Isovist analysis captures properties of space relevant for ... · level of single buildings, O’Neill ... Isovist analysis captures properties of space relevant for locomotion and

1 IntroductionSpatial properties of architecture as well as of open environments influence subjectiveexperience and spatial behaviour. Several theories, mainly originating from environ-mental psychology, see human behaviour and experience in close interdependence withthe spatial structure of environments. For example, evolution-based theories of environ-mental preferences such as `prospect and refuge' (Appleton 1988) or the framework ofKaplan (1987) suggest that preference patterns for certain environmental features orconfigurations originate from their earlier advantages for survival. While nowadaystheir relevance for humans may not be at first glance apparent, they may still appearas mean trends in preference ratings (Balling and Falk 1982; Kaplan 1992).

Also, systematic relations between various features of space and human navigationbehaviour have been demonstrated in several studies. On a large-scale level, for example,Wiener and Mallot (2003) have revealed an influence of environmental regions onhuman navigation and route planning behaviour (see also Wiener et al 2004). On thelevel of single buildings, O'Neill (1992) found that way-finding performance decreasedwith increasing plan complexity. At the level of single places, Janzen et al (2000)investigated the influence of the shape of intersections within an environment on way-finding performance. When navigating oblique-angled intersections, subjects' error ratedepended on which branch they entered (see also Janzen et al 2001).

While the initial statement is therefore strongly corroborated by a multitude of singlefindings, a direct comparison of empirical studies is often difficult, and also individualtheories have not yet been integrated into a more general predictive or explanatorymodel of spatial behaviour. One main reason for this seems to be that most studiesand theories in the field of spatial cognition have made use of qualitative descriptionsof a few specific environmental features, which can be ascribed to the lack of a com-prehensive formalised description system for environmental properties. In order to beuseful for this purpose, such a description system has to fulfill the following requirements.

Isovist analysis captures properties of space relevantfor locomotion and experience

Perception, 2007, volume 36, pages 1066 ^ 1083

Jan M Wienerô#Á, Gerald Franz½Á, Nicole Rossmanith½, Andreas Reichelt½,Hanspeter A Mallotô, Heinrich H Bu« lthoff½ôCognitive Neuroscience, Department of Zoology, University of Tu« bingen, D 72076 Tu« bingen, Germany;e-mail: [email protected]; ½Max Planck Institute for Biological Cybernetics,Spemannstrasse 38, D 72076 Tu« bingen, Germany; e-mail: [email protected],[email protected]; #Current address: CNRS, Colle© ge de France, Laboratoire dePhysiologie de la Perception et de l'Action, F 75005 Paris, France; e-mail: [email protected] 6 March 2006, in revised form 3 November 2006; published online 29 June 2007

Abstract. In a series of exploratory experiments we investigated interrelations between structureand shape of architectural indoor spaces on the one hand, and affective experience and naviga-tion behaviour on the other hand. For this, isovist-based descriptions of 16 virtual indoor sceneswere correlated with behavioural data from the experimental tasks. For all tasksötwo activenavigation tasks and an introspective appraisal of experiential qualitiesöstrong correlationsbetween subjects' behaviour and a small set of quantitative measurands derived from the isovistswere found. The outcomes suggest that isovist analysis captures behaviourally relevant propertiesof space and is therefore a promising general means for predicting central experiential qualities ofarchitecture and navigation behaviour.

DOI:10.1068/p5587

Á Jan Wiener and Gerald Franz contributed equally to this work.

First, it has to provide quantitative comparability between arbitrarily shaped environ-ments. Second, the criteria for building up the model should be objectively definable.In addition to these formal requirements, the descriptive system has to capturea major share of biologically and psychologically relevant properties of the analysedenvironment.

In the following section, several approaches for describing spatial properties ofenvironments are briefly reviewed. In accordance with the criteria outlined above, threeexperiments were performed to test an isovist-based description system combining localspatial information with global graph structures for its ability to capture behaviourallyrelevant properties of environments at the scale level of architectural indoor spaces.The results support the general potential of the chosen approach.

2 BackgroundSeveral disciplines already offer systems and models for describing aspects of spatialenvironments in a formalised manner. In architectural construction, for example, build-ings are specified by a combination of lists of structural elements (walls, windows,columns, etc) and scale plans. While the quantitative description of individual architec-tural elements is well elaborated and standardised, the geometrical and topologicalstructure is normally represented graphically, and therefore cannot be quantitativelycompared. In response to these shortcomings, compositional approaches (eg Krier 1989;Ching 1996; Leyton 2001) have been developed in architectural theory and designpractice that define more or less formal languages consisting of geometric primitivesand basic operations. Here, the idea is to generate arbitrarily complex forms andstructures by applying sequences of transformations on these primitives. The mathemat-ically most formal directions have been called shape grammars (Stiny and Gips 1972)that suggest close relations between structural logic of a description and architecturalquality. While the methods mentioned above have been successfully applied as guide-lines in exploratory design phases and may analytically allow retracing the steps ofthe genesis of shapes from the plan view perspective of the designers, they turned outnot to be ideal for purely comparative analyses of the final shape, since a reversedecomposition into geometric primitives and operations is often ambiguous and dis-regards the experience of an inside observer.

Phenomenology provides an alternative approach, concentrating particularly on theintrospective experience of observers. In everyday language, non-trivial forms are oftencompared by using intermediate concepts such as complexity and regularity. In empiri-cal aesthetics these properties are termed collative variables that have been defined asassessment criteria of the structural properties of a stimulus array (cf Berlyne 1960,1972; Wohlwill 1976). Collative variables offer an intuitive common denominator forthe comparison of a wide range of objects and environments even across categoryboundaries. Unfortunately, this universal scope makes a strict formalisation or a genericimplementation of these comprehensive concepts very difficult, but at least partialrelations between collative variables and physical properties could be established.

