features were aligned in the mean position. Texture deviations were encoded by a Red–Green–Blue (RGB) triplet reflecting the texture of a given point on the mean face shape for any given frame. These values do not represent departures from the mean texture; they represent the color of a pixel when that frame is feature aligned. 
Thus, for every pixel of every frame, a 5-element vector, describing optic flow deviation from the mean in the x and y dimensions, and an RGB triplet, describing the texture variation for each point on the mean face shape, was derived. For each frame, these pixel vectors were concatenated to produce 500 frame vectors of length 5 × image width × image height, to which PCA was then applied. A compressed movie file depicting the first eight principal components can be viewed in the Supplementary material accompanying this article. 
The adapting stimuli (Figure 2) were still image reconstructions of points in the PCA space. The A and B pair was a projection of 2.15 standard deviations (SDs) either side of the sequence mean, along the dimension specified by the first principal component. The C and D pair represented corresponding points on the second principal component. The expressions within each pair are thus on diametrically opposite sides of the expression space (“anti-expressions”). 
Figure 2
 
(Top) The four anti-expressions used as adapting stimuli, from left to right A, B, C, D. (Middle) The AB test continuum ranging from 1.5 SDs toward A, depicted on the left, to 1.5 SDs toward B, depicted on the right. (Bottom) The CD continuum ranging from 1.5 SDs toward C, depicted on the left, to 1.5 SDs toward D, depicted on the right. A movie file of the first 8 principal components is included in the Supplementary material accompanying this article.
Figure 2
 
(Top) The four anti-expressions used as adapting stimuli, from left to right A, B, C, D. (Middle) The AB test continuum ranging from 1.5 SDs toward A, depicted on the left, to 1.5 SDs toward B, depicted on the right. (Bottom) The CD continuum ranging from 1.5 SDs toward C, depicted on the left, to 1.5 SDs toward D, depicted on the right. A movie file of the first 8 principal components is included in the Supplementary material accompanying this article.
The test stimuli were drawn from two continua of static images derived by sampling the first and second principal components at seven equidistant points ranging from −1.5 to +1.5 SDs from the mean (hereafter referred to as the AB and CD continua). Thus, the AB test stimuli appeared to morph steadily from 1.5 SDs of posture A toward 1.5 SDs of B in equidistant 0.5 SD steps (Figure 2). In contrast, the CD test stimuli morphed from 1.5 SDs in the C direction to 1.5 SDs toward D. The central stimulus in both continua corresponded to the sequence mean. 
Procedure
Adaptation condition was manipulated within subjects, while test continuum was manipulated between subjects. Half the participants were therefore required to make binary judgments of stimuli from the AB continua, having adapted to A, B, C, or D or following no adaptation. The other half were required to make binary judgments of stimuli from the CD continua. The decision to manipulate test dimension between subjects was taken to constrain the amount of testing to be completed by each subject. However, this aspect of the design does not compromise the strength of the inferences that may be drawn about the independence of the neural representation of the two dimensions. If the AB and CD dimensions are encoded by overlapping neural substrates, the group tested on the AB dimension should show shifts having adapted to C or D, while the group tested on the CD dimension should show shifts having adapted to A or B. 
The experiment was conducted on a personal computer in a darkened room. Stimuli were presented on a CRT monitor at a viewing distance of approximately 60 cm. Participants completed four blocks of 35 trials under each condition, equating to twenty blocks in total. In all, testing took approximately 4 h per participant and was completed over 3–4 separate sessions. Blocks were run in a randomized order, with the only constraint that no two consecutive blocks were ever of the same condition. Participants were given a short break between blocks. 
Prior to the adaptation procedure, it was necessary to train participants to label the expressions at the opposing ends of the test continua. This was achieved using a short training procedure. Having first viewed the extremes of the appropriate test continuum labeled either A and B or C and D, participants were presented with the unlabeled stimuli in a randomly alternating sequence and asked to identify each expression by pressing the appropriate key on the keyboard. The adaptation procedure only commenced once participants had responded correctly on ten consecutive training trials. 
The first trial of each adapted block was preceded by an initial adaptation period of 30 s. Subsequent trials were preceded by 10-s periods of top-up adaptation. The offset of the adapting stimulus was followed by a central fixation dot presented for 500 ms and then one of the test stimuli presented for 750 ms. A blank display was then presented for 1000 ms, at which point participants made a binary judgment, by responding A/B or C/D depending on which extreme they perceived the test stimulus to be closer to. 
In order to prevent any low-level retinotopic aftereffects, the adapting and test stimuli were presented both at different locations and different scales. Adapting stimuli subtended approximately 12° of visual angle and were presented at the center of the display. The test stimuli appeared smaller, subtending approximately 8° and could be centered anywhere on a notional circle with a radius of approximately 4° from the display center. 
Results
Two participants (1 allocated to the AB test continua and 1 to the CD continua) were excluded from the analysis due to unreliable estimates of their baseline functions (their unadapted PSEs were not within 0.5 SD unit of the veridical mean). For the remaining participants, psychometric functions were modeled by fitting cumulative Gaussian functions. Adaptation is defined as a shift of the point of subjective equivalence (PSE) toward the adapting stimulus, indicating that neutral stimuli appear less like the adapting stimulus and more like the stimulus at the other pole of the continuum. While we had no a priori reason to believe that discrimination sensitivity would vary as a function of the adapting condition, the standard deviations of the underlying Gaussian error distributions were also estimated for each subject; however, no significant effects were revealed. 
The effects of the various adapting conditions on the PSEs can be seen in Figure 3. The data were analyzed using within-subjects ANOVAs. Where sphericity could not be assumed, the statistics reported are subject to the Greenhouse–Geisser correction. The combined data were initially analyzed using a mixed model ANOVA with adapting condition (no adaptation, adapt to A, adapt to B, adapt to C, adapt to D) as a within-subjects factor and test dimension (AB or CD) as a between-subjects factor. The analysis revealed a highly significant adaptation condition × test dimension interaction [F(4,48) = 13.9, p < 0.001, η 2 = 0.537], indicating that the effects of the adapting conditions differed across the test dimensions. To better understand this interaction, the effects within the AB and CD groups were considered in more detail. 
Figure 3
 
