Isovist analysis captures properties of space

relevant for locomotion and experience

Jan M. Wiener 1,3,4, Gerald Franz2,4, Nicole Rossmanith2, Andreas Reichelt2,

Hanspeter A. Mallot1, & Heinrich H. Bülthoff2

Revision 2, November 3, 2006

1Cognitive Neuroscience, Department of Zoology, University of Tübingen

72076 Tübingen, Germany,

Phone: +49 (0)7071 2978830

Fax: +49 (0)7071 292891

E-mail:hanspeter.mallot@uni-tuebingen.de

2Max Planck Institute for Biological Cybernetics, Spemannstrasse 38

72076 Tübingen, Germany,

Phone: +49 (0)7071 601601

Fax: +49 (0)7071 601616

E-mail:{gerald.franz, heinrich.buelthoff}@tuebingen.mpg.de

3current address:

CNRS, Collège de France, Laboratoire de Physiologie de la Perception et de l’Action

75005 Paris, France,

Phone: +33 (0)1 44 27 14 21

Fax: +33 (0)1 44 27 13 82

E-mail:jan.wiener@college-de-france.fr

4Jan Wiener and Gerald Franz contributed equally to this work.

1

Abstract

A series of exploratory experiments is presented that investigated interrela-

tions between structure and shape of architectural indoor spaces on the one hand

and affective experience and navigation behavior on the other hand. For this,

isovist-based descriptions of 16 virtual indoor scenes were correlated with be-

havioral data from the experimental tasks. For all tasks, two active navigation

tasks and an introspective appraisal of experiential qualities, strong correlations

between subjects’ behavior and a small set of quantitative measurands derived

from the isovists were found. The outcomes suggest that isovist analysis cap-

tures behaviorally relevant properties of space and is therefore a promising gen-

eral means to predict central experiential qualities of architecture and navigation

behavior.

2

1 Introduction

Spatial properties of architecture as well as of open environments influence subjec-

tive experience and spatial behavior. Several theories mainly originating from envi-

ronmental psychology see human behavior and experience in close interdependency

to the spatial structure of environments. For example, evolutionary based theories

of environmental preferences such as “prospect and refuge” (Appleton, 1988) or the

framework of Balling & Falk (1987) suggest that preference patterns for certain en-

vironmental features or configurations originate by their former advantageousness

for survival. While nowadays their relevance for humans may not be at first glance

apparent, they still appear for example as mean trends in preference ratings (Balling

& Falk, 1982; Kaplan, 1992).

Also systematic relations between various features of space and human navigation

behavior have been demonstrated in several studies. On a large-scale level, for exam-

ple Wiener & Mallot (2003) have revealed an influence of environmental regions on

human navigation and route planning behavior (see also Wiener, Schnee, & Mallot,

2004). On the level of single buildings, O’Neill (1992) found that wayfinding per-

formance decreased with increasing plan complexity. At the level of single places,

Janzen, Herrmann, Katz, & Schweizer (2000) investigated the influence of the shape

of intersections within an environment on wayfinding performance. When navigat-

ing oblique angled intersections, subjects’ error rate depended on which branch they

entered (see also Janzen, Schade, Katz, & Herrmann, 2001).

While the initial statement is therefore strongly corroborated by a multitude of sin-

gle findings, a direct comparison of empirical studies is often difficult, and also an

integration of the individual theories into a more general predictive or explanatory

model of spatial behavior has not yet been done. One main reason for this seems to

be that most studies and theories in the field of spatial cognition have rather made

use of qualitative descriptions of few specific environmental features, which can be

ascribed to the lack of a comprehensive formalized description system for environ-

mental properties. In order to be useful for this purpose, such a description system

has to fulfill the following requirements: First, it has to provide quantitative com-

parability between arbitrarily shaped environments. Second, the criteria to build up

the model should be objectively definable. In addition to these formal criteria, it has

to capture a major share of biologically and psychologically relevant properties of

the analyzed environment.

3

In the following section several approaches for describing spatial properties of en-

vironments are briefly reviewed. In accordance with the criteria outlined above,

three experiments tested an isovist based description system combining local spatial

information with global graph structures for its ability to capture behaviorally rele-

vant properties of environments at the scale level of architectural indoor spaces. The

results support the general potential of the chosen approach.