In spatial cognition and artificial-intelligence, environments are often describedwith graph abstractions. Graphs serve as models of the mental representation ofenvironments, allowing the derivation of testable working hypotheses for the structure,format, and content of spatial memory. Furthermore, graphs have been used todescribe environments by the set of possible movement actions (Scho« lkopf and Mallot1995). In cognitive science, the most commonly used graph is probably the place graph,in which nodes correspond to single places or positions within an environment, and edgesdescribe the connectivity between nodes (eg Kuipers 1978; Leiser and Zilbershatz 1989;Chown et al 1995). In their most basic form, place graphs are parsimonious and purelytopological representations of space, in which nodes carry the local position information

Isovists predict spatial experience and behaviour 1067

necessary for identifying the corresponding place. Edges contain local navigation rules,such as `turn left' or `follow the road', that allow navigating between nodes. Metricalinformation, such as distance and direction, may be additionally provided.

Originating from a purely analytical and descriptive perspective on architecture,the technique of space syntax has been developed (Hillier and Hanson 1984; Hillier1998). Space syntax is a set of technologies for the analysis of spatial configurations,also using simple graphs solely consisting of paths and nodes. This analytical reduc-tion of space to mere topological mathematical information facilitates calculation ofcharacteristic values that can be interpreted, for instance, as connectivity, centrality,or control level, and thus directly compared. The central aim of space syntax hasalways been the identification of variables that determine the social meaning andbehaviourally relevant aspects of architectural spaces. Original space syntax has beendeveloped to analyse large-scale spatial configurations from the room layout of buildingcomplexes to whole cities. Hence, spatial properties of environments smaller than roomswere not adequately represented. For analysing spatial characteristics of smaller environ-ments, Benedikt (1979) proposed isovists as objectively determinable basic elements.Isovists capture local spatial properties by describing the visible area from a givenobservation point with the use of viewshed polygons. In order to better describe thespatial and configurational characteristics of an environment as a whole, Turner et al(2001) have proposed the technique of visibility graph analysis that combines globalspace syntax graphs and local isovist visibility information. This technique offersfurther second-order measures for example on visual stability that may be relevantfor locomotion and navigation. A more detailed description of isovist analysis andvisibility graph techniques as considered in this study is given in section 4.3.

The relevance of isovists and visibility graphs, originally derived from abstractspatial analysis, was rather weakly backed by psychophysical empirical findings (foran early empirical study see Benedikt and Burnham 1985). However, isovists describespatial properties from an inside beholder-centred perceptual perspective, and visibilitygraphs share many characteristics of models of spatial memory from cognitive science(cf Franz et al 2005). Indeed, there is direct empirical evidence that these techniquescapture environmental properties of space that are useful as predictors for spatialbehaviour and experience. For example, case studies on spatial behaviour in the TateGallery (Turner and Penn 1999) have revealed high correlations between visibilitygraph measures and the statistical dispersal of visitors. Furthermore, in a recent studyFranz et al (2005) compared experiential qualities of arbitrarily shaped architecturalspaces with isovist measures. They found that already a few isovist measures describingvisual characteristics from the observation points were quite sufficient to explain thevariance in the affective appraisals of the environments. Nevertheless, elementarystudies testing the perceptibility of isovists or correlating isovist measures with naviga-tion behaviour at the level of trajectories are still missing

3 ObjectivesThe overall aim of this study was to explore the suitability of isovist graphs as genericdescription systems capturing behaviourally relevant properties of spatial form andconfigurations at the scale level of architectural indoor spaces. In order to identifypromising generic spatial descriptors, the experiments presented here were thereforedesigned to compare variables derived from isovists and visibility graphs with bothspatial experience and behaviour. Furthermore, our study allowed insights into per-ceptual and cognitive processes underlying the statistically observable behaviouralpatterns. As a first step, we tested the perceptibility of isovists as well as relationsbetween isovist measures and exploration behaviour at the level of trajectories. Forthese purposes, a set of 16 virtual indoor scenes was designed. In active navigation

1068 J M Wiener, G Franz, N Rossmanith, and coauthors

tasks, subjects were asked to navigate to positions that either maximised or minimisedthe visible area. The performance of subjects in finding these positions, as well as thepaths they took to reach them, ie their trajectories, were recorded. By semantic differentialratings, appraisals of the experiential qualities of the scenes were queried. We tested forcorrelations between characteristic values derived from the isovists and behavioural dataconsisting of ratings, performance measures, and trajectory descriptions.

4 General material and methods4.1 Experimental setupThe experiments were designed by making use of a virtual-reality (VR) experimentalparadigm. VR simulations combine flexibility, controlled laboratory conditions, and agood degree of perceptual realism (Bu« lthoff and van Veen 2001), and therefore allowa systematic variation of spatial properties of the simulated environments. The virtualscenes were created with the modeling software Autodesk ADT and 3ds max (discreet).A detailed description of the virtual environments is given below. In a pilot stagewe tested a 1808 semicylindrical projection system, a large flat back-projection system,and a desktop VR setup for their suitability for conducting the experiments. The twolarge-scale projection systems used earlier caused strong motion or simulator sicknessin a majority of the pilot subjects; some of these responded with strange motionpatterns in order to avoid the unpleasant visual experience. Therefore, the experi-ments in this study made use of a conventional desktop VR setup which allowed allparticipants to complete the experimental tasks and to intuitively interact with thesimulated environments. The visual scenery was displayed with a simulated field ofview of 90 deg673 deg. Subjects were seated in front of a 21 inch standard CRTscreen at a distance of approximately 50 cm, resulting in a physical field of view of�32 deg624 deg. A customary joypad was used as the interaction device. The visualscenery was rendered in real time on standard PCs (1.0 GHz Pentium III, nVidiaGeForce 2 GTS graphics cards) running a C�� simulation software that was designedand programmed especially for psychophysical VR experiments (Franz and Weyel 2005).

