psychology paper

Copyright 1997 Psychonomic Society, Inc. 102

When people give directions or decide what route to take from one place to another, they often rely on memories of the locations of objects in the environment. To under- stand how these and other spatial problems are solved, we must understand how information about location is mentally represented. More specifically, we need to under- stand what frames of reference are used to encode loca- tion. Just as parallels of latitude and meridians of longitude provide a language for specifying locations on the earth, we need to discern what language is used in memory to specify where objects are located in the environment.

Memory for location could be encoded with respect to frames of reference that depend on the observer’s point of view (e.g., retinal coordinates) or frames of reference that do not depend on the observer’s point of view (e.g., scene-centered coordinates). In a viewpoint-dependent representation, familiar views should be more accessible than novel views, whereas in a viewpoint-independent representation, familiar and novel views should be equally accessible (Tarr, 1995).

An effective method of measuring the accessibility of spatial memories is to have observers make judgments of relative direction on the basis of their memories of a spa- tial layout (see, e.g., Levine, Jankovic, & Palij, 1982). For example, examine Figure 1 (with “viewing position a” at the bottom), and then make the following judgments of relative direction without looking at the figure: (1) Point to the shoe as if standing at the jar, facing the clock. (2) Point to the clock as if standing at the jar, facing the

book. The imagined heading in the f irst judgment is aligned with the viewing perspective, and hence is “fa- miliar,” whereas the imagined heading in the second judg- ment is not aligned with the viewing perspective, and hence it is “novel.”1 Judgments of the first kind are typi- cally easier than judgments of the second kind (e.g., Levine et al., 1982; Presson & Hazelrigg, 1984). The difference in difficulty indicates that the underlying mental representa- tion is viewpoint dependent. If the mental representation of Figure 1 were viewpoint independent, both of these judg- ments would be equally easy; the familiar perspective (1) and the novel perspective (2) would be equally accessible.

The viewpoint dependence of spatial memories has been well established for small spaces such as maps (e.g., Evans & Pezdek, 1980; Levine et al., 1982; Presson & Hazelrigg, 1984; Thorndyke & Hayes-Roth, 1982), and more recently for large spaces when observers are limited to a single view of the space (e.g., Presson & Montello, 1994; Rieser, 1989; Roskos-Ewoldsen, McNamara, Shel- ton, & Carr, in press). However, there are situations in which memories of large spaces seem to be viewpoint in- dependent (e.g., Evans & Pezdek, 1980; Presson, DeLange, & Hazelrigg, 1989; Thorndyke & Hayes-Roth, 1982). The findings of such studies raise questions about when spa- tial memories appear to be viewpoint dependent and when they appear to be viewpoint independent.

Similar issues have arisen in investigations of visual object recognition. Recent studies indicate that mental rep- resentations of objects may consist of a collection of viewpoint-dependent representations (e.g., Edelman & Bülthoff, 1992; Tarr, 1995; Tarr & Pinker, 1989; but see Biederman & Gerhardstein, 1995). Each representation corresponds to a familiar view of the object. Judgments such as recognition and handedness are accomplished by matching the visual stimulus with the representations in memory. If there exists a viewpoint-dependent represen- tation that corresponds to the orientation of the stimulus, recognition is fast and accurate. If no such representation exists, a normalization procedure ensues to match the

The research reported in this paper was supported by National Sci- ence Foundation Grant SBR-9222002. We are grateful to Ted Payne for writing the experimental program, to Jeffery Franks for the use of his laboratory space, and to Kyle Cave and Jeffrey Schall for their com- ments on the research. We also thank Nancy Franklin, Arthur Glenberg, and an anonymous reviewer for their comments and suggestions on an earlier draft. Correspondence should be addressed to T. P. McNamara, Department of Psychology, 301 Wilson Hall, Vanderbilt University, Nashville, TN 37240 (e-mail: mcnamara@ctrvax.vanderbilt.edu).

Multiple views of spatial memory

AMY L. SHELTON and TIMOTHY P. MCNAMARA Vanderbilt University, Nashville, Tennessee

Recent evidence indicates that mental representations of large (i.e., navigable) spaces are viewpoint dependent when observers are restricted to a single view. The purpose of the present study was to de- termine whether two views of a space would produce a single viewpoint-independent representation or two viewpoint-dependent representations. Participants learned the locations of objects in a room from two viewpoints and then made judgments of relative direction from imagined headings either aligned or misaligned with the studied views. The results indicated that mental representations of large spaces were viewpoint dependent, and that two views of a spatial layout appeared to produce two viewpoint-dependent representations in memory. Imagined headings aligned with the study views were more accessible than were novel headings in terms of both speed and accuracy of pointing judgments.