2 Background

Several disciplines already offer systems and models for describing aspects of spa-

tial environments in a formalized manner. In architectural construction, for exam-

ple, buildings are specified by a combination of lists of constructive elements (walls,

windows, columns, etc.) and scale plans. While the quantitative description of the

individual architectural elements is well elaborated and standardized, the geometri-

cal and topological structure is normally represented graphically, and therefore can-

not be quantitatively compared. In response to these shortcomings, compositional

approaches (e.g., Krier, 1989; Ching, 1996; Leyton, 2001) have been developed in ar-

chitectural theory and design practice that define more or less formal languages con-

sisting of geometric primitives and basic operations. Here the idea is to generate ar-

bitrarily complex forms and structures by applying sequences of transformations on

these primitives. The mathematically most formal directions have been called shape

grammars (Stiny & Gips, 1972) that suggest close relations between the structural

logic of a description and architectural quality. While the mentioned methods have

successfully been applied as guidelines during exploratory design phases and may

analytically allow for a retrace of steps of the genesis of shapes from the plan view

perspective of designers, they turned out not to be ideal for purely comparative anal-

yses of the final shape, since a reverse decomposition into geometric primitives and

operations is often ambiguous and disregards the experience of an inside observer.

Phenomenology provides an alternative approach particularly concentrating on the

introspective experience of observers. In everyday language, non-trivial forms are

often compared using intermediate concepts such as complexity and regularity. In

empirical aesthetics these properties are termed collative variables that have been

defined as assessment criteria of the structural properties of a stimulus array (cf.

Berlyne, 1960, 1972; Wohlwill, 1976). Collative properties offer an intuitive common

denominator for the comparison of a wide range of objects and environments even

4

across category boundaries. Unfortunately this universal scope makes a strict for-

malization or a generic implementation of these comprehensive concepts very diffi-

cult, yet at least partial relations between collative variables and physical properties

could be established.

In spatial cognition and artificial intelligence environments are often described using

graph abstractions. Graphs serve as models of the mental representation of environ-

ments, allowing the derivation of testable working hypotheses for the structure, for-

mat, and content of spatial memory. Furthermore graphs have been used to describe

environments by the set of possible movement actions (Schölkopf & Mallot, 1995).

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

edges describe the connectivity between nodes (e.g., Kuipers, 1978; Leiser & Zilber-

shatz, 1989; Chown, Kaplan, & Kortenkamp, 1995). In their most basic form place

graphs are parsimonious and purely topological representations of space, in which

nodes carry the local position information necessary to identify the corresponding

place. Edges contain local navigation rules, such as ’turn left’ or ’follow road’, that

allow navigating between nodes. However, metrical information such as distance

and direction might be additionally associated.

Originating from a purely analytical and descriptive perspective on architecture, the

technique of space syntax has been developed (Hillier & Hanson, 1984; Hillier, 1998).

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 a calculation

of characteristic values that can be interpreted for instance as connectivity, central-

ity, or control level and thus directly compared. The central aim of space syntax

has always been the identification of variables that determine the social meaning

and behaviorally relevant aspects of architectural spaces. Original space syntax has

been developed to analyze large-scale spatial configurations from the room layout

of building complexes to whole cities. Hence, spatial properties of environments

smaller than rooms were not adequately represented. For analyzing spatial charac-

teristics of smaller environments, Benedikt (1979) has proposed isovists as objectively

determinable basic elements. Isovists capture local spatial properties by describing

the visible area from a given observation point using viewshed polygons. In order

to better describe the spatial and configurational characteristics of an environment

as a whole, Turner, Doxa, O’Sullivan, & Penn (2001) have proposed the technique

5

of visibility graph analysis that combines global space syntax graphs and local isovist

visibility information. This technique offers further second-order measurands like

for example on visual stability that may be relevant for locomotion and navigation.

A more detailed description of isovist analysis and visibility graph techniques as

considered in this study is given in Section 4.3.

Originally derived from abstract spatial analysis, the relevance of isovists and vis-

ibility graphs was rather weakly backed by psychophysical empirical findings (for

an early empirical study see Benedikt & Burnham, 1985). However, isovists describe

spatial properties from an inside beholder-centered perceptual perspective, and visi-

bility graphs share many characteristics of models of spatial memory from cognitive

science (cf. Franz, Mallot, & Wiener, 2005). Indeed, there is first empirical evidence

that these techniques capture environmental properties of space that are useful as

predictors for spatial behavior and experience. For example, case studies on spatial

behavior in the Tate Gallery (Turner & Penn, 1999) have revealed high correlations

between visibility graph measurands and the statistical dispersal of visitors. Further-

more, a recent study by Franz, von der Heyde, & Bülthoff (2005) compared experi-

ential qualities of arbitrarily shaped architectural spaces with isovist measurands.