4.2 The virtual environmentsThe study was based on a set of 16 virtual indoor scenes that was derived from stimuliused by Franz et al (2004). The scenes represented diverse spatial situations within afictional art gallery; they were derived from simple rectangular rooms by varying thenumber of alcoves and connections to adjacent spaces. The floor plans of these indoorscenes are displayed in figure 1. The walls of the indoor scenes were repetitively drapedwith unobtrusive similar paintings (46 portraits of Picasso's blue-and-pink period) tostrengthen the art-gallery character. Other surface properties as well as the lighting andillumination levels were constant in all scenes (see figure 2 for examples of screenshots).Note that, in contrast to Franz et al (2004), a technically different lighting model(ambient-occlusion-based per-vertex lighting) was used in order to make the stimulireal-time-capable.

4.3 Formal description of the environmentsIn order to relate subjects' experience and behaviour to the shape and structure of thecorresponding spaces, a generic formal description of the virtual indoor scenes wasrequired. For this purpose, isovist analysis appeared to offer a suitable level of detailand abstraction, since it translates perceptual and spatial properties of architectural spaceinto simple polygons (see figure 3). From the isovist polygons, several basic geometricdescriptors can be derived such as area, perimeter length, number of vertices, lengthof open or closed edges. These basic measures can be combined to generate furtherintegrated values.


1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Figure 1. Floor plans of the 16 virtual indoor scenes used in the experiments. The indices areused in the text in order to refer to the individual environment. The dot in the centre of eachroom marks the starting position for the experimental tasks.

Figure 2. Three screen shots of the virtual indoor scenes as experienced by the subjects. This andfigures 3, 7, and 8 can be seen in colour on the Perception website at http://www.perceptionweb.com/misc/p5587/.

(a) (b) (c)

area

perimeter

open edge

closed edge

vertices

observationpoint

Figure 3. Generating isovists. (a) A hypothetical indoor environment; (b) the gray area is visible fromthe person's observation point within the environment; (c) the resulting isovist and its basic measures.


http://www.perceptionweb.com/misc/p5587/

http://www.perceptionweb.com/misc/p5587/

Isovists basically describe local physical properties of spaces with respect toindividual observation points. The technique of visibility graph analysis as developedby Turner et al (2001) overcomes this limitation by encoding the intervisibility of multi-ple observation points distributed regularly over the whole environment. This techniqueallows an integrative consideration of regional or global properties and makes thecomputational analysis more efficient. Typical visibility graph measures are, for instance,neighbourhood size (ie the number of directly connected graph vertices, correspondingto isovist area) and clustering coefficient (ie the relative intervisibility within a neigh-bourhood).

For the analysis in this study, a technical approach similar to visibility graphs wasused to approximate isovists: the 16 virtual indoor scenes were analysed by calculatingisovist measures and visibility graphs on a 50 cm grid covering each environment.Since the applied correlation analysis required single characteristic values for eachscene and measure, the resulting values were averaged over each environment. A list ofthe isovist and visibility graph measures that were calculated for the 16 indoor environ-ments is given below. For the analysis, a special isovist analysis tool was used; the toolis free software and available at http://www.kyb.mpg.de/�gf/anavis.4.3.1 Isovist-derived measures in these studies. While it is possible to generate a virtu-ally infinite number of measures by combining basic isovist measures, in this studyinitially six measures (isovist area, number of vertices, jaggedness, openness, clusteringcoefficient, revelation) were selected to describe the simulated environments. This initialselection was on the one hand motivated by the aim to test typical measures fromthe isovist literature (cf Turner et al 2001), on the other hand they appeared promisingto represent the basic psychologically and behaviourally relevant spatial qualities:spaciousness (Joedicke 1985), openness/enclosure (recently, Stamps 2005), and complexity(classically, Berlyne 1972; Kaplan 1988b), as suggested by theories of architecture andenvironmental psychology. For a more detailed description of the mathematical and psycho-logical background of the measures, please refer to Franz and Wiener (2005).

A calculation of internal correlations revealed that, in the 16 virtual environmentsof this study, the mean jaggedness, openness, revelation, and clustering variables werehighly interdependent (r 2 4 0:81), implicating that magnitudes and directions of corre-lations between these measures and dependent variables would be widely identical.Therefore, in order to increase the statistical power of the analysis, the experimentalanalysis concentrated solely on the three most independent isovist measures: meanisovist area, number of vertices, and jaggedness:4.3.1.1 Isovist area. The area of the floor surface visible from a single observation point.Environments consisting of few large and open areas normally feature a higher meanisovist area as compared to environments consisting of small and confined spaces.4.3.1.2 Number of vertices. This is the number of vertices making up the outline of anisovist polygon; it captures the absolute number of features of environments such aswall segments or alcoves. It is therefore a measure for aspects of complexity.4.3.1.3 Jaggedness. The jaggedness of an isovist as an integrative measure is calculatedmathematically as the squared isovist perimeter divided by the isovist area. It describesthe concavity of an isovist polygon; its inverse has been sometimes described as thecompactness measure. Jaggedness is related to the density of features, and has beenshown to capture perceived complexity of polygon outlines and building silhouettes(Berlyne 1972; Stamps 2000). In this study, owing to the high level of intercorrelationsto the variables openness, clustering coefficient, and revelation, it also captured the relativedegree of enclosure and visual stability of the environments.


4.4 Statistical analysisAnalyses were done with the open-source software mathematics packages Octave(http://www.octave.org) and R (http://www.r-project.org). For all statistical analyses, therating data were treated as even-interval-scaled. Linear correlation coefficients r werecalculated with Pearson's product moment correlation; p values indicate the probabilityof the non-directional null hypothesis: p -values below 0.05 were treated as significantcorrelations (*), p-values below 0.01 as highly significant (**). Confidence intervals(95% CI), describing the likely range of the general population correlation coefficients,were obtained from a Fisher r-to-z transformation. The characterisation of effectsizes corresponds to the framework of Cohen (1988); their derivation from correlationcoefficients follows the recommendations of Hopkins (2000).

