Mirror-image confusions: Implications for representation and processing of object orientation

Cognition 116 (2010) 110–129

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Cognition

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Mirror-image confusions: Implications for representation and processingof object orientation

Emma Gregory *, Michael McCloskeyDepartment of Cognitive Science, Johns Hopkins University, MD, United States

a r t i c l e i n f o

Article history:Received 14 April 2009Revised 26 March 2010Accepted 16 April 2010

Keywords:Spatial cognitionOrientationMirror imagesObject representationVision

0010-0277/$ - see front matter � 2010 Elsevier B.Vdoi:10.1016/j.cognition.2010.04.005

* Corresponding author. Address: Cognitive ScienHopkins University, 3400 North Charles Street, BUnited States. Tel.: +1 410 516 4945.

E-mail address: [email protected] (E. Greg

a b s t r a c t

Perceiving the orientation of objects is important for interacting with the world, yet littleis known about the mental representation or processing of object orientation informa-tion. The tendency of humans and other species to confuse mirror images provides apotential clue. However, the appropriate characterization of this phenomenon is notentirely clear, in part because the stimuli used in most previous studies were notadequate for distinguishing various forms of mirror-image and non-mirror-image error.In the present study we explore the nature of mirror-image confusion and what thephenomenon can reveal about object-orientation representations. We report severalexperiments in which participants reported the orientations of pictures. In all of theexperiments mirror-reflection errors were more frequent than other orientation errors.However, whereas mirror-image confusion has previously been described as a tendencyto confuse stimuli that are related by reflection across an extrinsic (usually vertical) axis,the vast majority of mirror-image errors in our experiments were reflections across anobject axis. This finding calls into question several hypotheses proposed to explainmirror-image confusion. We describe a coordinate-system orientation representation(COR) hypothesis that can account for our results (McCloskey, Valtonen, & Sherman,2006). COR assumes that orientation representations map an object-centered referenceframe onto a reference frame extrinsic to the object, with this mapping specified byseveral parameters. According to COR, mirror-image confusions and other orientationerrors arise from failures in representing or processing specific parameters. Consideredin light of COR, our results suggest that orientation representations are compositional,and that object-centered reference frames play a central role in orientationrepresentation.

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1. Introduction

Information about the orientation of objects is impor-tant for many perceptual, motor, and cognitive functions.For example, perceiving the direction in which predators

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ce Department, Johnsaltimore, MD 21218,

ory).

or prey are facing is a life-or-death matter for many crea-tures; a person reaching out to grasp an object must appre-hend how that object is oriented in order to position herhand appropriately; and the interpretation of a sceneinvolving two people may be quite different dependingupon whether the people are turned toward or away fromone another.

Despite the importance of orientation, little isknown about how object orientation information isrepresented or processed. One potential clue is the fasci-nating tendency of humans and other animals to confuse

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E. Gregory, M. McCloskey / Cognition 116 (2010) 110–129 111

mirror images.1 Difficulties in remembering (and some-times even perceiving) distinctions between mirror imageshave been reported in normal children and adults, in chil-dren and adults with developmental or acquired cognitivedeficits, and in a variety of non-human species (e.g., Aaron& Malatesha, 1974; Biederman & Cooper, 1991; Bornstein,1982; Davidoff & Warrington, 2001; Davidson, 1935; Farrell,1979; Gibson, Gibson, Pick, & Osser, 1962; Mackintosh &Sutherland, 1963; McCloskey, 2009; McCloskey et al.,1995; McCloskey, Valtonen, & Sherman, 2006; Priftis, Rus-coni, Umilta, & Zorzi, 2003; Riddoch & Humphreys, 1988;Rollenhagen & Olson, 2000; Rudel & Teuber, 1963; Sekuler& Houlihan, 1968; Sekuler & Pierce, 1973; Stankiewicz,Hummel, & Cooper, 1998; Stein & Mandler, 1974; Suther-land, 1957a, 1957b; Turnbull & McCarthy, 1996; Valtonen,Dilks, & McCloskey, 2008; Wolff, 1971).

Fig. 1 illustrates some of the reported mirror-image dif-ficulties. Panel A presents a typical response from a studyin which adults were asked to draw a United States pennyfrom memory (Nickerson & Adams, 1979). All of the partic-ipants included Lincoln’s head in their drawings, but halfdrew the profile facing the wrong way. (For similar resultssee, e.g., Jones, 1990; Jones & Martin, 1992; Martin & Jones,1995.)

Fig. 1B and C presents two stimulus pairs that have fig-ured prominently in studies of mirror-image confusion. Intasks requiring memory for stimulus orientation, humanchildren and non-human animals from a variety of spe-cies have difficulty with these mirror-image pairs (e.g.,Casey, 1984; Corballis & Zalik, 1977; Fellows & Brooks,1973; Huttenlocher, 1967b; Mackintosh & Sutherland,1963; Over & Over, 1967; Rudel & Teuber, 1963; Serpell,1971; Stein & Mandler, 1974; Sutherland, 1957a, 1957b,1960). For example, Rudel and Teuber (1963) tested chil-dren between three and eight years of age in tasks thatrequired them to learn which of two stimuli (e.g., thetwo oblique bars in Fig. 1B) had been arbitrarily desig-nated the ‘‘correct” one. On each trial the two stimuliwere presented simultaneously, the child chose the stim-ulus he or she thought was correct, and the experimenterprovided feedback. For the mirror-image pairs in Fig. 1Band C, very few of the 3–5-year-olds learned to selectthe correct stimulus consistently, and substantial propor-tions of the 6–8-year-olds also failed to learn the discrim-ination. When, however, the stimulus pair consisted of ahorizontal bar and a vertical bar, even the youngestchildren performed well. Sutherland (1957b) reportedanalogous results from studies of octopuses: The animals

1 A mirror image is produced by reflecting a figure across an axis. Forexample, lower-case d is a left–right mirror image of lower-case b,produced by reflecting the b across a vertical axis. The term mirror imageis sometimes used to refer only to left–right reflections such as b and d;however, we use the term more broadly to include other reflections as well.In our usage, for instance, inverting a figure by reflecting it across ahorizontal axis produces an up-down mirror image (as in b ? p). Also,although reflection across an axis amounts to a rotation in depth, wereserve the term rotation for rotations in the picture plane, both for clarityof exposition and because we will argue that reflections and picture-planerotations are different at the level of underlying object-orientationrepresentations.

readily learned a horizontal-vs.-vertical discrimination,but had much more difficulty with mirror-image obliqueorientations. (For review of similar results from othernon-human species see Appelle (1972) and Tee and Rie-sen (1974).)

Mirror-image confusions have also been observed inhumans with cognitive deficits (e.g., Davidoff & Warring-ton, 1999, 2001; McCloskey, 2009; McCloskey et al.,2006; Priftis et al., 2003; Valtonen et al., 2008). Turnbulland McCarthy (1996) described patient RJ, a 61-year-oldman with bilateral parietal damage who was apparentlyunable to perceive the difference between a picture andits left–right mirror image. When asked to say which ofthree pictures differed from the other two, RJ was 100%correct if the discrepant picture differed from the othersin some visual detail, or was rotated 180� relative to theother pictures. However, he was less than 50% correctwhen the discrepant picture differed by a left–right reflec-tion (Fig. 1D).

2. Characterizing the mirror-image confusionphenomenon

Mirror-image confusion is usually characterized as atendency to confuse left–right mirror images—that is,stimuli related by reflection across a vertical axis, suchas those in Fig. 1. However, this characterization is notentirely satisfactory. In the first place, a substantial bodyof evidence demonstrates that up-down mirror images(e.g., a square open at the top vs. a square open at thebottom) are also prone to confusion (e.g., Bornstein,Gross, & Wolf, 1978; Davidson, 1935; Gibson et al.,1962; Huttenlocher, 1967a, 1967b; McCloskey, 2009;McCloskey & Rapp, 2000; McCloskey et al., 1995; Sekuler& Houlihan, 1968; Sekuler & Pierce, 1973; Sekuler &Rosenblith, 1964; Wolff, 1971; Woloszyn & Sheinberg,2006).

Furthermore, the stimuli used in most previous mirror-image confusion studies are not adequate for isolating aspecific mirror-image relationship as the cause of the ob-served confusions (Howard, 1982). Consider first theextensively-studied pair of oblique bars in Fig. 1B. Theconfusability of these bars is usually attributed to the factthat they are left–right mirror images. However, eitherbar can be transformed into the other not only by aleft–right reflection, but also by an up-down reflection,or by a rotation in the picture plane. In other words, thesespatial relationships are confounded. One may thereforeask which relationship(s) between the bars underlie thetendency to confuse them. For example, might the rota-tional relationship be relevant? One of the oblique barsis rotated (i.e., tilted) 45� clockwise from vertical, whereasthe other is tilted 45� counterclockwise. Accordingly, acreature (e.g., a child or octopus) who encoded andretained the tilt amount (45�) but failed in encoding orremembering the tilt direction (clockwise or counter-clockwise from vertical) would confuse the two stimuli.On this account the oblique bars are confusablebecause they differ only in direction of tilt, and notbecause one is a (left–right or up–down) reflection of

Fig. 1. Examples from prior studies of mirror-image confusion. (A) Reprinted from Nickerson and Adams (1979), with permission from Elsevier. (D)Reprinted from Turnbull and McCarthy (1996), with permission from Taylor & Francis, Ltd., http://www.informaworld.com.