They found that already a few isovist measurands describing visual characteristics

from the observation points were widely sufficient to explain the variance in the af-

fective appraisals of the environments. Nevertheless, elementary studies testing the

perceptibility of isovists or correlating isovist measurands with navigation behavior

at the level of trajectories are still missing.

3 Objectives

The overall aim of this study was to explore the suitability of isovist graphs as

generic description systems capturing behaviorally relevant properties of spatial

form and configurations at the scale level of architectural indoor spaces. In order to

identify promising generic spatial descriptors, the presented experiments therefore

compared variables derived from isovists and visibility graphs with both spatial ex-

perience and behavior. Furthermore, the study allowed for insights into perceptual

and cognitive processes underlying the statistically observable behavioral patterns.

As first step, the perceptibility of isovists as well as relations between isovist mea-

surands and exploration behavior at the level of trajectories were tested. For these

purposes, a set of 16 virtual indoor scenes was designed. In active navigation tasks

6

subjects were asked to navigate to positions that either maximized or minimized the

visible area. Subjects’ performance of finding these positions as well as the paths

subjects took to reach these positions, i.e. their trajectories, were recorded. By se-

mantic differential ratings, appraisals of the experiential qualities of the scenes were

queried. The analysis tested for correlations between characteristic values derived

from the isovists and behavioral data consisting of ratings, performance measures,

and trajectory descriptors.

4 General material and methods

4.1 Experimental setup

The experiments were designed using a virtual reality experimental paradigm. Vir-

tual reality simulations combine flexibility, controlled laboratory conditions, and a

good degree of perceptual realism (Bülthoff & van Veen, 2001) and therefore allow

a systematic variation of spatial properties of the simulated environments. The vir-

tual scenes were created using the modeling software Autodesk ADT and 3ds max

(discreet). A detailed description of the virtual environments is given below. A pilot

stage tested a 180◦ semi-cylindrical projection system, a large flat back projection sys-

tem, and a desktop VR setup on their suitability for conducting the experiment. The

two large-scale projection systems caused strong motion or simulator sickness in a

majority of the pilot subjects, some of them responded with strange motion patterns

in order to avoid the unpleasant visual experience. Therefore, the presented experi-

ments made use of a conventional desktop VR setup which allowed all participants

to complete the experimental tasks and to intuitively interact with the simulated

environments. The visual scenery was displayed with a simulated field of view of

90◦x73◦. Subjects were seated in front of a 21” standard CRT screen at a distance

of approximately 50 cm, resulting in a physical field of view of circa 32◦x24◦. A

customary joypad was used as interaction device. The visual scenery was rendered

in realtime on standard PCs (1.0 GigaHz Pentium III, nVidia GeForce 2 GTS graph-

ics cards) running a C++ simulation software that was designed and programmed

especially for psychophysical virtual reality experiments (Franz & Weyel, 2005).

7

4.2 The virtual environments

The study was based on a set of sixteen virtual indoor scenes that was derived from

stimuli used by Franz, von der Heyde, & Bülthoff (2004). The scenes represented

diverse spatial situations within a fictive art gallery, they were derived from simple

rectangular rooms by varying the number of alcoves and connections to adjacent

spaces. The floor plans of these indoor scenes are displayed in Figure 1. The walls

of the indoor scenes were repetitively draped with unobtrusive similar paintings (46

portraits of Picasso’s blue and pink period) to strengthen the art gallery character.

Other surface properties as well as the lighting and illumination level were constant

over all scenes (see Figure 2 for examplary 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 stimuli realtime-capable.

—————— insert figure 1 about here ——————————

—————— insert figure 2 about here ——————————

4.3 Formal description of the environments

In order to relate subjects’ experience and behavior to the shape and structure of the

corresponding spaces, a generic formal description of the virtual indoor scenes was

required. For this purpose, isovist analysis appeared to offer a suitable level of detail

and abstraction, since it translates perceptual and spatial properties of architectural

space into simple polygons (see Figure 3). From the isovist polygons several basic

geometric descriptors can be derived such as area, perimeter length, number of ver-

tices, length of open or closed edges. These basic measurands can be combined to

generate further integrated values.

—————— insert figure 3 about here ——————————

Isovists basically describe local physical properties of spaces with respect to indi-

vidual observation points. The technique of visibility graph analysis as developed

by Turner et al. (2001) overcomes this limitation by encoding the intervisibility of

multiple observation points distributed regularly over the whole environment. This

technique allows for an integrative consideration of regional or global properties

8

and makes the computational analysis more efficient. Typical visibility graph mea-

surands are for instance neighborhood size (i.e. the number of directly connected

graph vertices, corresponding to isovist area) and clustering coefficient (i.e. the rela-

tive intervisibility within a neighborhood).