5 Experiment 15.1 ObjectiveIn accordance with the overall objective of investigating interrelations between spatialproperties and spatial behaviour, the purpose of the initial experiment was twofold:first, to test whether basic isovist properties can be perceived at all, and, second, toexplore correlations between mean isovist measures (see section 4.3) and behaviouraldata. The behavioural data were gained both from a navigation task and a ratingof experiential qualities in different virtual environments. We hypothesised that thedifferently shaped environments used in this experiment systematically influenced sub-jects' responses to both tasks. If the isovist measures captured behaviourally relevantproperties, significant correlations with the dependent variables were expected.

5.2 Method5.2.1 Experimental procedure. In each of the 16 indoor scenes (see section 4.2 and figure 1),subjects had to do a twofold navigation task followed by a semantic differential ratingof experiential qualities. Only after completing both experimental tasks, they proceededto the next indoor scene. The 16 indoor scenes were presented in a random order.A complete experimental session took about 40 min.

At the beginning of the active navigation task, subjects were placed at the fixedstarting position of the virtual indoor scene (see figure 1) facing a random direction.Subjects were then asked to navigate to the position within the scene that maximisedthe visible area (corresponding to maximal isovist area) as well as to the positionwithin the scene that minimised the visible area (corresponding to minimal isovistarea). Before the experiment, subjects were carefully instructed that their task was notto maximise or minimise the visible area with respect to a single gaze direction, butthe area revealed by a complete 3608 rotation. During the experiment, the positionthat maximised visible area was referred to with the catchphrase `best overview place'and the position that minimised visible area was referred to with the catchphrase`best hiding place'. Again, subjects were carefully instructed that best overview placeand best hiding place were just catchphrases and that their task was to maximise orminimise the visible area. The order in which subjects had to locate these two positionswas randomised for each room. Subjects were instructed to solve the task quickly andas accurately as possible. A chosen position was confirmed by pressing a button onthe joypad; only these final positions were recorded.

The second experimental task was a rating of the experiential qualities of the16 scenes by the common semantic differential-scaling technique. At the beginning ofeach trial, subjects were automatically moved back to the initial starting position(roughly the centre of the room: see figure 1), again facing a random direction. After abutton on the joypad was pressed, the ratings were collected in a random sequence.


The rating was performed by manipulating an analog slider on the input device. Inorder to provide visual feedback, a scale and the currently selected value were displayednear the lower border of the screen. During the rating task, subjects were allowed tomove freely through the environments.

5.2.2 Variables of interest. During the navigation task, subjects were asked to move tothe position that maximised the isovist area (best overview place) and to the positionthat minimised the isovist area (best hiding place). For each indoor scene, subjects'performance was evaluated by comparing the isovist area of the chosen positions withthe isovist areas of the positions with the actually highest and lowest values.

The virtual indoor scenes differed with respect to the size of the isovists at thepositions with the largest and smallest isovist areas. In order to compare performancebetween different environments, subjects' navigation data were normalised accordingto the range of isovist sizes occurring in the particular scene [see formula (1) andformula (2)]. This performance measure ranges from 0 to 1: if subjects showed perfectbehaviour with respect to finding the positions that maximised and minimised theisovist area, performance was 1.

Pmax�r� �Isub�r� ÿ Imin�r�Imax�r� ÿ Imin�r�

(1)

Pmin�r� � 1ÿ Isub�r� ÿ Imin�r�Imax�r� ÿ Imin�r�

(2)

with r � identity of virtual indoor scene; Pmax�r� � performance for finding the posi-tion with the highest control value for room r ; Pmin�r� � performance for finding theposition with the lowest control value for room r ; Isub�r� � size of isovist correspond-ing to subject's chosen position; Imin�r� � size of isovist corresponding to position withlowest control value for room r ; Imax�r� � size of isovist corresponding to positionwith highest control value.

The rating task comprised six core aspects of environmental experience representedby pairs of oppositional adjectives (cf table 1). Subjects could differentiate their apprais-als using a seven-step Likert-like scale. The rating categories were selected to representmajor dimensions of affective experience (pleasingness, beauty, and interestingness), aswell as denotative and collative properties that were expected to be potentially relevantfor the navigation task (experienced spaciousness, clarity, and complexity). For the corre-lation analysis, the rating results of each scene were averaged by category over all subjects.

5.2.3 Participants. Sixteen subjects (eight female) voluntarily participated in the exper-iment, they were paid 8 per hour. Subjects were mostly university students aged20 ^ 25 years.

Table 1. English translations and original terms of the rating categories used in the semanticdifferential. The experiments were conducted in German language.

Category English English German Germanlow extreme high extreme low extreme high extreme

Interestingness boring interesting langweilig interessantPleasingness unpleasant pleasant unangenehm angenehmBeauty ugly beautiful ha« sslich scho« nSpaciousness narrow spacious eng weitComplexity simple complex einfach komplexClarity unclear clear unu« bersichtlich u« bersichtlich


5.3 Results5.3.1 Navigation task. Overall, subjects showed a similar performance (P) in finding thepositions having the smallest and the largest isovist area (smallest isovist: P � 0:92 � 0:02;largest isovist: P � 0:90� 0:02, t-test: t15 � 0:96, p � 0:3). In some of the virtual indoorscenes subjects reached performance measures over 0.97. In scene 10 they reached 1.0for finding the best hiding place, which means that all subjects actually found theposition that minimised the visible area (cf figure 4).