112 E. Gregory, M. McCloskey / Cognition 116 (2010) 110–129

the other.2 Our aim here is not to argue for any particularinterpretation of oblique-bar confusions, but rather to point

2 Bryant (1969), Bryant (1973) has argued that young children fail toencode the amount as well as the direction of tilt. Bryant (1973) tested 4–7-year-old children in a successive match-to-sample task. On each trial anoriented sample bar was presented; then, the sample was removed, and fiveseconds later two choice lines were presented. The child’s task was to selectthe choice bar that matched the sample. The children performed well whenone of the choices was horizontal or vertical and the other was oblique, but haddifficulty when both choice stimuli were oblique. In fact, two non mirror-image obliques (i.e., two bars tilted in different directions and by differentamounts) were just as confusable as two mirror-image obliques. To explainthese results Bryant proposed that children encoded the bars only as matchingor mismatching the orientation of visual features in the environment (e.g., anedge of a stimulus card, a side of a doorframe). Bryant argued that becauseenvironmental features are typically horizontal or vertical, an oblique bar willusually be encoded simply as mismatching environmental features, leadingchildren to confuse any two obliques. Like the tilt-direction account, Bryant’sinterpretation assumes that the confusability of mirror-image obliques is notdue to the fact that one is a left–right reflection of the other.

out that the studies with oblique-bar stimuli fail to estab-lish which relationship(s) between the bars underlie theobserved confusions.

Confounding of reflectional and rotational relationshipsarises whenever stimulus objects are symmetric across oneor more object axes. As illustrated in Fig. 2A, an oblique barmay be thought of as an object with a principal axis ofelongation, and a secondary axis perpendicular to the prin-cipal axis.3 The bar is symmetric across both the principaland secondary object axes, and because of these symmetriesvarious orientation relationships are confounded. In contrastthe comb in Fig. 2B is asymmetric across both primaryand secondary object axes, and the asymmetries allow for

3 We use the terms principal axis and secondary axis merely to distinguishthe two object axes from one another, without implying that the axesnecessarily play qualitatively different roles in mental objectrepresentations.

http://www.informaworld.com

Fig. 2. (A) An oblique-bar stimulus, illustrating its symmetry across principal and secondary object axes. (B) A stimulus that is asymmetric across bothprincipal and secondary object axes. (C) Left–right reflection (reflection across a vertical axis) of the stimulus in (B). (D) 90� Counterclockwise picture-planerotation of the stimulus in (B), from 45� clockwise relative to vertical, to 45� counterclockwise. (E) Reflection of the stimulus in (B) across its principal axis.


differentiation of the reflectional and rotational relation-ships that are conflated for the oblique bars. For example,left–right reflection (reflection across a vertical axis) and90� counterclockwise rotation (from a 45� clockwise tilt rel-ative to vertical, to a 45� counterclockwise tilt) yield differ-ent results, as shown in Fig. 2C and D.

Even more pervasive than confounds related to stimu-lus symmetry are confounds resulting from a failure toseparate object axes from extrinsic axes. With the excep-tion of the oblique-bar stimuli, virtually all of the stimuliin studies of mirror-image confusion have been presentedwith object axes parallel to extrinsic vertical and horizon-tal axes. Consider Fig. 1E, which shows a stimulus pictureand the copy made by AH, a young woman with a develop-mental deficit in perceiving the location and orientation ofvisual stimuli (McCloskey, 2009; McCloskey et al., 1995,2006). The pitcher was presented in an upright orientation,and consequently the pitcher’s axes were aligned with axesextrinsic to the pitcher (e.g., AH’s body axes, environmen-tal axes defined by the walls of the testing room or by thesheet of paper on which the stimulus was printed).4 As aconsequence, AH’s reflection error could be describedeither as a left–right reflection across an extrinsic verticalaxis, or as a reflection across the pitcher’s principal axisof elongation. Extrinsic- and object-axis reflections can beunconfounded by presenting (asymmetric) stimuli withobject axes tilted relative to extrinsic axes. For example, gi-ven the tilted comb in Fig. 2B, a left–right reflection across

4 Note that by extrinsic axis we mean any axis not defined on the basis ofthe stimulus object. Extrinsic axes may include egocentric axes, orallocentric axes defined on the basis of environmental features.

an extrinsic vertical axis (Fig. 2C) is clearly different from areflection across the comb’s principal axis (Fig. 2E).5

Because of the confounds in previous studies, theappropriate characterization of the mirror-image confu-sion phenomenon, and therefore the theoretical implica-tions of the phenomenon, are not at all clear. In thisarticle we first report a series of experiments in whichadult participants were tested with tilted asymmetricstimuli under conditions designed to elicit errors in mem-ory for orientation. We then discuss the implications of ourresults for prior interpretations of mirror-image confusion.Finally, we present an explicit hypothesis concerning men-tal representations of object orientation, arguing that thehypothesis provides a framework for interpreting our find-ings, and defines issues for future research.

3. Experiment 1

In Experiments 1a and 1b pictures of objects wereshown briefly, and participants reported the orientationof each object. In Experiment 1a the stimulus objects wereoriented horizontally, vertically, or diagonally, and partici-pants responded by drawing. In Experiment 1b the stimuliwere presented at less prototypical orientations, and mem-ory for orientation was tested with a forced-choice proce-dure. Experiment 1b also imposed a task-irrelevantmemory load: Participants attempted to remember a 7-di-git number while performing the orientation task.

5 See Driver and Halligan (1991) for a use of tilted asymmetric stimuli todistinguish hemispatial neglect related to object axes from neglect relatedto extrinsic axes.

Fig. 3. Stimulus photographs for Experiments 1 and 2.


3.1. Method

3.1.1. Experiment 1aStimuli were created from 16 photographs of common

objects (see Fig. 3). The photographs were taken under uni-form lighting and edited in Adobe Photoshop to removethe backgrounds. Each object was photographed with itsaxis of elongation parallel to the camera’s sensor plane,and each photograph was asymmetric along both planarobject axes. All of the objects were polyoriented (Leek,1998). In contrast to mono-oriented objects, polyorientedobjects are not associated with a single canonical uprightorientation and are regularly viewed at a variety of orien-tations (although some orientations may be more commonthan others). Polyoriented objects were chosen to mini-mize potential response biases that might occur withmono-oriented stimuli (e.g., a bias toward drawing an ob-ject in the canonical orientation).6

6 The decision to limit stimuli to polyoriented objects and the require-ment that objects be asymmetric across two object axes jointly had theconsequence that most of the stimulus objects were tools or otherimplements.

Each stimulus object appeared in 16 different orienta-tions, consisting of picture-plane rotations in 45� incre-ments of the original (vertical) photograph and itsreflection across the principal object axis (see Fig. 4A).The complete stimulus set consisted of 256 oriented pic-tures (16 objects � 16 orientations). For each stimulus ob-ject the principal axis subtended approximately 9.5� ofvisual angle. All stimuli were presented on a whitebackground.

Participants were 30 undergraduate students at JohnsHopkins University. Each received either pay or extra cred-it in a course. Each participant received 128 total stimuli.All 256 stimuli were presented across every two partici-pants, so that each stimulus was presented 15 times acrossthe 30 participants. Order of presentation was randomizedfor each participant, with the exception that at least twotrials intervened between successive presentations of thesame object.

The participant sat facing a computer screen at a dis-tance of approximately 45 cm. On each trial two stimuluspictures were presented in succession, and the participantthen attempted to draw each object in the depicted orien-tation. A trial began with presentation of a fixation cross

Fig. 4. (A) The 16 orientations at which stimuli were presented in Experiments 1a, 2, and 3. (B) The 16 stimulus orientations in Experiment 1b.


in the center of the screen. When the participant presseda key, the fixation point disappeared and the first stimu-lus picture was displayed at the center of the screen for500 ms, followed by a 250-ms pattern mask. The secondstimulus was then presented for 500 ms, followed againby a 250-ms mask. Immediately after offset of the mask,a cross was displayed, indicating that the participantcould begin responding. The participants drew the targetobjects on response sheets divided into three panels.The left panel contained three dots; the center and rightpanels provided the name of the first and second targetobject, respectively, at the bottom and were otherwiseblank. The participant first connected the dots to form atriangle, creating a brief delay before the participant drewthe stimulus objects. Then the participant drew the firstand second objects. The experimenter monitored thedrawing responses, asking for clarification if the orienta-tion of a depicted object was unclear. Ten practice trialspreceded the test trials.