For the analysis in this study, a technical approach similar to visibility graphs was

used to approximate isovists: the sixteen virtual indoor scenes were analyzed by

calculating isovist measurands and visibility graphs on a 50 cm grid covering each

environment. Since the applied correlation analysis required single characteristic

values for each scene and measurand, the resulting values were averaged over each

environment. A list of the isovist and visibility graph measurands that were cal-

culated for the 16 indoor environments is given below. For the analysis a spe-

cial isovist analysis tool was used, the tool is free software and available at http:

//www.kyb.mpg.de/~gf/anavis.

Isovist derived measurands in these studies. While it is possible to generate a vir-

tually infinite number of measurands by combining basic isovist maesurands, in this

study initially six measurands (isovist area, number of vertices, jaggedness, open-

ness, clustering coefficient, revelation) were selected to describe the simulated envi-

ronments. This initial selection was on the one hand motivated by the aim to test

typical measurands from the isovist literature (cf. Turner et al., 2001), on the other

hand they appeared promising to represent the basic psychologically and behav-

iorally relevant spatial qualities spaciousness (e.g., Joedicke, 1985), openness/enclosure

(e.g., recently Stamps, 2005), and complexity (e.g., classically Berlyne, 1972; Kaplan,

1988b), as suggested by theories of architecture and environmental psychology. For a

more detailed description of the measurands’ mathematical and psychological back-

ground, please refer to Franz & Wiener (2005).

A calculation of internal correlations revealed that in the 16 virtual environments

of this study the mean jaggedness, openness, revelation, and clustering variables

were highly interdependent (r2>.81), implicating that magnitudes and directions of

correlations between these measurands and dependent variables would be widely

identical. Therefore, in order to increase the statistical power of the analysis, the ex-

perimental analysis concentrated solely on the three most independent isovist mea-

surands mean isovist area, number of vertices and jaggedness:

Isovist area The area of the floor surface visible from a single observation point. En-

9

vironments consisting of few large and open areas normally feature a higher

mean isovist area as compared to environments consisting of small and con-

fined spaces.

Number of vertices The number of vertices making up the outline of an isovist

polygon. This descriptor captures the absolute number of features of environ-

ments such as wall segments or alcoves. It is therefore a measure for aspects of

complexity.

Jaggedness The jaggedness of an isovist as an integrative measurand that is calcu-

lated mathematically as the squared isovist perimeter divided by the isovist

area. It describes the concavity of an isovist polygon, its inverse has been

sometimes described as the compactness measure. Jaggedness is related to

the density of features and has been shown to capture perceived complexity of

polygon outlines and building silhouettes (Berlyne, 1972; Stamps, 2000). In this

study, due to the high level of intercorrelations to the variables openness, clus-

tering coefficient, and relevation, it also captured the relative degree of enclosure

and visual stability of the environments.

4.4 Statistical analysis

Analyses were done using the open source software mathematics packages Octave

(http://www.octave.org) and R (http://www.r-project.org). For all statistical

analyses, the rating data was treated as even interval scaled. Linear correlation co-

efficients r were calculated using Pearson’s product moment correlation, p-values

indicate the probability of the non-directional null hypothesis. P-values below .05

were treated as significant correlations. Confidence intervals (95% CI), describing the

likely range of the general population correlation coefficients, were obtained from a

Fisher r-to-z transformation. The characterization of effect sizes corresponds to the

framework of Cohen (1988), their derivation from correlation coefficients follows the

recommendations of Hopkins (2000).

10

5 Experiment 1

5.1 Objective

In accordance with the overall objective of investigating interrelations between

spatial properties and spatial behavior, the purpose of the initial experiment was

twofold: First to test whether basic isovist properties can be perceived at all, and

second, to explore correlations between mean isovist measurands (see Section 4.3)

and behavioral data. The behavioral data were gained both from a navigation task

and a rating of experiential qualities in different virtual environments. It was hy-

pothesized that the differently shaped environments used in this experiment sys-

tematically influenced subjects’ responses in both tasks. If the isovist measurands

captured behaviorally relevant properties, significant correlations with the depen-

dent variables were expected.

5.2 Method

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

rating of experiential qualities. Only after completing both experimental tasks, they

proceeded to the next indoor scene. The 16 indoor scenes were presented in random-

ized order. A complete experimental session took about 40 minutes.