Mean PSEs observed plotted as a function of adapting condition. No adaptation baseline (top pane); adaptation to A and B (middle pane); adaptation to C and D (bottom pane). Error bars denote standard error of the mean.
Figure 3
 
Mean PSEs observed plotted as a function of adapting condition. No adaptation baseline (top pane); adaptation to A and B (middle pane); adaptation to C and D (bottom pane). Error bars denote standard error of the mean.
Group AB
A within-subjects ANOVA across the congruent adapting conditions (adapt-A, no adaptation, adapt-B) revealed a significant main effect of adapting condition [F(2,12) = 25.9, p < 0.001, η 2 = 0.812]. The effect size observed represents a large effect (Cohen, 1988). Planned contrasts indicated that the PSEs were significantly shifted toward A following adaptation to A (M = −0.48, SD = 0.26) compared to the no adaptation baseline condition (M = 0.00, SD = 0.18) [t(6) = 8.5; p < 0.001 (two-tailed)]. Similarly, the PSEs showed a significant shift toward B following adaptation to B (M = 0.34, SD = 0.41) compared to the no adaptation baseline condition [t(6) = 2.4; p = 0.05 (two-tailed)]. However, a within-subjects ANOVA across orthogonal adapting conditions (adapt-C, no adaptation, adapt-D) failed to reveal a significant main effect of adapting condition [F(2,12) = 1.87, p = 0.20] indicating that the PSE did not vary as a function of adapting condition. 
Group CD
A within-subjects ANOVA across the congruent adapting conditions (adapt-C, no adaptation, adapt-D) revealed a highly significant main effect of adapting condition [F(2,12) = 25.3, p < 0.001, η 2 = 0.808]. This effect size again represents a large effect (Cohen, 1988). Planned contrasts indicated that the PSE shifted significantly toward C following adaptation to C (M = −0.33, SD = 0.27) compared to the no adaptation baseline condition (M = −0.04, SD = 0.10) [t(6) = 3.14; p < 0.025 (two-tailed)]. Similarly, the PSE shifted significantly toward D following adaptation to D (M = 0.40, SD = 0.26) compared to the no adaptation baseline condition [t(6) = 4.80; p < 0.01 (two-tailed)]. Crucially, a within-subjects ANOVA across the orthogonal adapting conditions (adapt-A, no adaptation, adapt-B) revealed only a marginally significant effect of adapting condition [F(2,12) = 4.05, p = 0.082]. A paired t-test confirmed that the mean congruent shift (difference between adapt-C and adapt-D) was significantly larger than the mean orthogonal shift (difference between adapt-A and adapt-B) [t(6) = 2.5; p < 0.05 (two-tailed)]. Thus, as with the AB group, PSEs shifted substantially less when the adapting condition was orthogonal to the test dimension. 
Discussion
We sought to investigate the neural coding of naturally occurring facial expressions using an approach analogous with the “face-space” framework employed successfully to the study of identity coding. PCA was applied to a sequence of images depicting an actor reciting question and answer jokes. Having established the mean posture and dimensionality present within the sequence, two orthogonal pairs of anti-expressions were derived. We found that adapting to each of the four postures selectively biased perception toward the corresponding anti-expression, with little or no shift observed in the orthogonal direction. 
Our results are consistent with previous findings suggesting that perception of facial posture may be mediated by dimensional coding (Benton et al., 2007; Ellamil et al., 2008; Fox & Barton, 2007; Hsu & Young, 2004; Rutherford et al., 2008; Skinner & Benton, 2010; Webster et al., 2004). These studies indicate that adapting to emotional expressions biases perception away from that prototype. However, without an accurate data-driven estimate of the mean posture, it has been impossible to test whether perception is biased toward the corresponding anti-expressions. Additional ambiguity has developed with previous findings (Hsu & Young, 2004; Rutherford et al., 2008) suggesting that the dimensionality within posture space does not conform to the semantic dimensionality suggested during the study of basic emotions (Ekman, 1992a, 1992b). Due to the poor grasp of this dimensionality, it has not been possible to predict a priori whether an adapting stimulus will produce a perceptual shift. 
Using an optic-flow technique for extracting the relationship between frames of a single sequence (Berisha et al., 2010; Cowe, 2003; Johnston et al., 1999, 1992), we successfully derived a data-driven estimate of the mean expression from 500 unique exemplars. This is the first time anti-expressions have been derived using a mean expression constructed from a dense sampling of expression space. Our findings indicate that adapting to a particular expression biases perception toward its anti-expression, while adapting to orthogonal postures does not produce a perceptual shift. These data suggest that the visual system may represent facial postures in the way that it represents identity; as points or directions within a multidimensional space (Leopold et al., 2001, 2005; Rhodes et al., 2010). 