7 The 30 participants viewed a total of 3840 target stimuli, four of whichwere excluded from analyses due to procedural mishaps during testing. Theremaining 3836 drawings were scored independently by two coders whowere unaware of the correct responses. Coder agreement was 97%.Disagreements were resolved by a third coder who was also naive to thecorrect responses. Seven drawings caused three-way discrepancies andwere excluded from analyses. Six additional drawings were classified bythe coders as ambiguous and were also excluded, leaving 3823 drawings foranalysis.

3.1.2. Experiment 1bStimuli were the same as in Experiment 1a, except that

the orientations were 45� increments starting from 22.5�rather than 0� (see Fig. 4B). The participants, 16 under-graduate students at Johns Hopkins University, each sawall 256 stimuli across 128 trials. Each trial began with a2-s presentation of a 7-digit number, after which thetwo target pictures were presented as in Experiment 1a.Next, memory for target orientation was tested withforced-choice arrays that presented all 16 possibleorientations of the target stimulus. Finally, the partici-pant typed the 7-digit number using the computerkeyboard.

3.2. Results

In Experiment 1a the participants’ drawings werescored by coding which of the 16 possible stimulus orien-

tations most closely matched the drawing.7 The depictedorientation was correct in 56% of the drawings (2135/3823). Accuracy was 57% (1095/1913) for cardinal (horizon-tal or vertical) stimuli and 54% (1040/1910) for obliques,t(29) = 1.19, p > .20. In Experiment 1b, which included onlyoblique stimuli, accuracy on the forced-choice orientationtest was 43% (1751/4096).

3.2.1. Error types: oblique stimuliFor each target stimulus, one of the 16 possible re-

sponse orientations is correct, and the remaining 15 areincorrect. The erroneous orientations fall into three majorcategories: mirror-reflection, picture-plane rotation, andmixed (reflection plus rotation) errors (see Fig. 5). For ob-lique stimuli four different types of mirror-reflection errorcan be distinguished. In object principal axis (OPA) errorsthe stimulus object is reflected across its own principalaxis of elongation, and in object secondary axis (OSA) er-rors the object is reflected across its own secondary axis.In extrinsic vertical axis (EVA) errors the stimulus objectis reflected across a vertical axis extrinsic to the object,and in extrinsic horizontal axis (EHA) errors the stimulusis reflected across an extrinsic horizontal axis. Picture-plane rotation errors may be divided into seven types:+45�, �45�, +90�, �90�, +135�, �135�, and 180�. Theremaining four incorrect orientations for each stimulus fallinto the mixed (reflection plus rotation) error category.

According to the typical characterization of mirror-im-age confusion as a tendency to confuse stimuli related byleft–right reflection across a vertical axis, we should expect

Fig. 5. Possible orientation error types for oblique stimuli, divided into three categories: mirror reflections, picture-plane rotations and mixed errors. Forthe picture-plane rotations, + indicates rotation in the clockwise direction, and � counterclockwise rotation (OPA = object principal axis reflection;OSA = object secondary axis reflection; EVA = extrinsic vertical axis reflection; EHA = extrinsic horizontal axis reflection).

Fig. 6. (A) Error distribution for oblique stimuli in Experiment 1a. The value for mixed errors is the mean across the four individual forms of mixed error. (B)Error distribution for oblique stimuli in Experiment 1b. The value for mixed errors is the mean across the six individual forms of mixed error.


to observe a predominance of extrinsic vertical axis (EVA)reflections. However, this expectation was not confirmed.

Fig. 6A presents the distribution of errors across types inExperiment 1a. Analysis of variance indicated that the er-


rors were not distributed uniformly, F(14, 406) = 40.3,p < .001. (All ANOVAs reported in this article were Geis-ser–Greenhouse corrected for non-sphericity.) Tukey’sHSD tests demonstrated that reflections across the objectprincipal axis (OPA errors) were more frequent than anyother error type (p < .05). Also, 45� rotations were morefrequent than rotations of 135� or 180�. Reflections acrossextrinsic axes (EVA and EHA errors) were infrequent.

Fig. 6B presents the error distribution from Experiment1b. Errors were not uniformly distributed across types,F(16, 240) = 29.31, p < .001. Once again, object principalaxis reflections (OPA errors) were more frequent thanany other type of error (p < .05), and extrinsic-axis reflec-tions (EVA and EHA errors) were infrequent. Also, 45� rota-tions were more frequent than error types other than OPAerrors (p < .05). In the secondary number-recall task partic-ipants accurately recalled 48% of the 7-digit numbers. Per-

Fig. 7. (A) Possible reflection error types for vertical stimuli and

Fig. 8. Error distribution for cardinal stimuli in Experiment 1a. The value for m

formance on the object orientation task was virtuallyidentical for correct and incorrect number-recall trials.

3.2.2. Error types: cardinal stimuliBecause cardinal stimuli confound object and extrinsic

axes, mirror-reflection errors for these stimuli cannot beinterpreted unambiguously: Any reflection error for a car-dinal stimulus may be described either as a reflectionacross an object axis or as a reflection across an extrinsicaxis. Nevertheless, the inclusion of cardinal stimuli inExperiment 1a allows us to ask whether the error patternfor cardinals is consistent with the pattern we find forthe obliques.

Across the set of cardinal orientations, four types ofreflection error are possible, but two of these can occuronly for vertical stimuli, and two can occur only for hori-zontal stimuli. Fig. 7A presents the two possible reflection

(B) possible reflection error types for horizontal stimuli.

ixed errors is the mean across the six individual forms of mixed error.


errors for vertical targets. An OPA/EVA error could be areflection across the object principal axis (OPA error) or areflection across an extrinsic vertical axis (EVA error); anOSA/EHA error could be a reflection across either the objectsecondary axis (OSA error) or an extrinsic horizontal axis(EHA error). Fig. 7B shows the possible reflections for hor-izontal targets: OPA/EHA (reflection across the object prin-cipal axis or an extrinsic horizontal axis) and OSA/EVA(reflection across the object secondary axis or an extrinsicvertical axis).

Fig. 8 presents the distribution of errors across types forthe cardinal stimuli in Experiment 1a. Because each reflec-tion error type could occur only for horizontal or only forvertical stimuli, the figure provides frequencies of other er-ror types separately for horizontal and vertical stimuli. Fre-quencies can therefore be compared across all error types.As in the case of the oblique stimuli, the most common er-rors for the cardinals were (certain forms of) mirror reflec-tion, and 45� rotations. Reflection errors potentiallyinterpretable as object principal axis reflections (OPA/EVA and OPA/EHA) were significantly more frequent thanthe other reflection error types (OSA/EVA and OSA/EHA),p < .01 by Scheffé test. Although the confounding of objectand extrinsic axes precludes firm conclusions, this findingsuggests that for the cardinal stimuli, as for the obliques,the reflection errors were predominantly reflections acrossan object principal axis.

3.3. Discussion

Three findings from Experiment 1 deserve emphasis.First, the error patterns were very similar in Experiments1a and 1b, despite the differences in stimulus orientationsand test procedures. Second, mirror-image confusionswere prominent among the errors for both oblique and car-dinal stimuli. Third, and most important, the various possi-ble forms of mirror-image error were not equally common.Most previous discussions of mirror-image confusion havetaken for granted that mirror-image stimuli are confusablebecause they are related by left–right reflection across anextrinsic vertical axis, such as the observer’s body midlineor a vertical environmental feature. Despite the fact thatextrinsic and object axes have usually been confounded,researchers have not entertained the possibility that themirror-image relationship giving rise to confusion is reflec-tion across an object axis. However, when we uncon-founded object and extrinsic axes by presentingobliquely-oriented stimuli, we found that extrinsic-axisreflection errors rarely occurred. Instead most mirror-im-age errors took the form of reflections across an object axis.

4. Experiment 2

Experiment 2 examined whether the Experiment 1 re-sults were robust across changes in memory demands,stimulus viewing conditions, retention interval, andinstructions to participants. In Experiment 2a eight ratherthan two target stimuli were presented on each trial, stim-ulus exposure duration was increased from 500 ms to 1 s,and the stimuli were not masked. In Experiment 2b partic-

ipants viewed 16 unmasked stimuli for 25 s each, and weretested 24 h later. Also, Experiment 2b used an incidentallearning procedure in which participants were unawarethat memory for orientation would be tested.