Psychonomic Bulletin & Review 1997, 4 (1), 102-106

MULTIPLE VIEWS OF SPATIAL MEMORY 103

stimulus to the representation that is most similar in ori- entation; this normalization procedure leads to longer recognition times and more errors. The normalization pro- cess has been characterized as mental rotation of the un- familiar view to the familiar view (e.g., Tarr, 1995; Tarr & Pinker, 1989). Highly familiar objects can be recognized equally well from nearly any perspective because they have been experienced from nearly every perspective.

We hypothesized that similar processes may occur in spatial memory. Small spaces or maps are generally learned from a small number of views, usually just one. Hence, they would be mentally represented in a single viewpoint-dependent representation. Large (i.e., naviga- ble) spaces, on the other hand, are generally learned by exploration and from many different perspectives. Mem- ories of large spaces may appear to be viewpoint inde- pendent because of the presence in memory of multiple views (e.g., Evans & Pezdek, 1980). Retrieving and using information about spatial relations relative to a novel view may require minimal transformation of an existing view in memory.

The present study is a first step in the attempt to un- ravel the role of multiple views in spatial memory. Ob- servers learned the locations of objects in a room from two views and subsequently made judgments of relative direction from several imagined headings. We hypothe- sized that two views would produce two viewpoint- dependent representations in memory. Imagined head- ings corresponding to the learned views should therefore show an advantage over all novel imagined headings.

Although several previous investigations have allowed the participants to experience a space from more than one orientation (e.g., Hintzman, O’Dell, & Arndt, 1981; Presson, DeLange, & Hazelrigg, 1987), various features of these studies have precluded a clear answer to the question posed in this paper. To our knowledge, the pres- ent experiment is the first in which observers learned a large (i.e., navigable) spatial layout by sight, but were limited to a small number of well-specified views.

METHOD

Subjects Twenty-four students (16 undergraduate, 8 graduate) consented to

participate in return for extra credit and/or research experience. Half the subjects were male and half were female.

Materials and Design Two configurations of seven objects each were constructed. The ob-

jects were common, visually distinct, had monosyllabic names, and shared no primary semantic associations (e.g., a book, a lamp, etc.). Ob- jects were placed on a 3 � 3 m clear plastic sheet in one half of a large room. Two viewing positions differing by 90º were selected and kept constant across the two configurations. Orthogonal views were chosen to maximize the unique information afforded by each view.

Each test trial was constructed from three objects in the display and required subjects to point to an object as if standing in a particular po- sition within the display; for example, “Imagine you are standing at the jar and facing the shoe. Point to the clock.” Two of the objects estab- lished the imagined station point and heading (e.g., jar and shoe), and the third object was the target (e.g., clock). Although these judgments may involve imagined translations (e.g., from the actual viewing posi- tion to the imagined station point), the effects of these translations would be very small compared with the effects of imagined rotation (e.g., Easton & Sholl, 1995; Rieser, 1989) and were not examined.

The principal independent variable was imagined heading. Eight equally spaced headings were used. To facilitate exposition, headings were arbitrarily labeled counterclockwise from 0º to 315º in 45º steps beginning with viewing position a (Figure 1). For example, 0º corre- sponds to all headings aligned with viewing position a (e.g., book– wood; jar– clock); 90º corresponds to all headings aligned with viewing position b (e.g., jar–book; clock–wood); and 270º corresponds to all headings contra-aligned with viewing position b (e.g., book–jar; wood– clock). Each configuration yielded 24 object-pair headings, three in- stances of each of the eight imagined headings. Each object-pair heading was used with three different targets for 72 trials, 9 at each imagined heading.

Pointing direction (the direction of the target object relative to the heading) was varied systematically by dividing the space into six areas, front-right (0º–60º), right (60º–120º), back-right (120º–180º), and so on. Subjects experienced approximately equal instances of each point- ing direction with at least one instance of each direction at every imag- ined heading.

Procedure All subjects learned and were subsequently tested on one of the two

configurations. The factorial combination of configuration and order of viewing (a–b vs. b –a) produced four groups of subjects. Subjects were randomly assigned to groups with the constraint that each group contain an equal number of males and females.

Learning phase. Each subject was instructed to learn the objects and their locations for a spatial memory test, and then was blindfolded and led to a viewing position (viewing position a or b in Figure 1). The sub- ject viewed the display for 30 sec, and then was required to close his or her eyes and to point to and name each object. This study–test sequence was repeated until subjects could point to and name all the objects cor- rectly two times in a row. Subjects were then blindfolded and walked di- rectly to the second viewing position. The study–test sequence was re- peated at the second viewing position. Before moving from a particular viewing position, subjects were offered additional viewing time, and most chose to view the display for 5–10 additional seconds at each po- sition. All subjects were highly familiar with the locations of the ob- jects at the end of the learning phase.