While there appears to be considerable overlap between the neural representation of emotional expressions (Hsu & Young, 2004; Rutherford et al., 2008; Skinner & Benton, 2010), the first two principal modes of variation identified by PCA appear to be represented by independent populations. Previous findings suggest that one would be unable to replicate the present effects with stimuli derived from prototypical emotional expressions. If, for example, participants adapted to disgust and were tested on a fear–happy continuum, it is likely that perception would be biased toward happy, due to the overlapping representations of fear and disgust (Hsu & Young, 2004; Rutherford et al., 2008; Skinner & Benton, 2010). The dimensionality within expression space may, therefore, be determined by the naturally occurring variance present within facial postures rather than adhering to any semantic dimensionality present within human emotions (Ekman, 1992a, 1992b). Some of the opponent pools defining this dimensionality may respond maximally to meaningful postures: For example, both aftereffects (Hsu & Young, 2004; Rutherford et al., 2008; Skinner & Benton, 2010) and PCA (see the fifth principal component in Supplementary materials) suggest that a smile–frown dimension accounts for a considerable portion of the natural variance. However, other opponent pools may respond maximally to seemingly “meaningless” postures that nevertheless describe unique portions of variance. 
The novelty in the present study lies in its departure from conventional theories of expression perception, which presuppose that expression is represented in a manner corresponding to the semantic taxonomies of human emotion. The visual system, during ontogeny, knows nothing about the semantics of human emotion but must, nevertheless, describe the natural image variation it encounters. The problem faced by the PCA algorithm is similar to that posed to the visual system—how to describe this natural variation accurately and robustly, using the fewest number of dimensions. While we would not want to suggest there is anything intrinsically “special” about the particular dimensions extracted here (the 500 images on which the PCA was performed represent a small fraction of the variation in facial postures we encounter everyday), it is interesting that the visual system and the PCA algorithm concur that it is efficient to represent these modes of variation separately. In this respect, the present findings accord with suggestions that several aspects of face perception can be modeled using PCA (Burton, Jenkins, Hancock, & White, 2005; Calder & Young, 2005; Furl, Phillips, & O'Toole, 2002). 
The present study also demonstrates that novel expressions can produce perceptual aftereffects, comparable to the aftereffects observed with novel identities. Whereas previous studies have used prototypical emotional expressions highly familiar to observers, the present study used statistically derived postures that were in all likelihood novel to observers. Traditionally, aftereffects have been taken as evidence of dedicated channels or populations coding for particular stimulus attributes; “if you can adapt it, it's there” (Mollon, 1974). However, the recent aftereffects produced by novel exemplars are hard to reconcile with this view (Thompson & Burr, 2009). After all, it is difficult to conceive of a dedicated representation for a facial posture never previously encountered. Adaptation to novel exemplars may instead suggest that a dimensionality extracted from an observer's previous experience of the natural variation may be used to represent novel instances using combinations of weights within a more permanent space. Nevertheless, the nature of the perceptual learning responsible for such a perceptual scaffold needs to be carefully considered. In particular, it is remains to be discovered how adaptation to specific descriptions interacts with adaptation to the representational systems on which these descriptions are based. 
In summary, the effects observed suggest that naturally occurring facial expressions may be represented as points or directions within a multidimensional space akin to the face-space framework conceptualized for identity coding. Analogous with effects observed with identity (Leopold et al., 2001, 2005; Rhodes & Jeffery, 2006), adapting to a particular expression caused a perceptual shift in the direction of the corresponding anti-expression, whereas adapting to an expression orthogonal to the test dimension produced little or no aftereffect. While we leave open the question of whether identity and expression spaces are independent, these data suggest that expressions may be represented by opponent-coded dimensions, which describe efficiently the naturally occurring variation in facial posture rather than a dimensionality based on a semantic taxonomy of human emotions. 
Supplementary Materials
Supplementary Movie - Supplementary Movie 
Supplementary Movie 1. Dynamic representation of the output of the PCA cycling sinusoidally from +2.15 SDs to - 2.15 SDs along each component. The adapting and test stimuli were still image reconstructions of points from the first and second principal components. 
Acknowledgments
The research reported in this article was supported by the Engineering and Physical Science Research Council (EPSRC) and by a doctoral studentship awarded by the Economic and Social Research Council (ESRC) to Richard Cook. 
Commercial relationships: none. 
Corresponding author: Richard Cook. 
Email: r.cook@ucl.ac.uk. 
Address: Cognitive, Perceptual and Brain Sciences Research Department, University College London, London WC1H 0AP, UK. 
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Figure 1
 