4.1. Method

4.1.1. Experiment 2aStimuli were the same as in Experiment 1a. Each of the

eight target stimuli presented on a trial depicted a differentobject and a different orientation. Participants were 48adults who received pay or extra credit in a course at JohnsHopkins University. Each participant received two trials, or16 total stimuli, across which each object and each orien-tation were presented once. Across every 16 participants,each of the 256 stimuli was presented once. Memory fortarget orientation was tested with forced-choice arrays asin Experiment 1b. On each trial the eight stimulus pictureswere presented successively for 1 s each, with a 1 s blankinterval between pictures. The participant then saw the re-sponse array for the first target stimulus, followed by thearray for the second target and so forth, until all eight tar-gets had been tested.

4.1.2. Experiment 2bSixteen undergraduate students at Johns Hopkins Uni-

versity participated in exchange for extra credit in a course.Participants were informed that their job was to learn thespellings of nonwords, so that they could recall the spell-ings on tests to be administered after an intervening dis-tractor task and on the following day. Thirty nonwords(e.g., phlieves) were then presented one at a time on a com-puter screen, and each was read aloud by the experi-menter. Next, a mental imagery task was introduced withthe rationale of minimizing the participant’s ability to re-hearse the nonword spellings in the interval betweenstudy and test. Participants were informed that they wouldsee pictures of objects, make mental images of these ob-jects, and then answer questions on the basis of theirimages. The participants were told that the questionswould concern the colors, component parts, and shapesof the objects, and that consequently they should payattention to these object properties. Examples of the ques-tion types were provided. No mention was made of the ob-jects’ orientations.

Each participant viewed each of the 16 objects in one ofits 16 possible orientations, with each object appearing at adifferent orientation. Across the 16 participants, each ofthe 256 object-orientation combinations was presentedonce. For each participant, the 16 stimulus pictures werepresented three times. On each presentation the stimuliwere presented one at a time, and each object appearedin the same orientation on all three presentations. On thefirst presentation the 16 stimuli were presented for 5 seach, with the object’s name (e.g., comb) displayed be-neath the picture. The participant was instructed to notethe name and relevant properties (color, parts, shape) foreach object. On the second presentation the participantviewed the object for 5 s. A beep then signaled the partic-ipant to close her eyes, and form a mental image of thestimulus. A second beep 5 s later signaled the participant

Table 1Error distribution for oblique stimuli in Experiments 2a, 2b and 3.

Error type Number of errors

Experiment 2a Experiment 2b Experiment 3

OPA 71 20 279OSA 19 1 261EVA 10 0 21EHA 10 0 26+45� 11 16 15�45� 9 13 19+90� 13 0 35�90� 11 3 22+135� 7 0 11�135� 8 1 13180� 11 0 99Mixed 9 2 8

Note: The values for mixed are means across individual types of mixederrors.


to open her eyes and check the accuracy of her imageagainst the stimulus during the next 5 s. After all 16 stimulihad been presented, the participant answered a color, part,or shape question for each stimulus (e.g., What color wasthe switch on the flashlight?; Was there a cap on thepen?; Was the handle of the hairbrush straight or curved?).The third presentation of the stimuli was the same as thesecond, except that different color, part, and shape ques-tions were asked at the end. The session concluded witha spelling test for the 30 nonwords.

On the following day the participant returned to the laband was tested on spelling the nonwords. Finally, the par-ticipant was unexpectedly asked to draw each object as itwas oriented during stimulus presentation. The names ofthe 16 objects were presented as cues.

4.2. Results

In Experiment 2a, accuracy on the forced-choice orien-tation tests was 43% (167/384) for oblique stimuli and52% (198/384) for cardinal stimuli. In Experiment 2b par-ticipants accurately oriented their drawings for 51% (62/122) and 74% (94/127) of the oblique and cardinal stimuli,respectively.8

Errors for oblique stimuli were distributed non-uni-formly across types in both Experiment 2a, F(14, 658) =18.0, p < .001, and Experiment 2b, F(14, 210) = 12.10,p < .001 (see Table 1). Object principal axis reflections(OPA errors) were the most common errors in both exper-iments, significantly exceeding the frequency of all othererror types in Experiment 2a, and all other types except45� rotations in Experiment 2b (ps < .05). Reflections acrossextrinsic axes (EVA and EHA errors) were infrequent inExperiment 2a, and did not occur at all in Experiment 2b.

Table 2 presents the error distribution for cardinal stim-uli. In both Experiment 2a and 2b the error types poten-tially interpretable as object-axis reflections (OPA/EVAand OPA/EHA errors) occurred significantly more oftenthan any of the other error types (ps < .05).9

8 Drawings were scored as in Experiment 1a. Agreement between thetwo coders was 96%, and discrepancies were resolved by a third coder.Seven ambiguous drawings were excluded from analyses.

9 Although we focus on mirror-reflection errors in this article, a fewpoints about the picture-plane rotations are also worth making. In bothExperiment 1a and 1b 45� rotations were more common than largerrotations (e.g., 135�), suggesting that rotation errors occurred when aparticipant had only a vague memory for the tilt of a stimulus object, andconsequently responded with an orientation that was substantially but(usually) not grossly incorrect. In Experiment 1a rotations that transformedan oblique to a cardinal orientation were no more frequent than cardinal-to-oblique rotations (221 vs. 229 errors, respectively). However, oblique-to-cardinal rotations (35 errors) were slightly more frequent than cardinal-to-oblique rotations (20 errors) in Experiment 2a, and much more frequent inExperiment 2b (30 oblique-to-cardinal vs. 5 cardinal-to-oblique). Theseresults suggest that in Experiments 2a and 2b, but not in Experiment 1a,participants were biased toward responding with a cardinal orientationwhen uncertain. This bias may have contributed to the significantly higheraccuracy for cardinal than for oblique stimuli in Experiment 2b (74% vs.51%), t(15) = 4.37, p < .01, and to the marginally significant cardinaladvantage in Experiment 2a (52% vs. 43%), t (47) = 1.93, p < .06. InExperiment 1a, where no bias toward cardinal orientations was evident,cardinals and obliques did notdiffer in accuracy (57% vs. 54%), t(29) = 1.19,p > .10. (Cardinal-oblique comparisons cannot be made for Experiment 1b,because all of the stimulus and response orientations were oblique.)

4.3. Discussion

Experiments 2a and 2b yielded error patterns very sim-ilar to those from Experiments 1a and 1b: Mirror-imageconfusions were the most frequent errors, and these confu-sions predominantly took the form of reflections across ob-ject and not extrinsic axes. The concordance of resultsacross experiments occurred despite substantial variationin stimulus exposure duration (500 ms to 25 s), retentioninterval (a few seconds to 24 h), number of target stimulipresented on each trial (2–16), and other factors. Taken to-gether, the findings of the various experiments demon-strate that the predominance of object- over extrinsic-axis reflections obtains over a range of conditions.

5. Experiment 3

Stimuli in Experiments 1a–2b were photographs offamiliar objects. In Experiment 3, however, the stimuliwere simple drawings of unfamiliar artificial objects. Theexperiment had two goals. The first was to ask whetherthe general pattern of mirror-image confusions observedin the earlier experiments—high rates of object-axis reflec-tions with few extrinsic-axis reflections—would generalizeto a different type of stimulus. The second goal was to lookmore closely at the object-axis reflection errors. Althoughreflections across object axes were the most frequent er-rors in Experiments 1 and 2, the two possible forms of ob-ject-axis reflection were not equally common. Reflectionsacross the object principal axis (OPA errors) occurred withhigh frequency, but reflections across the object secondaryaxis (OSA errors) were much less frequent. In Experiment 3we explored the relative frequency of the two types of ob-ject-axis reflection, asking whether the predominance ofOPA over OSA errors obtains regardless of circumstances,or whether instead the frequency of OSA errors mightequal or exceed that of OPA errors under some conditions.

In reflections across the object principal axis (OPA er-rors) the principal axis is oriented correctly, but the sec-ondary object axis is flipped. For example, in the OPAerror in Fig. 5 the orientation of the comb’s principal axisis correct (with the handle side of the axis below and to

Table 2Error distribution for cardinal stimuli in Experiments 2a, 2b and 3.

Error type Number of errors

Experiment 2a Experiment 2b Experiment 3

Vertical stimuli horizontal stimuli Vertical stimuli Horizontal stimuli Vertical stimuli Horizontal stimuli

OPA/EVA 40 – 10 – 129 –OPA/EHA – 38 – 10 – 125OSA/EVA – 16 – 2 – 140OSA/EHA 12 – 1 – 109 –+45� 4 2 1 3 18 15�45� 3 3 0 1 12 15+90� 4 2 0 0 5 9�90� 2 5 0 0 12 3+135� 2 0 0 0 8 14�135� 2 4 0 0 10 3180� 10 11 0 1 35 27Mixed 3 2 0 1 10 9

Note: The values for mixed are means across individual types of mixed errors.