At the beginning of the active navigation task, subjects were placed at the fixed start-

ing position of the virtual indoor scene (see Figure 1) facing a random direction. Sub-

jects were then asked to navigate to the position within the scene that maximized the

visible area (corresponding to maximal isovist area) as well as to the position within

the scene that minimized the visible area (corresponding to minimal isovist area).

Before the experiment, subjects were carefully instructed that their task was not to

maximize or minimize the visible area with respect to a single gaze direction, but the

area revealed by a complete 360◦ rotation. During the experiment, the position that

maximized visible area was referred to with the catchphrase best overview place and

to the position that minimized visible area was referred to with the catchphrase best

hiding place. Again, subjects were carefully instructed that best overview place and best

hiding place were just catchphrases and that their task was to maximize or minimize

the visible area. The order in which subjects had to locate these two positions was

randomized for each room. Subjects were instructed to solve the task quickly and as

11

accurate as possible. A chosen position was confirmed by pressing a button on the

joypad, only these final positions were recorded.

The second experimental task was a rating of the experiential qualities of the 16

scenes using the common semantic differential scaling technique. At the beginning

of each trial, subjects were automatically moved back to the initial starting position

(roughly the center of the room: see Figure 1), again facing a random direction. After

pressing a button on the joypad, the ratings were collected in a random sequence.

The rating was performed by manipulating an analog slider on the input device.

In order to provide visual feedback, a scale and the currently selected value were

displayed near the lower border of the screen. During the rating task, subjects were

allowed to freely move through the environments.

Variables of interest. During the navigation task, subjects were asked to move to

the position that maximized the isovist area (best overview place) and to the position

that minimized the isovist area (best hiding place). For each indoor scene, subjects’

performance was evaluated by comparing the isovist area of the chosen positions

with the 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 the po-

sitions with the largest and smallest isovist area. In order to compare performance

between different environments, subjects’ navigation data were normalized accord-

ing to the range of isovist sizes occurring in the particular scene (see Formula 1 and

Formula 2). This performance measure ranges from 0 to 1. If subjects showed per-

fect behavior with respect to finding the positions that maximized and minimized

the isovist area, performance was 1.

Pmax(r) =Isosub(r) − Isomin(r)Isomax(r) − Isomin(r)

(1)

Pmin(r) = 1−Isosub(r) − Isomin(r)Isomax(r) − Isomin(r)

(2)

with:

r = idendity of virtual indoor scene

Pmax(r) = performance for finding the position with the highest control value for room r

12

Pmin(r) = performance for finding the position with the lowest control value for room r

Isosub(r) = size of isovist corresponding to subject’s chosen position

Isomin(r) = size of isovist corresponding to position with lowest control value for room r

—————— insert table 1 about here ——————————

The rating task comprised six core aspects of environmental experience represented

by pairs of oppositional adjectives (cf. Table 1). Subjects could differentiate their ap-

praisals using a seven step Likert-like scale. The rating categories were selected to

represent major dimensions of affective experience (pleasingness, beauty, and inter-

estingness), as well as denotative and collative properties that were expected to be

potentially relevant for the navigation task (experienced spaciousness, clarity, and

complexity). For the correlation analysis, the rating results of each scene were aver-

aged by category over all subjects.

Participants. 16 subjects (8 female, 8 male) voluntarily participated in the experi-

ment, they were paid 8 Euro per hour. Subjects were mostly university students at

an age of 20-25 years.

5.3 Results

Navigation task. Overall, subjects showed a similar performance (P) in finding the

positions having the smallest and the largest isovist area (smallest isovist: P=.92 ±

.02; largest isovist P=.90 ± .02, t-test: t=.96, df = 15, p=.3). In some of the virtual

indoor scenes subjects reached performance measures over .97. In scene 10 they

reached 1.0 for finding the best hiding place, which means that all subjects actually

found the position that minimized the visible area (cf. Figure 4).

While performance of female and male subjects did not differ with respect to find-

ing the best overview place (female: P=.88 ± .02, male: P=.91 ± .02, t-test: t=-1.66 ,

df=14, p=.12), male subjects showed better performance in finding the best hiding

place as compared to female subjects (female: P=.88 ± .03, male: P=.96 ± .02, t-test:

t=-3.96, df=14, p

second trial were therefore analyzed independent of the specific navigation task. On

average, subjects needed 44.24 ± 3.78 secs for the first trial and 20.39 ± 2.20 secs

for the second trial (t-test: t=8.7, df=15, p

(r=.58, p=.02) which could indicate large effects. Additionally, a moderate statisti-

cal relation between navigation performance and experienced pleasingness of the

rooms was probable (r=.45, p=.08) , although this result was not significant.