Test phase. After learning the spatial layout, subjects were taken to another room to be tested. The test trials were presented on a Macintosh computer. Subjects first received instructions on using the program and four practice trials involving locations on the campus. Each test trial was initiated by the subject and proceeded as follows: The heading was printed at the top of the screen (e.g., “Imagine you are standing at the

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Viewing Position a

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Figure 1. One of the spatial layouts used in the experiment.

104 SHELTON AND MCNAMARA

jar and facing the shoe.”). The subject clicked the mouse to indicate when he/she had adopted the heading. The name of the target object was then displayed (e.g., “Point to the clock”), along with a circle and a mov- able line. The subject used the mouse to position the line on the circle to represent the direction the target would be if the subject were in the imagined position. This circle-and-line display simulated the hand-held dials used in previous studies (e.g., Rieser, 1989).

RESULTS

Although each trial provided three measures, only two will be reported: pointing accuracy (the absolute angu- lar difference between the actual and the judged direc- tion of the target) and pointing latency (the time from the appearance of the target to the pointing response).2 These dependent variables were analyzed separately using split- plot factorial analyses of variance (ANOVAs) with terms for group, sex, imagined heading, and pointing direction. Because of the large number of main effects and inter- actions, an alpha level of .01 was used. Only statistically reliable effects are discussed. Error bars in all figures are ±1 SEM as estimated from the appropriate ANOVA.

The effect of imagined heading was signif icant for both pointing accuracy [F(7,112) � 15.87], and pointing latency [F(7,112) � 7.91]. As Figure 2 indicates, imagined headings aligned with the two familiar views (0º and 90º) show signif icantly lower angular errors [F(1,112) � 98.78] and shorter latencies [F(1,112) � 36.26] than all

other imagined headings. Mean angular errors for familiar and novel headings were 18.8º and 33.3º, respectively, and mean response latencies for familiar and novel head- ings were 16.8 and 22.7 sec, respectively. Pairwise com- parisons indicated that the two familiar views did not dif- fer (ts < 1). Pointing judgments from the imagined heading of 45º (which is between the two study views) were faster than judgments from 315º or 135º [F(1,112) � 8.87], but not more accurate [F(1,112) � 1.87].

The main effect of pointing direction was also signif- icant for both accuracy [F(5,80) � 12.34] and latency [F(5,80) � 4.25]. For accuracy (Figure 3a), the mean an- gular errors increased as pointing direction varied from in front of the subject to behind the subject. Contrasts re- vealed that front (FR and FL) was more accurate than back (BR and BL) and sides (R and L), and that sides were more accurate than back. For latencies (Figure 3b), the trend was much less pronounced. Front directions were faster than back and marginally faster than sides, but sides and back were not significantly different. The effects of pointing direction on accuracy and latency are broadly consistent with other investigations of how ob- servers parse surrounding space into regions (e.g., Frank- lin, Henkel, & Zangas, 1995).

In accuracy, but not latency, pointing direction inter- acted with imagined heading [F(35,560) � 3.36]. This interaction did not compromise any of the conclusions reached from the omnibus effect of imagined heading (Figure 2a). In particular, angular error for all pointing directions was lower for imagined headings of 0º and 90º (the studied views) than for other headings. The inter- action revealed that pointing judgments to the left or to the right were easier when they were made toward or away from a study view than when they were made in other directions. This effect accounts for most of the sav- ings in angular error in Figure 2a for headings of 180º and 270º.

DISCUSSION

These results suggest that mental representations of large (i.e., navi- gable) spaces are viewpoint dependent, and that two views of a spatial layout produce two viewpoint-dependent representations in memory. Imagined headings aligned with the study views were easier to retrieve (as assessed by accuracy and latency) than were novel headings.

It is instructive to compare the results of the present study with the results of an experiment in which subjects received only one view of the space (Roskos-Ewoldsen et al., in press, Experiment 2). These two experiments used the same spatial layouts and very similar procedures. The difference in mean angular error between familiar and novel head- ings was 14.5º in the present study and 11.8º in the single-view study. Similarly, the difference in mean response latency was 5.9 sec in the present study and 5.5 sec in the single-view study. If multiple views of a space had resulted in generalization across novel headings, we would have expected the differences to decrease when we added a second study view. On the contrary, the difference between familiar and novel headings when subjects saw two views of the layout was as large as, if not larger than, the difference when subjects learned a single view. These data indicate that an additional view did not lead to the formation of a viewpoint-independent representation in memory.

To retrieve information about a novel heading, subjects must have transformed an existing representation in memory. An obvious candi- date for this transformation is mental rotation (Shepard & Cooper,

Figure 2. (a) Mean angular error and (b) latency of pointing judgments as a function of imagined heading (± SEM ).