Fig. 9. Examples of stimuli from the four conditions of Experiment 3(LL = large principal and secondary-axis features; LS = large principal andsmall secondary-axis features; SL = small principal and large secondary-axis features; SS = small principal and secondary-axis features).


the left of the teeth side), but the secondary axis is flipped(teeth side down and to the right instead of up and to theleft). Conversely, in reflections across the object secondaryaxis (OSA errors) the secondary axis has the correct orien-tation but the principal axis is reversed. This characteriza-tion of the object-axis reflections suggests a possibleinterpretation for the higher frequency of OPA than OSA er-rors in Experiments 1a–2b. For most of the stimulus ob-jects (see Fig. 3) the features differentiating the two sidesof the principal axis seem more salient than the featuresdifferentiating the sides of the secondary axis. In the caseof the knife, for example, the blade and handle differentiatethe two sides of the principal object axis, but the featuresthat distinguish the sides of the secondary axis (e.g., sharpvs. dull edge of blade) are not as salient. As a consequence,less attention and processing effort may have been direc-ted to secondary-axis features than to principal-axis fea-tures, leading to poorer memory for secondary-axisorientation, and hence to higher rates of OPA errors thanOSA errors.

If this interpretation is correct, the relative frequency ofOPA and OSA errors should vary with the relative salienceof the features that distinguish the sides of the secondaryand principal object axes, respectively. The use of artifi-cial-object stimuli in the present experiment allowed usto test this prediction. As illustrated in Fig. 9, each objectconsisted of an elongated bar with a different shape oneach side and at each end. The shapes or features on theends of the bar differentiated the sides of the principal ob-ject axis, and those on the sides of the bar differentiatedsides of the secondary axis. We manipulated the salienceof the differentiating features by varying their size. Fourobject types were created: LL (large principal and second-ary-axis features), SS (small principal and secondary-axisfeatures), LS (large principal and small secondary-axis fea-tures), and SL (small principal and large secondary-axisfeatures).

Across the full set of stimulus objects, feature saliencewas equated for principal and secondary object axes: foreach axis, half of the objects had large features and halfhad small features. If, therefore, the incidence of OPA er-rors and OSA errors is determined by the salience of these

differentiating features, we would expect OSA errors to beas frequent as OPA errors for the stimulus set taken as awhole. Furthermore, we would expect the relative fre-quency of OPA and OSA errors to vary with the relative sal-ience of the principal- and secondary-axis features. For LSobjects, in which the principal-axis features are more sali-ent than the secondary-axis features, OPA errors should bemore frequent than OSA errors. However, this patternshould be reversed for SL objects, in which feature salienceis higher for the secondary axis than for the principal axis.

5.1. Method

Participants were 32 undergraduate students at JohnsHopkins University. Eight stimulus objects were created,each with a different combination of features (e.g., square,wedge, pentagon, half circle); most features appeared inmore than one object. Four versions of each object (LL,SS, LS, SL) were created by varying the size of the features.

Fig. 10. (A) Frequency of OPA and OSA errors for oblique stimuli in theLS and SL conditions of Experiment 3. (B) Frequency of potential OPAand OSA errors for cardinal stimuli in the LS and SL conditions ofExperiment 3.


Large features were more than twice the area of small fea-tures. Each object appeared in the same 16 orientations(eight oblique, eight cardinal) used in Experiments 1aand 2. The design therefore included 512 stimuli (8shapes � 4 feature-size conditions � 16 orientations). Eachparticipant received 128 stimuli, and across the set of 32participants every stimulus was presented eight times. Atthe beginning of each trial, a 7-digit number was presentedfor 3 s. A single stimulus object was then displayed for700 ms, followed by a pattern mask for 250 ms, a 5 s blankinterval, and a 16-alternative forced-choice array. Afterselecting a response from the array, the participant enteredthe 7-digit number on the keyboard.

5.2. Results

Overall accuracy was 60% (2463/4096). Accuracy didnot differ between obliques (59%) and cardinals (61%),t(31) = 1.05, p > .25, or across the four feature-salience con-ditions: 60%, 62%, 60%, and 59% for LL, LS, SL, and SS condi-tions, respectively, F < 1. Participants accurately recalled51% of the 7-digit numbers, and performance on the orien-tation task did not differ for correct and incorrect number-recall trials.

For the oblique stimuli errors were distributed non-uni-formly across types, F(14, 434) = 69.4, p < .001. The errordistribution, collapsed across feature-salience conditions,is shown in Table 1. As predicted, the relative frequencyof object secondary-axis reflections (OSA errors) was muchhigher than in the previous experiments. Whereas OSA er-rors were far less frequent than OPA errors in Experiments1a–2b, in Experiment 3 OSA and OPA errors did not differin frequency, and both were significantly more frequentthan any other error type (ps < .05). As in the precedingexperiments, extrinsic vertical axis reflections (EVA andEHA errors) were quite infrequent.

The four feature-salience conditions yielded very simi-lar error patterns, except for OPA and OSA errors in theLS and SL conditions (see Fig. 10A). As predicted, OPA er-rors were more frequent than OSA errors in the LS condi-tion, but the opposite was true in the SL condition,F(1, 31) = 14.23, p < .001, for the interaction. (For LL andSS conditions OPA and OSA errors were approximatelyequal in frequency.)

For the cardinal stimuli errors were non-uniformly dis-tributed across types, F(16, 496) = 30.4, p < .001 (see Table2). Errors potentially interpretable as object principal-axisreflections (OPA/EVA and OPA/EHA errors) did not differ infrequency from potential object secondary-axis reflections(OSA/EVA and OSA/EHA errors), and these errors weremore frequent than all other error types (ps < .05).Fig. 10B presents the frequency of potential OPA and OSAerrors for the LS and SL conditions. As for the oblique stim-uli, potential OPA errors were more frequent than potentialOSA errors in the LS condition, with the opposite being truein the SL condition, F(1, 31) = 11.28, p < .01.

5.3. Discussion

Two outcomes of Experiment 3 are noteworthy. First,as in the previous experiments reflections across object

axes were frequent, and reflections across extrinsic axesrarely occurred. Second, the results of Experiment 3 clar-ify the findings from the earlier experiments concerningthe relative frequency of object principal axis reflections(OPA errors) and object secondary-axis reflections (OSAerrors). In Experiments 1 and 2 the features that distin-guished the sides of object axes were usually more sali-ent for principal than for secondary object axes, and inthese experiments OPA errors were much more frequentthan OSA errors. In Experiment 3, however, feature sal-ience was equated between principal and secondary ob-ject axes for the stimulus set as a whole, and theoverall frequency of OSA errors was as high as that ofOPA errors. Furthermore, when feature salience wasmanipulated, the relative frequency of OPA and OSA er-rors varied accordingly.

The stimuli in Experiment 3 were highly artificial, andwe cannot be certain that they were processed in the samemanner as real objects. In light of this caveat, we concludesimply that the results from all of the experiments are con-sistent with the hypothesis that OPA and OSA error fre-quencies are determined by the salience of the featuresdifferentiating the sides of the secondary and principalaxes, respectively.

Interestingly, the variation across feature-salience con-ditions in frequency of OPA and OSA errors was apparentlya function of the relative and not the absolute salience ofthe principal- and secondary-axis features. Overall accu-racy did not vary across feature-salience conditions; for


example, participants were no less accurate in the SS(small–small) condition than in the LL (large–large) condi-tion. Furthermore, the total number of object-axis reflec-tions (OPA errors + OSA errors) did not differ acrossconditions. These results indicate that the small (low-sal-ience) features were not inherently more difficult to en-code or remember than the large (high-salience) features.Accordingly, the variation across conditions in relative fre-quency of OPA and OSA errors is most plausibly attributedto tradeoffs in allocation of attention or processing effortbetween axes with high- and low-salience features. Whenprincipal- and secondary-axis features were equal in sal-ience (LL and SS conditions), both object axes receivedapproximately equal attention and effort, resulting inapproximately equal numbers of OPA and OSA errors.When, however, the principal and secondary axes differedin feature salience (LS and SL conditions), less attentionand effort were allocated to the less salient features, lead-ing to differences in frequency between OPA and OSAerrors.

6. General discussion

The present study explored the tendency of humans toconfuse mirror-image stimuli. We argued that because ofconfounds in prior studies of mirror-image confusion, theimplications of the results are unclear. In most studiesthe intrinsic axes of the stimulus objects were alignedwith extrinsic horizontal and vertical axes, with the con-sequence that the observed mirror-image confusionscould have been reflections across object axes, ratherthan (as has usually been assumed) reflections acrossextrinsic axes. Also, in some studies the stimuli weresymmetric about one or both object axes, with the conse-quence that mirror-reflection errors could not be distin-guished from errors involving rotation in the pictureplane.