While performance of female and male subjects did not differ with respect tofinding the best overview place (female: P � 0:88� 0:02, male: P � 0:91� 0:02, t-test:t14 � ÿ1:66, p � 0:12), male subjects showed better performance in finding the besthiding place than female subjects (female: P � 0:88� 0:03, male: P � 0:96� 0:02, t-test:t14 � ÿ3:96, p 5 0:01). The average navigation time of female and male subjects differedsignificantly (females: 41:45� 2:84 s, males: 23:67� 1:06 s, t-test: t14 � 4:15, p 5 0:001).

The sequence of the two navigation tasks (finding best overview place and findingbest hiding place) was randomised for each subject. Response times for the first andthe second trial were therefore analysed independently of the specific navigation task.On average, subjects needed 44:24� 3:78 s for the first trial and 20:39� 2:20 s for thesecond trial (t-test: t15 � 8:7, p 5 0:001). The response times between the navigationtasks did not significantly differ within the first and second trial.

5.3.2 Correlations between navigation performance and isovist measures. In both naviga-tion tasks, subjects' performance was strongly negatively correlated with the meanmeasures for jaggedness (finding best hiding place r � ÿ0:62, p � 0:01; finding bestoverview place r � ÿ0:87, p 5 0:001), corresponding to large effect sizes (see figure 5).

1.0

0.8

0.6

0.4

0.2

0.0

Perform

ance

(a) (b)

Figure 4. Subjects' average performance per scene. (a) Finding the position that minimises theisovist area (best hiding place); (b) finding the position that maximises the isovist area (bestoverview place). The error bars display �1 SEM.

1.0

0.5

0.0

ÿ0.5

ÿ1.0

Correlationcoefficient,

r

isovist area number of vertices jaggedness

HP OP HP OP HP OP

(a) (b) (c)

Figure 5. Correlation between sub-jects' performance finding the besthiding place (HP) and best over-view place (OP) on the one handand mean isovist measures on theother hand: area, jaggedness, andnumber of vertices.


In contrast to that, performance did not significantly correlate with the mean measuresfor isovist area (hiding r � ÿ0:03, p � 0:93; overview r � 0:24, p � 0:37) and onlymarginally with the number of isovist vertices (hiding r � ÿ0:45, p � 0:08; overviewr � ÿ0:49, p � 0:06), corresponding to trivial or at most moderate effects.

5.3.3 Rating task. Also, several strong correlations between single isovist measures andthe corresponding averaged ratings were found (see figure 6). Average isovist area washighly correlated with rated pleasingness (correlation coefficient r � 0:80, p 5 0:01),beauty (r � 0:65, p 5 0:01), and spaciousness (r � 0:74, p 5 0:01). Similarly large oreven very large effect sizes were found for the average number of isovist polygonvertices. This measure turned out to be strongly interrelated with experienced com-plexity (r � 0:81, p 5 0:01), interestingness (r � 0:78, p 5 0:01), and clarity (r � ÿ0:73,p 5 0:01). Additionally, several significant correlations to the isovist measure jaggednesswere found. Owing to the level of intercorrelation between this variable and the number ofvertices, however, jaggedness statistically did not explain further variance in the ratings.

5.3.4 Correlations between navigation performance and ratings. A comparison betweenrated experience and subjects' performance in the navigation tasks rendered an unevenresult for the two navigation tasks. For finding the best hiding place, no signifi-cant correlation with any rating dimension was found (explained variance r 2 5 0:11),corresponding to at most small effects. However, the environments in which subjectsperformed well in finding the best overview place were rated less interesting (r � ÿ0:63,p 5 0:01), less complex (r � ÿ0:54, p � 0:03), but clearer (r � 0:57, p � 0:02) andmore spacious (r � 0:58, p � 0:02) which could indicate large effects. Additionally, amoderate statistical relation between navigation performance and experienced pleasing-ness of the rooms was probable (r � 0:45, p � 0:08), although this result was notsignificant.

5.4 DiscussionIn each of the 16 virtual indoor scenes, subjects had the task of finding the bestoverview place and the best hiding place. Overall, they showed a remarkably goodperformance in both navigation tasks. It is interesting to briefly consider some of theperceptual and cognitive processes required to successfully master the tasks of findingthe positions within an environment that maximise and minimise the visible areawhen performing a 3608 turn. The VR setting used in this study restricted subjects'horizontal viewing field of view to 908 (as opposed to a little bit more than 1808 inreality). Thus, in order to assess the visible area from an arbitrary position within anenvironment, visuo-spatial information obtained from different viewing directions hadto be integrated, either by combining a series of visual snapshots or in the form of

isovist area number of vertices jaggedness1.0

0.0

ÿ1.0Correlationcoefficient,

r

pl be in co cl sp pl be in co cl sp pl be in co cl spRating category Rating category Rating category

Figure 6. Linear correlations between the selected isovist measures and averaged rated experientialqualities of the scenes in experiment 1. The rating categories were pleasingness (pl), beauty (be),interestingness (in), complexity (co), clarity (cl), and spaciousness (sp).


a more abstract representation. In any case, this integrated information had to bememorised in order to perform comparisons of the visible area at different positionswithin the environment. Furthermore, independently of the specific sequence in whichsubjects solved the two tasks, the first navigation trial took considerably longer thanthe second one. This result suggests that during the second trial, subjects relied alsoon knowledge acquired during the first trial. A possible line of argumentation is thatduring the first trial subjects remembered some quantitative measures describingthe visible area along their trajectories and that this information was reused during thesecond navigation trial. In our view, however, it appears more likely that, duringthe first trial, subjects explored the environment and either generated a spatial memoryof its shape or already memorised potential positions of the other extremum. Thismemory then allowed them to act faster in the second trial. All in all, subjects' highperformance levels demonstrate that they were able to perceive and process the visuo-spatial information that is described by the basic isovist area property very well.