MULTIPLE VIEWS OF SPATIAL MEMORY 105

1982). In fact, most subjects reported after the experiment that they tried to imagine either rotating the configuration of objects or rotating themselves in the configuration. When the data from imagined headings were collapsed according to the angular distance to the nearest study view, the rate of rotation as indexed by the slope of the best fitting lin- ear function was about 14º/sec. This rate is well within the limits pro- posed in previous work on mental rotation (e.g., Shepard & Hurwitz, 1984; Shepard & Metzler, 1971) and indeed is on the slow side.

The speeded performance at 45º compared with that at all other novel headings suggests that this heading was more accessible (Figure 2b). There are at least two plausible explanations of this savings in perfor- mance. First, when people were moved between the two viewpoints dur- ing the learning phase, they might have updated the locations of the ob- jects relative to themselves. Given that the 45º heading was aligned with a perspective that would be available during movement, there might have been improved speed as a result of having locomoted through that region of the space (we emphasize, however, that subjects were blind- folded while they were moved and never experienced the space between 0º and 90º visually). This explanation is consistent with data on real versus imagined locomotion. Rieser (1989; see also, Presson & Mon- tello, 1994) showed that judgments of relative direction were easy to make from novel imagined headings if observers were allowed to rotate their bodies before making the judgment.

A second explanation of the savings in response latency at headings of 45º follows from recent research on visual object recognition. Bülthoff and Edelman (1992) and Tarr (1995), for example, have found that a novel view of an object “between” two closely spaced study views (referred to as “interpolation”) may be recognized as easily as the study views, whereas the difficulty of recognizing a novel view that is “be-

yond” two study views (referred to as “extrapolation”) is an increasing function of the angular distance to the nearest study view. In our exper- iment, an imagined heading of 45º corresponds to interpolation because it is between the study views of 0º and 90º. The mechanisms that give rise to these effects in object recognition are not well understood. How- ever, these effects are predicted by viewpoint-dependent models of ob- ject recognition (e.g., Poggio & Girosi, 1990), and hence do not indicate that viewpoint-independent representations were being formed.

The present experiment cannot distinguish between these two alter- native explanations of the speeded performance on imagined headings of 45º. This finding, however, does not compromise the conclusion that two viewpoint-dependent representations were formed in memory.

If multiple views of a spatial layout are represented in memory, then with a sufficient number of views, memory for a space might appear to be viewpoint independent (see, e.g., Evans & Pezdek, 1980; Thorndyke & Hayes-Roth, 1982). It is natural to ask, however, whether a small number of additional views, beyond just two, would produce a viewpoint- independent representation in memory. Several lines of evidence sug- gest that the answer to this question is “no.” The existence of binocular stereo demonstrates that the visual system can reconstruct much of the spatial structure of the world from two views (viz., the two eyes), and Koenderink and van Doorn (1991) have proven that the affine structure of a spatial array can be reconstructed from two views alone. In general, additional views in excess of two do not facilitate the perception of geo- metric structure. More direct evidence can be found in an experiment reported by Diwadkar and McNamara (in press). Observers saw a col- lection of objects from a single view and then learned to recognize the scene from this study view and three additional “training” views (pre- sented as digitized images). Recognition performance indicated that all four familiar views were represented in memory, and that novel views were recognized by normalization to the nearest study or training view. Fi- nally, comparison of the results of the single-view and the two-view ex- periments (discussed above) indicates that an additional view of a spa- tial layout does not facilitate the retrieval of information about novel views. Collectively, these observations suggest that a small number of additional views of a space would not produce a viewpoint-independent representation of the space.

The parallels between our results and those obtained in recent in- vestigations of visual object recognition are striking (e.g., Edelman & Bülthoff, 1992; Tarr, 1995). In both domains, spatial relations are encoded with respect to reference frames that depend on point of view. Multiple views of a scene or an object appear to produce multiple viewpoint- dependent representations in memory, not a single viewpoint-independent representation. Apparently, interobject and intraobject spatial relations are represented and processed in similar ways by the human brain.

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Figure 3. (a) Mean angular error and (b) latency of pointing judgments (± SEM ) as a function of pointing direction: FR, front-right; R, right; BR, back-right; BL, back-left; L, left; and FL, front-left.

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NOTES

1. These judgments also require that an equivalence be established between “up–down” and “forward–backward.” Apparently this trans- formation is natural and effortless, because people have no difficulty with it.

2. We also measured the time from trial onset until the subject clicked the mouse indicating the adoption of a heading. An analysis of variance revealed no significant effects or interactions for this measure. Appar- ently, subjects did not adopt a heading until the target object was also present.

(Manuscript received February 26, 1996; revision accepted for publication June 18, 1996.)