We avoided these confounds by presenting asymmetricstimuli with object axes tilted relative to extrinsic axes.Across five experiments varying widely in stimulus expo-sure duration, memory load, retention interval, test type,and instructions to participants, a consistent patternemerged. Consistent with prior claims about the confus-ability of mirror images, mirror-reflection errors occurredmore often than other forms of orientation error. However,whereas prior discussions have typically taken for grantedthat the mirror images subject to confusion are reflectionsacross an extrinsic vertical axis (e.g., the observer’s bodymidline or a vertical environmental axis), we found thatthe vast majority of mirror-image errors were reflectionsacross object axes. Reflections across extrinsic axes wererare in all of our experiments.

Future studies may conceivably find that stimuli relatedby extrinsic-axis reflections engender confusion under cer-tain conditions. Nevertheless, the present results makeclear that any potential explanation for the confusabilityof mirror images must address the tendency to confusestimuli related by reflection across object axes. In the fol-lowing section we examine previous interpretations ofmirror-image confusion in light of this point.

7. Interpretations for mirror-image confusion

7.1. Irrelevance of mirror-image distinctions

The most common interpretation for mirror-image con-fusion alludes to the supposed irrelevance of mirror-imagedistinctions in visual perception (e.g., Bornstein, 1982; Cor-ballis & Beale, 1983; Gibson et al., 1962; Gross & Bornstein,1978; Sutherland, 1957a). According to this interpretation,the difference between mirror images is almost alwaysirrelevant for determining the identity of an object—forexample, the identity of a coffee cup remains the samewhether it is viewed with handle facing left or handle fac-ing right—and perceptual processes may consequently failto encode or retain information about mirror-imagedistinctions.

The irrelevance interpretation is usually stated in termsof left–right mirror images (i.e., extrinsic vertical axisreflections), but could also be formulated in object-axisterms, to assert that orientation differences resulting fromobject-axis reflections are irrelevant to object identity, andso are often ignored in perception and memory. Regardlessof the specific formulation, however, the irrelevance ac-count has two major flaws.

First, the account focuses exclusively on the visual sys-tem’s role in object recognition, ignoring the fact that vi-sion also serves a variety of other purposes, many ofwhich require orientation information (e.g., reaching forobjects, interpreting visual scenes, using landmarks to nav-igate the environment). Second, the irrelevance accountfails to explain why confusability should be limited to mir-ror images. The point that differences between mirrorimages are—irrelevant to object identity applies equallyto any other orientation difference—for example, an appleretains its identity when turned on its side. If the visualsystem ignores differences that are irrelevant to objectidentity, we should presumably expect all orientation dif-ferences to be equally subject to confusion. However, bothour results and previous findings clearly demonstrate thatsome orientation differences are far less confusable thanothers; for example, in our experiments participants weremuch less likely to confuse a target orientation with a 90�or 135� picture-plane rotation than with an object princi-pal axis reflection.

7.2. Left–right non-distinctiveness

A second interpretation for mirror-image confusioncites the lack of distinctive differences between the leftand right sides of bodies, brains, and environments (e.g.,Bornstein, 1982; Corballis, 1988; Corballis & Beale, 1976,1983; Farrell, 1979; Goldmeier, 1936; Goldmeier, 1972;Rock, 1973; Sutherland, 1960). For example, the top andbottom of the human body are distinctively different,whereas the left and right sides are much more similar toone another.

The left–right non-distinctiveness hypothesis predictsconfusions between a target and its left–right mirror image(i.e., extrinsic vertical axis reflection). Hence, the hypothe-sis cannot account for our results, which showed a


predominance of object-axis reflection errors with fewextrinsic vertical axis reflections. As we discuss in a latersection, however, the notion of non-distinctiveness mayhave value for understanding mirror-image confusion,when applied to object rather than extrinsic axes.

7.3. Reduction and duplication coding

Corballis and Beale (1976) drew a distinction betweenreduction and duplication coding. Reduction codinghypotheses attribute mirror-image confusions to represen-tations that are inherently incapable of encoding mirror-image distinctions (just as a black-and-white photographis incapable of representing color distinctions). In contrastduplication coding hypotheses assume that when a visualstimulus is encoded, both a representation of the actualorientation and a representation of the left–right mirror-image orientation are generated.

7.3.1. Reduction codingThe reduction coding hypothesis has been applied to

mirror-image confusions in children, non-human animals,and brain-damaged patients (e.g., Bryant, 1969, 1973;Corballis, 1988; Corballis & Beale, 1976; Davidoff & War-rington, 1999, 2001; Deutsch, 1955; Sutherland, 1957a;Turnbull & McCarthy, 1996). Most versions of the hypoth-esis posit representations incapable of encoding the dis-tinction between a stimulus and its left–right mirrorimage (extrinsic vertical axis reflection). In light of ourfindings, however, the hypothesis could be formulated inobject-axis terms, by positing representations incapableof distinguishing orientations that differ by reflectionacross an object principal and/or secondary axis.

Even in this form, however, the reduction codinghypothesis has significant shortcomings. First, no clearmotivation is apparent for positing representations thatcannot capture certain mirror-image distinctions, yet canencode other mirror-image distinctions, as well as orienta-tion distinctions not involving mirror reflection. Also, areduction coding account cannot easily accommodate ourresults. Consider Experiment 3, in which the incidence ofOPA and OSA (object secondary axis) errors varied withthe salience of the features for the principal and secondaryobject axes. To explain these results a reduction codinghypothesis would have to make the unmotivated assump-tion that participants relied upon multiple forms of repre-sentation, with different forms predominating in differentfeature-salience conditions (i.e., representations incapableof differentiating a stimulus and its principal axis reflectionin the condition yielding more OPA than OSA errors, andrepresentations incapable of differentiating a stimulusand its secondary axis reflection in the condition yieldingmore OSA than OPA errors).

Still further multiplication of representational assump-tions is required by the fact that all of our experiments—and many previous studies (e.g., Farrell, 1979; Priftiset al., 2003; Rudel & Teuber, 1963; Sekuler & Houlihan,1968; Vogel, 1980)—found above-chance performanceeven on the orientation distinctions giving rise to confu-sion. In our experiments, for example, participants showeda strong tendency to confuse a target with one or more of

its object-axis reflections, but were still far more likely torespond correctly than to make an OPA or OSA error (orany other type of error). To accommodate this pattern ofresults, a reduction coding hypothesis would have to positnot only representations incapable of distinguishing spe-cific forms of object-axis reflections (to account for theOPA and OSA errors), but also representations capable ofencoding all of the reflectional and rotational distinctionstested in the experiments (to account for the high propor-tions of correct responses). In light of these points a reduc-tion coding account appears not only unmotivated but alsounwieldy, especially given that (as we discuss in a latersection) our results can be interpreted in terms of a singleform of representation.

7.3.2. Duplication codingSeveral duplication-coding interpretations have been

proposed in the context of left–right mirror-imageconfusion (e.g., Corballis, 1988; Corballis & Beale, 1983;Deregowski, McGeorge, & Wynn, 2000; Heilman, Howell,Valenstein, & Rothi, 1980; Lambon-Ralph, Jarvis, & Ellis,1997; Noble, 1968; Orton, 1937). With one exception(Deregowski et al., 2000) the accounts are variants of amirror engram hypothesis (e.g., Aaron & Malatesha, 1974;Corballis & Beale, 1983; Heilman et al., 1980; Lambon-Ralph et al., 1997; Mello, 1965; Noble, 1968; Orton,1937). This hypothesis assumes that when an object is pre-sented visually, a representation of the object’s actual ori-entation is generated in one cerebral hemisphere, and arepresentation of the left–right mirror image—a mirror en-gram—is created in the other hemisphere, creating the po-tential for mirror-image confusions. The postulation ofmirror engrams is often motivated by reference to homo-topic connections between hemispheres, the notion beingthat when a representation is generated in one cerebralhemisphere, the interhemispheric connections will leadto creation of a mirror-image representation in the oppo-site hemisphere (e.g., Noble, 1968).

The mirror engram hypothesis can be questioned onboth logical and empirical grounds. Interhemispherictransfer of information, even if via homotopic connections,would not necessarily produce a mirror-reflected neuralrepresentation (whatever exactly that might mean). Also,even if the neural representation in one hemisphere werea mirror reflection of that in the other hemisphere, thetwo representations would not necessarily represent mir-ror-image orientations. For example, given a neural repre-sentation specifying the correct orientation for the letter b,the mirror image of that representation would not neces-sarily represent the mirror-image orientation d. Further-more, the principal findings cited in support of thehypothesis (e.g., Mello, 1965; Noble, 1968) can plausiblybe explained without positing mirror engrams (see, e.g.,Hamilton & Tieman, 1973; Lehman & Spencer, 1973;Tieman, Tieman, Brody, & Hamilton, 1974), and resultsinconsistent with at least some forms of the hypothesishave been reported (e.g., Corballis, Miller, & Morgan,1971; Fisher & Camenzuli, 1987; Kosslyn, LeSueur, Dror,& Gazzaniga, 1993; Storandt, 1974).