The strong gender difference as regards navigation times might be hypotheticallyexplained by assuming different levels of familiarity between female and male partici-pants with interactive computer-simulated environments such as first-person computergames and with game controllers. The much smaller differences in task performance,however, suggest that this presumed factor was of minor importance for performingthe experimental task.

The basic initial hypothesis that isovists capture behaviourally relevant environ-mental properties was supported by the result that the isovist measure jaggedness wasstrongly negatively correlated with navigation performance. This outcome may be inter-preted as follows: studies on polygon outlines (Berlyne 1972) and building silhouettes(Stamps 2000) have shown that the jaggedness measure (ie polygon perimeter2=area)corresponds well to introspectively rated shape complexity. Pointing in the samedirection, the results of the rating tasks showed positive correlations between jagged-ness and rated complexity, and negative correlations between jaggedness and clarity.Taken together, jaggedness can be seen as a measure describing aspects of visualcomplexity such as information density. In a spatial context, jaggedness may addition-ally characterise configurational complexity, leading to an increased task difficulty,which may implicate a negative influence on navigation performance. Although thenegative correlation between navigation performance and the number of isovist verticesdid not reach statistical significance, it points in the same direction. The low levelof correlations to isovist area basically suggests that the measured behaviour is scale-independent.

The apparent statistical relations between the navigation task and the rating resultsmay, however, be also interpreted in a different way: since the navigation task alwayspreceded the ratings, the latter might have been influenced by the subjective experienceof the preceding task. For example, the rated complexity of an indoor scene maybasically mirror the effort or the subjectively perceived difficulty of the navigation taskswithin that scene. This interpretation gains some support by the moderate positivecorrelation between experienced pleasingness and navigation performance, althoughthis relation did not reach the chosen significance level of p � 0:05. In order to test thisalternative explanation, experiment 2 was conducted.

6 Experiment 26.1 ObjectiveThis experiment was designed as a control condition to discriminate between the alter-native explanations of experiment 1, namely that differences in the ratings either reflectdifferences of the environments or differences in the navigation experience.


For this purpose, solely the rating task of experiment 1 was repeated, the navigationtask was skipped, and the ratings were done from a fixed central observation point.Comparing the rating results of the two experiments allowed us to determine the impactof navigation on the experiential qualities in experiment 1.

6.2 MethodThe procedure of this experiment was identical to the rating task of experiment 1 (seesection 5.2), except for the fact that subjects' movements were restricted to rotationalmovements only. That is to say, subjects were stationary at the starting position markedin figure 1. A complete experimental session had a duration of about 20 min. Thirteennaive paid subjects (seven female, all mostly university students) voluntarily partici-pated in the experiment. The analysis compared the means and variance of the samplesbetween the experiments and tested for correlations. For the correlation analysis, therating results of each scene were averaged by category over all subjects.

6.3 ResultsNo significant differences were found between the mean ratings of the two experiments(see figure 7a). If anything, a slight non-significant tendency ( p � 0:22) was found thatscenes were perceived as more interesting in experiment 2. The pattern of correlationsbetween mean isovist measures and rated experiental qualities of the scenes in experi-ment 2 was very similar to experiment 1 (cf figure 6). Analogously, the ratings ofthe both sessions were all positively correlated (see figure 7b); the correlation coeffi-cient r varied from 0.49 (beauty) to 0.88 (spaciousness and complexity). The overallvariance between the scenes was almost identical in both experiments (cf figure 8b).

7

6

5

4

3

2

1

Ratingscore

pl be in co cl sp pl be in co cl spRating category Rating category

(a) (b)

Experiment

1

2

0.70**

0.49

0.78**

0.88**

0.77**

0.88**

p � 0:76 p � 0:54 p � 0:22 p � 0:72 p � 0:71 p � 0:62


r

1

0

ÿ1

Figure 7. Mean scores over all ratings (a) and correlations between the ratings of experiment 1 andexperiment 2 (b). The rating categories were pleasingness (pl), beauty (be), interestingness (in),complexity (co), clarity (cl), and spaciousness (sp).

2.0

1.5

1.0

0.5

0.0

Meanstandard

ratings

pl be in co cl sp pl be in co cl spRating category Rating category

(a) (b)

Experiment

1

2

p � 0:89 p � 0:74 p � 0:76 p � 0:42 p � 0:11 p � 0:01

Figure 8. Bar plots illustrating the variances of the ratings within the scenes (a) and betweenthe scenes of experiment 1 and experiment 2 (b). The rating categories were pleasingness (pl),beauty (be), interestingness (in), complexity (co), clarity (cl), and spaciousness (sp).


The variance within the scenes was very similar between the two conditions except ofspaciousness (figure 8a). In experiment 2 spaciousness ratings differed more betweensubjects than in experiment 1 ( p � 0:01, not corrected for multiple comparisons).

6.4 DiscussionThe high correlations between ratings of experiment 1 and experiment 2 together withthe lack of significant absolute sample differences demonstrated that the averageappraisals were very similar in both experiments. The potential slight tendency observedin experiment 2 to rate the scenes generally more interesting might be explained by theshorter exposure time in this experiment, a factor that is known to affect arousal ratings(cf eg Franz 2005, pages 164 ^ 166). Apart from that, this overall outcome suggests thatthe navigation task including free exploration in experiment 1 had very little influenceon the rating task. Therefore, the negative correlation between task difficulty and pleas-ingness might be rather interpreted within a broader context of general preferencesfor environments that are clear and easily legible (Kaplan 1988a; Nasar 1998), a rela-tion which also makes sense from the initially reviewed evolutionary perspective. Thesame theoretical framework may also provide an alternative explanation for the poten-tial negative influence of self motion on room interestingness. The mystery theory(Kaplan 1988a) suggesting that spatial situations that only promise the gain of infor-mation when moving (as in experiment 2) are more interesting than the same spatialsituations after actual exploration (as in experiment 1). An analysis comparing therating variance within and between the scenes could provide for an alternative explana-tion of the rather low correlation in the beauty rating category (r � 0:49, p � 0:06)between the experiments. In both experiments the rating variance within the sceneswas remarkably similar over all categories (figure 8a), while the variance betweenthe scenes varied depending on the rating category (figure 8b). The differences of themean ratings between the scenes were lowest in the beauty-rating category; in otherwords, all scenes were perceived as being similarly beautiful. Hence, in the beautycategory individual differences between the subjects had a much stronger influence onthe correlation between the experiments than in the other ratings, and the apparenteffect could therefore be explained by the small number of participants.