(Left) Schematic representation of principal component analysis. PCA identifies a set of dimensions that allow the most efficient description of the natural variation. Crucially, the resulting axes are orthogonal, that is to say there is no correlation in the variance of the morphable model for each expression described by the dimensions. (Right) Representation of the expression space. A and B anti-expressions correspond to points equidistant from the mean on the first principal component, while C and D anti-expressions are points equidistant from the mean on the second principal component. It was predicted that adapting to an expression should bias perception in the direction of its anti-expression, but adapting to an orthogonal expression should have little effect.
Figure 1
 
(Left) Schematic representation of principal component analysis. PCA identifies a set of dimensions that allow the most efficient description of the natural variation. Crucially, the resulting axes are orthogonal, that is to say there is no correlation in the variance of the morphable model for each expression described by the dimensions. (Right) Representation of the expression space. A and B anti-expressions correspond to points equidistant from the mean on the first principal component, while C and D anti-expressions are points equidistant from the mean on the second principal component. It was predicted that adapting to an expression should bias perception in the direction of its anti-expression, but adapting to an orthogonal expression should have little effect.
Figure 2
 
(Top) The four anti-expressions used as adapting stimuli, from left to right A, B, C, D. (Middle) The AB test continuum ranging from 1.5 SDs toward A, depicted on the left, to 1.5 SDs toward B, depicted on the right. (Bottom) The CD continuum ranging from 1.5 SDs toward C, depicted on the left, to 1.5 SDs toward D, depicted on the right. A movie file of the first 8 principal components is included in the Supplementary material accompanying this article.
Figure 2
 
(Top) The four anti-expressions used as adapting stimuli, from left to right A, B, C, D. (Middle) The AB test continuum ranging from 1.5 SDs toward A, depicted on the left, to 1.5 SDs toward B, depicted on the right. (Bottom) The CD continuum ranging from 1.5 SDs toward C, depicted on the left, to 1.5 SDs toward D, depicted on the right. A movie file of the first 8 principal components is included in the Supplementary material accompanying this article.
Figure 3
 
Mean PSEs observed plotted as a function of adapting condition. No adaptation baseline (top pane); adaptation to A and B (middle pane); adaptation to C and D (bottom pane). Error bars denote standard error of the mean.
Figure 3
 
Mean PSEs observed plotted as a function of adapting condition. No adaptation baseline (top pane); adaptation to A and B (middle pane); adaptation to C and D (bottom pane). Error bars denote standard error of the mean.
Supplementary Movie
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