Our results pose further problems for the mirror en-gram hypothesis. The hypothesis takes its motivation from


the division of the brain into left and right cerebral hemi-spheres, and therefore most naturally applies to potentialconfusions between left–right mirror images (i.e., extrinsicvertical axis reflections). To explain the predominance ofOPA errors in Experiments 1 and 2, the hypothesis wouldhave to assume that the mirror engrams generated byparticipants in these experiments encoded not the left–right reflection of a target stimulus, but rather its objectprincipal axis reflection. How this assumption could bemotivated by reference to cerebral hemispheres and inter-hemispheric connections is entirely unclear. Further, in thecase of Experiment 3 any duplication coding hypothesiswould have to assume that different mirror-imageorientations were encoded in different feature-salienceconditions.

This brief review of interpretations for mirror-imageconfusion indicates that each of the accounts has signifi-cant problems, including difficulties in explaining theresults of our experiments. In the following discussionwe examine mirror-image confusions and their implica-tions from a different perspective. We describe an explicithypothesis concerning the representation of object orien-tation information, arguing that this hypothesis providesa novel interpretation for mirror-image confusion, and alsothat our results support some of the major assumptions ofthe hypothesis.

Fig. 11. Representing polarity correspondences between object and

8. Representing orientation: the COR hypothesis

McCloskey and colleagues (McCloskey, 2009; McClos-key et al., 2006) have recently proposed a coordinate-sys-tem orientation representation (COR) hypothesis. CORposits that at some level(s) of the visual system the orien-tation of an object is represented as a relationship betweenan object-centered frame of reference and a second frameof reference extrinsic to the object. The object-centeredframe is defined by the object’s principal axis of elongationand a secondary axis orthogonal to the principal axis. Theextrinsic frame may be defined by the axes of the obser-ver’s body or on some non-egocentric basis (e.g., the direc-tion of the gravitational force, the walls of a room). Forpresent purposes we simply assume an extrinsic coordi-nate system with vertical and horizontal axes, withoutconsidering how the axes were defined. Each axis has apolarity, with one end designated positive (+) and theother negative (�).10 A number of researchers have previ-ously discussed orientation in terms of relationships be-tween reference frames (e.g., Davidoff & Warrington,2001; Harris, Harris, & Caine, 2001; Howard, 1982; Ittel-son, Mowafy, & Magid, 1991; Jolicoeur & Kosslyn, 1983;Priftis et al., 2003; Riddoch & Humphreys, 1988; Turnbull& McCarthy, 1996), and Corballis (1988) characterizes ori-entation specifically as a relationship between object-cen-tered and extrinsic frames. However these conceptions oforientation have not been developed into specific hypoth-eses about the form of object-orientation representations.

10 We discuss the hypothesis in terms of two-dimensional objects andreference frames. However, the assumptions could be extended straight-forwardly to three dimensions.

One major assumption of COR is that the object is rep-resented in an object-centered frame of reference. Thisassumption is grounded in prior theoretical discussionand empirical evidence: Object-centered representationshave previously been posited in research on normal andimpaired object recognition, impaired processing of objectorientation, and hemispatial neglect (e.g., Corballis, 1988;Driver, Baylis, Goodrich, & Rafal, 1994; Driver & Halligan,1991; Harris et al., 2001; Humphreys & Riddoch, 1984;Marr, 1982; Marr & Nishihara, 1978; Turnbull & McCarthy,1996; Warrington & Davidoff, 2000). For example, sometheories of object recognition (e.g., Biederman, 1987; Marr,1982; Marr & Nishihara, 1978) assume that recognition ismediated by viewpoint-independent object-centered rep-resentations. (For an alternative view holding that recogni-tion is based on viewpoint-dependent representations see,e.g., Tarr & Pinker, 1989.) Moreover, impairments in iden-tifying principal object axes, and hence in constructing ob-ject-centered representations, have been proposed toexplain certain cases of visual agnosia (e.g., Humphreysand Riddoch, 1984). Also, object-centered representationshave played an important role in interpreting object-basedneglect, in which a brain-damaged patient neglects oneside (e.g., the left side) of objects, as opposed to the left sideof egocentric or environmental space (e.g., Driver et al.,1994).

8.1. Relating object-centered and extrinsic frames of reference

According to COR, an object’s orientation relative to anextrinsic reference frame is represented by specifying therelationship between the axes of the object-centered frameand those of the extrinsic frame. For example, the orienta-tion of the comb in Fig. 11 could be represented by relating

extrinsic axes. The positive pole of the object principal axis is mappedonto the positive pole of the extrinsic vertical axis (positive polaritycorrespondence), and the negative pole of the object secondary axis ismapped onto the positive pole of the extrinsic horizontal axis (negativepolarity correspondence).


the comb’s principal axis to the extrinsic vertical axis, andthe comb’s secondary axis to the extrinsic horizontalaxis.11

COR assumes that the relationship between object andextrinsic axes is specified by polarity correspondence andtilt parameters. The polarity correspondence parametersspecify how the polarity of each object axis is related tothe polarity of the corresponding extrinsic axis. In the pres-ent example, the principal object axis is aligned with itspositive pole toward the positive pole of the correspondingextrinsic axis (i.e., the vertical axis), as illustrated in Fig. 11.We refer to this positive-to-positive polarity correspon-dence as a positive polarity mapping. In contrast, the sec-ondary axis has a negative polarity relation to itscorresponding (horizontal) extrinsic axis: The negativepole of the secondary object axis maps onto the positivepole of the extrinsic horizontal axis. For this stimulus thepolarity-correspondence component of the orientationrepresentation might look something like the following:

POLARITY CORRESPONDENCEPRINCIPAL-VERTICAL: +SECONDARY-HORIZONTAL: �The tilt component of an orientation representation

specifies the tilt of the object axes relative to the corre-sponding extrinsic axes. For a two-dimensional represen-tation, the tilt is always the same for both object-extrinsic axis pairs. For example, if an object’s principalaxis is tilted 30� clockwise from the extrinsic vertical axis,the secondary axis is also tilted 30� clockwise from thehorizontal axis. Hence, we assume that tilt is specified onlyonce in two-dimensional orientation representations.

According to COR, tilt is represented by indicating thedirection and magnitude of the angular displacement be-tween the object’s principal axis and the correspondingextrinsic axis. For example, in Fig. 11 the principal objectaxis is tilted 45� clockwise from the extrinsic vertical axis.Arbitrarily designating clockwise as the positive directionand counterclockwise as negative, tilt could therefore berepresented as follows:

TILTDIRECTION: +MAGNITUDE: 45�

8.2. Relating extrinsic frames to one another

Once a representation relating an object-based frame ofreference to an extrinsic frame has been generated from astimulus, this orientation representation might be used forvarious purposes (e.g., reaching for the object, describingthe object’s orientation verbally, drawing the object). Using

11 The COR hypothesis assumes that one component of an orientationrepresentation specifies which object axes are represented in relation towhich extrinsic axes (see McCloskey, 2009; McCloskey et al., 2006).However, this aspect of the posited representations is not relevant to theissues addressed in the present article. The interpretations we discuss areindependent of whether the object-to-extrinsic mapping is assumed to beprincipal-to-vertical and secondary-to-horizontal, or instead principal-to-horizontal and secondary-to-vertical.

an orientation representation to perform a task will often(and perhaps always) involve relating the original extrinsicreference frame to a different extrinsic frame appropriatefor the task. Consider a person who views a sheet of papershowing a picture of a comb, and copies the picture onto aresponse sheet (see Fig. 12). The person might representthe orientation of the comb by encoding the relationshipbetween the comb’s object-centered frame of referenceand an extrinsic frame defined by the stimulus sheet. Toproduce a correctly oriented copy, however, the personwill also need to relate the extrinsic stimulus-sheet frameto an extrinsic frame defined by the response sheet. Inother words, the person will need to represent the orienta-tion of the extrinsic stimulus-sheet frame relative to theextrinsic response-sheet frame. The COR hypothesis as-sumes that representing the orientation of one extrinsicframe relative to another is no different from representingthe orientation of an object-based frame relative to anextrinsic frame: polarity correspondences and tilt mustbe specified. For example, in the copying task a positivepolarity correspondence should be established betweenthe stimulus- and response-sheet horizontal axes, indicat-ing that the left and right sides of the stimulus sheet corre-spond to the left and right sides, respectively, of theresponse sheet (see Fig. 12).12

8.3. Orientation errors

The COR hypothesis assumes that orientation errors re-sult from failures in encoding, retaining, or processingcomponents of the posited orientation representations.Mirror-image confusions are attributed to failures affectingpolarity-correspondence components. Object-axis reflec-tions are assumed to result from polarity correspondenceerrors in relating an object-centered reference frame toan extrinsic frame. Consider the comb in Fig. 11. If thepolarity correspondence between the comb’s secondaryaxis and the extrinsic horizontal axis were misrepresentedas positive (positive secondary axis pole corresponding topositive horizontal axis pole) the result would be a reflec-tion across the comb’s principal axis (see OPA in Fig. 5).Similarly, misrepresenting the polarity correspondence be-tween the comb’s principal axis and the extrinsic verticalaxis would lead to a reflection across the comb’s secondaryaxis (OSA in Fig. 5). Note that polarity correspondence er-rors involving one object axis lead to reflections acrossthe other object axis.