Taken together, the comparative analysis of experiment 1 and experiment 2 demon-strated that differences within the mean ratings were mainly caused by differencesbetween the scenes, and were not an artifact caused by the navigation task. Altogether,remarkable similarities between the experiential qualities rated from a fixed position(experiment 2) and after free navigation (experiment 1) were found.

7 Experiment 37.1 ObjectiveExperiment 1 demonstrated that subjects' experience and behaviour in two specificnavigation tasksöfinding the positions that maximised and minimised the visible areawithin the 16 virtual environmentsöwas correlated with the isovist-derived measureof jaggedness. A significant share of both effects could be tentatively explained byascribing the relations to influences of visual or configurational complexity. The aim ofthis experiment was to test for similar influences of visuo-spatial properties of environ-ments on a finer scale level of spatial behaviour, more precisely on single movementdecisions and locomotion. For this, subjects' behaviour, when solving the task of find-ing the best overview place in the different environments was recorded and analysedat the level of trajectories.

7.2 Method7.2.1 Experimental procedure. The procedure in this experiment was a variation of thenavigation task of experiment 1 (see section 5.2). In contrast to the previous experiment,


subjects were only asked to find the best overview place and were instructed toapproach this place as directly and quickly as possible in order to induce a moredirect, goal-directed behaviour. Therefore, a complete experimental session took onlyabout 15 min. The experiment used the same setup and stimuli. 16 naive paid subjects(9 female, mostly university students) voluntarily participated in the experiment.

7.2.2 Variables of interest. During the experiment, subjects' trajectories, ie their positionand orientation over time, were recorded with a temporal resolution of 5 Hz. In orderto characterise the trajectories as a whole, several global descriptors were calculated,such as mean velocity during navigation, number of stops, and time travelled (seefigure 9 for the complete list of the trajectory derivatives). In order to reduce the influ-ence of individual differences between subjects, the trajectory data were z-transformedper subject. In addition to the trajectory derivatives, subjects' performance in findingthe best overview place was evaluated as described in experiment 1 (see section 5.2).These behavioural measures were correlated with the mean isovist measures of the 16virtual indoor scenes (cf section 4.3).

7.3 ResultsSubjects' mean performance in finding the best overview place was again very stronglycorrelated with mean jaggedness (r � ÿ0:73, p 5 0:01; 95% confidence interval 95% CI� ÿ0.90 to ÿ0.38). A weaker correlation, yet still strong effect, was found betweensubjects' mean performance and mean number of vertices (r � ÿ0:54, p � 0:05, 95% CI� ÿ0:82 to ÿ0:06), while no significant correlation was found between performance andmean isovist area (r � ÿ0:16, p � 0:57, 95% CI � ÿ0:60 to 0.36), indicating at mosta small effect. As expected, these results did not significantly differ from the results ofexperiment 1.

Male subjects showed better performance in finding the best overview place ascompared to female subjects (female: P � 0:88� 0:02, male: P � 0:94� 0:02, t-test:t14 � ÿ2:36, p 5 0:05). In contrast to experiment 1, female and male subjects did notdiffer with respect to response time, ie the time to solve the navigation task (female:42:3 � 4:45 s, male: 46:4� 7:58 s, t-test: t14 � ÿ0:33, p � 0:74). A weak non-significantcorrelation was found between subjects' performance and response times (r � ÿ0:30,p � 0:13).

As regards correlations between trajectory derivatives and mean isovist measures,strong correlations with mean number of vertices and mean jaggedness were found

isovist area number of vertices jaggedness1.0

0.5

0.0

ÿ0.5

ÿ1.0


r

time

angle

vel

ang

vel

dist

stops

perf

time

angle

vel

ang

vel

dist

stops

perf

time

angle

vel

ang

vel

dist

stops

perf

Figure 9. Correlations between trajectory derivatives and the isovist measures mean isovist area,mean number of vertices, and mean jaggedness. For the calculation of the trajectory derivatives,only data points after the initialisation of the first translation are taken into account. Trajectoryderivatives: timeöoverall navigation time, angleösum of turning angles, velang ömean angularvelocity, velömean locomotion velocity, distötravelled distance normalised by room size, stopsönumber of stops per distance, perfötask performance.


(see figure 9), while no significant correlations were found between subjects' behaviourand mean isovist area.

Jaggedness was highly correlated with the trajectory derivative, time (r � 0:66, p5 0:01).Correspondingly, positive correlations between jaggedness and travelled distance werealso found (r � 0:54, p 5 0:05). Furthermore, jaggedness was negatively correlatedwith average angular velocity during locomotion, ie subjects turned more slowlyin more complex environments (r � ÿ0:72, p 5 0:01), and positively correlated withsubjects' velocity during navigation (r � 0:52, p 5 0:05). All the reported correlationsprobably indicate large effect sizes. Strong and qualitatively very similar correla-tions were also found between the isovist measure mean number of vertices and time(r � 0:65, p 5 0:01), angle (r � 0:63, p 5 0:01), velocity (r � 0:63, p 5 0:01), and distance(r � 0:67, p 5 0:01).

7.4 DiscussionThe described correlations between the isovist measures jaggedness and number ofvertices on the one hand and single trajectory derivatives on the other hand as well asthe similar correlation patterns for mean jaggedness and mean number of vertices canbe interpreted in a coherent way: results of the rating task of experiment 1 suggestthat the isovist measures jaggedness and number of vertices can be seen as measuresdescribing different aspects of perceptual complexity of an environment (see sections5.3 and 5.4). The scale-independent measure jaggedness could capture primarily infor-mation density, whereas the number of vertices may describe the overall amountof information. It seems plausible that, in environments featuring high perceptualcomplexity, subjects on average not only perform worse, but also behave differently.In this case, they apparently needed more time and navigated longer distances beforechoosing the best overview position. The decrease in angular velocity during rotationsin environments with high jaggedness or number of vertices as well as the increase inoverall turning angle point in the same direction: in more complex environmentssubjects need more time to pick up task-relevant information and therefore turn moreslowly during navigation.

The increase in the speed of navigation in more complex environments is at firstglance counterintuitive. If subjects turned more slowly in complex environments, onewould expect them also to navigate more slowly. This result, however, can be tentativelyexplained by assuming an influence of the instructions for this experiment: subjectswere asked to approach the position allowing for the best overview as quickly anddirectly as possible. The increase in navigation speed could therefore reflect a compen-sation for the increase in time and travelled distance subjects need to solve the taskin more complex environments.

7.5 Transferability of findingsAs regards the general implications of these empirical observations, one might raisethe objection that the recorded behaviour was strongly influenced by the specific task, theway of interaction, and perceptual conditions of the VR setting. For example, it is knownthat space perception is distorted by both a narrow vertical field of view and by amismatch between the actual and rendered field of view (Psotka et al 1998; Arthur2000; Creem-Regehr et al 2005). Both of these effects were present in the experimentalsetup used for this study. While this consideration certainly suggests cautiousness withrespect to direct extension of these results, it seems nevertheless unlikely that theobserved effects were basically artifacts. For instance, subjects reached very good per-formance levels (above 90%) when faced with the tasks of finding the best overviewor best hiding place. This result demonstrates that, despite the mismatches betweenthe actual and the rendered field of view, subjects could perceive and use the relevantspatial information very well. Furthermore, to successfully master these navigation


tasks, a certain pattern of information pick-up, integration, and comparison over timehas to be accomplished. For example, in order to find the best overview or hidingplace in an environment consisting of multiple subspaces, these subspaces have to beexplored, their sizes have to be memorised and compared, and their spatial dimensionshave to be related to each other. This holds true for the real world as well as for anyVR setting.

In this study all trials were equally affected by the constant experimental condi-tions; it therefore seems justifiable to ascribe the observed differences mainly to thespatial and configurational differences of the stimuli. Moreover, since the observedrelations are readily interpretable and fit existing general theories, they are more thanqualified hypotheses on likely environmental influences on real-world behaviour. Inour view, it is justifiable to assume a high level of correspondences between real worldand virtual behaviour with regard to the relative directions and magnitudes of theobserved effects, because under both conditions behaviour depends on the perceptualand navigation context provided by the environment. Nevertheless, a direct transfer ofall the recorded behaviour patterns at the level of trajectories to a real-world scenarioseems inappropriate. Overall turning angle, for example, appears to be a behaviourthat is strongly influenced by the specific VR setting with its small field of view.In order to get an overview of the environment, subjects would have to carry outfast gaze shifts including head movements. In the current study they had to performrelatively slow rotations. Nonetheless, we are convinced that the strong positive corre-lation between overall turning angle and perceptual complexity primarily mirrors theincreased difficulty in acquiring and integrating task-relevant information in complexenvironments, a factor that would be present to the same extent in real-world scenarios.Thus, an increased perceptual complexity could result in an increase of eye and headmovements in the real world.

Altogether, the results provide the first evidence that isovists and their derivativeshave predictive power not only for overall performance in the task tested (see alsoexperiment 1), but also for spatial behaviour at the level of trajectories. While actual real-world predictions would certainly require comparative analyses addressing the specificdifferences, the general analytical approach promises novel insights into the percep-tual basis of locomotion and could in the long run produce qualified hypotheses forpeople's movement decisions.

8 ConclusionsWe investigated here interrelations between spatial properties of environments on theone hand and spatial experience as well as navigation behaviour on the other hand.Taken together, the experiments demonstrated strong influences of the environment onall experimental tasks. Furthermore, the technique of isovist analysis allowed the iden-tification and quantitative description of environmental factors that were systematicallyrelated to the recorded behaviour. For both experiential qualities and navigation per-formance, single isovist measures were already sufficient to explain a substantialshare of the variance in the mean behavioural data. The method of averaging isovistmeasures over the entire indoor environments yielded meaningful and discriminatoryglobal characteristic values. An additional indication for the behavioural relevanceof isovists can be derived from subjects' remarkably good performance in the naviga-tion task, demonstrating that basic characteristics of isovists, such as area, were readilyperceptible.

These findings suggest that in further experiments it would be worthwhile totranslate qualitative descriptions and explanatory theories for spatial preferencesand behaviour into empirically testable hypotheses that make use of isovist measures.


Of course, because of the limited number of tested scenes and the specific character ofthe navigation task, future work has to test the validity of the specific findings bothfor a broader range of spatial situations and for different kinds of spatial behaviour.It seems also worthwhile to test the generality of the findings with other more immer-sive, experimental setups or to run comparative studies in real-world environments.Altogether, the outcomes of this study suggest that the adopted descriptive approach,analysing space from an inside beholder-centred perspective, meets the initially postu-lated requirements for architectural description systems well. Isovist and visibility graphanalysis provides well-formalised, flexibly extendable, and generically applicable methodsto yield meaningful variables that have predictive power for human spatial experienceand behaviour.

Acknowledgments. This work was supported by the Deutsche Forschungsgemeinschaft (MA 1038/9-1) and the Max Planck Institute for Biological Cybernetics, Tu« bingen.

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