According to COR, reflections across an extrinsic axis re-sult from polarity correspondence errors in relating oneextrinsic reference frame to another. For example, in thehypothetical copying task (Fig. 12), misrepresenting thepolarity correspondence between the horizontal axes ofthe stimulus and response frames would lead to an extrin-sic vertical axis reflection (EVA in Fig. 5), and misrepresent-ing polarity correspondence for the vertical axes would

12 Although Fig. 12 illustrates a direct mapping between stimulus andresponse extrinsic frames, the mapping need not be direct. For example, therelationship between stimulus- and response-sheet frames might beestablished via one or more intervening egocentric reference frames.

Fig. 12. Polarity correspondences for a task in which a stimulus is copied onto a response sheet. Object axes are mapped onto the axes of an extrinsicreference frame defined by the stimulus page, and the axes of the extrinsic stimulus frame are mapped onto the axes of an extrinsic frame defined by theresponse page.


result in an extrinsic horizontal axis reflection (EHA inFig. 5).

COR also offers interpretations for errors not involvingmirror reflection. Picture-plane rotations are assumed toresult from failures in encoding, retaining, or processingthe tilt direction and/or tilt magnitude components of ori-entation representations. For example, 45� rotations, whichwere common in our experiments, may occur when tiltmagnitude representations are too vague to distinguishthe correct tilt from a tilt that differs by 45�. Mixed (reflec-tion plus rotation) errors (see Fig. 5 for examples) are attrib-uted to representational or processing failures involvingtwo or more components of an orientation representation.

8.4. The COR perspective on mirror-image confusion

As a potential interpretation for mirror-image confusionthe COR hypothesis has much to recommend it. First, thehypothesis provides a novel answer to the question ofwhy mirror images are prone to confusion: The representa-tions of mirror-image orientations are nearly identical,distinguished only by the value of a single polarity corre-spondence parameter. Consequently, any failure in encod-ing, retaining, or processing a polarity correspondencevalue will lead to a mirror-image error.

Second, COR distinguishes among multiple forms of mir-ror-image error—object principal axis reflections, objectsecondary-axis reflections, extrinsic vertical axis reflec-tions, extrinsic horizontal axis reflections—while at thesame time providing a unified interpretation for the variouserror types. According to COR, all forms of mirror reflectionarise from the same underlying orientation representa-tions, and more specifically from failures affecting polar-ity-correspondence components of these representations,but the different forms of reflection error are distinguishedby the particular polarity-correspondence componentimplicated in the error. For example, object principal axisreflections (OPA errors) are attributed to failures affectingthe polarity correspondence between an object secondaryaxis and an extrinsic axis.

Third, in contrast to reduction coding accounts the CORhypothesis need not posit multiple forms of representationto account for above-chance performance on orientationdistinctions giving rise to confusion. For example, our par-ticipants’ above-chance performance on the distinction be-tween a target and its object principal axis (OPA) reflectionis straightforwardly interpreted by assuming that theparticipants were often accurate in representing and pro-cessing the polarity correspondence between an object sec-ondary axis and the corresponding extrinsic axis. Thisinterpretation is perfectly consistent with the assumptionthat the observed OPA errors resulted from occasionalfailures affecting the same polarity-correspondencecomponent.

The COR hypothesis does not by itself offer specific pre-dictions about which forms of mirror-image error will bemost frequent. However, the hypothesis does provide afoundation for developing interpretations and predictions.For example, we suggested that OPA errors were more fre-quent than OSA errors in Experiments 1–2 because formost of our stimulus objects the sides of the secondary ob-ject axis were less distinctively different than the sides ofthe principal object axis, leading participants to flip thesecondary axis (OPA errors) more often than the principalaxis (OSA errors). COR allows us to ground this non-dis-tinctiveness interpretation in assumptions about underly-ing representations, by proposing that the lack ofdistinctive differences between the sides of secondary ob-ject axes led to difficulty in encoding or retaining polaritycorrespondences between secondary object axes andextrinsic axes.

This discussion suggests a prediction about left–rightmirror reflections (extrinsic vertical axis reflections).According to COR, left–right reflections result from failuresin encoding, retaining, or processing the polarity corre-spondence between the horizontal axes of two extrinsicreference frames. In our experiments left–right reflections(EVA errors) may have been rare because the left and rightsides of extrinsic horizontal axes were, for our normaladult participants, sufficiently distinct to prevent confu-


sion. Individuals for whom left and right are less clearlydifferentiated (e.g., young children) may be more proneto left–right mirror-image confusions. A more general pre-diction is that any variable affecting perception of, atten-tion to, or memory for, the differences between the sidesof an axis (e.g., salience of differentiating features, task rel-evance of the axis) will affect the likelihood of polarity cor-respondence errors involving that axis, and hence thelikelihood of the mirror reflections that result from theseerrors.

9. Levels of representation

Two questions we have not yet discussed concern thelevel(s) of representation giving rise to the orientation er-rors in our experiments. First, was performance in ourtasks mediated by visual representations, or by some otherform of representation? Our results are unlikely to havearisen from verbal coding of stimulus orientation. Experi-ment 2b used an incidental learning procedure in whichparticipants were unaware they would be tested on stimu-lus orientation, and hence had no motivation to encode ori-entations verbally. Also, in Experiment 1b generation andretention of verbal descriptions would probably have beendifficult, because participants were required to remembera 7-digit number while they performed the object orienta-tion task. Nevertheless, the error patterns in Experiments2b and 1b were consistent with those from the otherexperiments. Most probably, then, performance in all ofour experiments was mediated by visual orientation repre-sentations. However, another possibility is that object-ori-entation representations are multi-modal or amodal, suchthat representations of the same form are constructed fromboth visual and non-visual (e.g., tactile) stimuli, and mayinclude both visual and non-visual features. Experimentsexploring patterns of orientation errors with tactile stimulimight shed light on the issue.

The second levels-of-representation question concernsextrinsic reference frames: What specific extrinsic framesmediated performance in our tasks? Participants couldhave represented the orientations of the stimulus objectsby mapping object-centered frames onto egocentric frames(e.g., a body-based frame) and/or environmental frames(e.g., a frame based on the display screen). Experimentsthat dissociate potential extrinsic frames (e.g., by tiltingthe participant’s body) will be required to identify the rel-evant frames.

10. Implications for representation of orientation

Finally, we note that in addition to shedding light onmirror-image confusion our results suggest two generalconclusions about the representation of object orientation.The first is that object-orientation representations arecompositional—that is, the representations are composedof multiple components, each of which represents a differ-ent aspect of an object’s orientation (e.g., polarity corre-spondences between object and extrinsic axes, directionand magnitude of tilt between object and extrinsic axes).This conclusion follows from the systematic error patterns

observed in our experiments: Some types of error occurredmuch more frequently than others, and each of the com-mon error types (object principal axis reflections, objectsecondary-axis reflections, 45� rotations) could be attrib-uted to failures affecting a single specific representationalcomponent. We do not suggest that our results unequivo-cally support the specific COR assumptions about the com-ponents of orientation representations. We do assert,however, that any adequate account of object-orientationrepresentation will need to posit some form of composi-tional representation.

The second conclusion is that object-centered frames ofreference play an integral role in representation of objectorientation. This conclusion is suggested by the high ratesof object-axis reflections observed in our experiments. Aswe have seen, these errors can be interpreted straightfor-wardly given the COR assumption that orientation repre-sentations map an object-centered reference frame ontoan extrinsic frame. Conceivably, our results could be ex-plained without appeal to object-centered representations.At the least, however, the role of object-centered frames inorientation representation merits further investigation.

Acknowledgements

This work was supported by a NSF IGERT grant. Wethank Allison Leung, Eric Gou, Samantha Engel, BradleyBerk, Louisa Conklin, Jenna Rowen and Shaan Khurshidfor their help in collecting, coding and analyzing data.We also thank Daniel Dilks for helpful comments on themanuscript.

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Mirror-image confusions: Implications for representation and processing of object orientation

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