5.4 Discussion

In each of the 16 virtual indoor scenes, subjects had the task of finding the best

overview place and the best hiding place. Overall, they showed a remarkably good

performance in both navigation tasks. It is interesting to briefly consider some of

the perceptual and cognitive processes required to successfully master the tasks of

finding the positions within an environment that maximize and minimize the visi-

ble area when performing a 360◦ turn. The VR setting used in this study restricted

subjects’ horizontal viewing field of view to 90◦ (as opposed to a little bit more than

180◦ in reality). Thus, in order to assess the visible area from an arbitrary position

within an environment, visuo-spatial information obtained from different viewing

directions had to be integrated, either by combining a series of visual snapshots or

in form of a more abstract representation. In any case, this integrated information

had to be memorized in order to perform comparisons of the visible area at dif-

ferent positions within the environment. Furthermore, independent of the specific

sequence in which subjects solved the two tasks, the first navigation trial took con-

siderably longer than the second one. This result suggests that during the second

trial, subjects relied also on knowledge acquired during the first trial. A possible line

of argumentation is that during the first trial subjects remembered some quantitative

measures describing the visible area along their trajectories and that this information

was reused during the second navigation trial. To the authors’ view, however, it ap-

pears more likely that during the first trial, subjects explored the environment and

either generated a spatial memory of its shape or already memorized potential po-

sitions of the other extremum. This memory then allowed them to act faster in the

second trial. All in all, subjects’ high performance 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 hypothetically ex-

plained by assuming different levels of familiarity between female and male partic-

ipants with interactive computer-simulated environments such as first-person com-

puter games and with game controllers. The much smaller differences in task per-

15

formance, however, suggest that this presumable factor was of minor importance for

performing the experimental task.

The basic initial hypothesis that isovists capture behaviorally relevant environmen-

tal properties was supported by the result that the isovist measurand jaggedness was

strongly negatively correlated with navigation performance. This outcome may be

interpreted as follows: Studies on polygon outlines (Berlyne, 1972) and building

silhouettes (Stamps, 2000) have found that the jaggedness measurand (i. e. poly-

gon perimeter2/area) corresponds well to introspectively rated shape complexity.

Pointing in the same direction, the results of the rating tasks showed positive corre-

lations between jaggedness and rated complexity, and negative correlations between

jaggedness and clarity. Taken together, jaggedness can be seen as a measure describ-

ing aspects of visual complexity such as information density. In a spatial context

jaggedness may additionally characterize configurational complexity, leading to an

increased task difficulty which may implicate a negative influence on navigation per-

formance. Although the negative correlation between navigation performance and

the number of isovist vertices did not reach statistical significance, it points in the

same direction. The low level of correlations to isovist area basically suggests that

the measured behavior is scale-independent.

The apparent statistical relations between the navigation task and the rating results

may however be also interpreted in a different way: Since the navigation task always

preceded the ratings, the latter might have been influenced by the subjective expe-

rience of the preceding task. For example, the rated complexity of an indoor scene

may basically mirror the effort or the subjectively perceived difficulty of the naviga-

tion tasks within that scene. This interpretation gains some support by the moderate

positive correlation between experienced pleasingness and navigation performance,

although this relation did not reach the chosen significance level of p=0.05. In order

to test this alternative explanation, Experiment 2 was conducted.

6 Experiment 2

6.1 Objective

This experiment was designed as a control condition to discriminate between the al-

ternative explanations of Experiment 1, namely that differences in the ratings either

reflect differences of the environments or differences in the navigation experience.

16

For this purpose, solely the rating task of Experiment 1 was repeated, the naviga-

tion task was skipped, and the ratings were done from a fixed central observation

point. Comparing the rating results of the two experiments allowed to determine

the impact of navigation on the experiential qualities in Experiment 1.

6.2 Method

The procedure of this experiment was identical to the rating task of Experiment 1

(see Section 5.2), except for the fact that subjects’ movements were restricted to rota-

tional movements only. That is to say, subjects were stationary at the starting posi-

tion marked in Figure 1. A complete experimental session had a duration of about

20 minutes. 13 naive paid subjects (7 female, 6 male, mostly university students)

voluntarily participated in the experiment. The analysis compared the means and

variance of the samples between the experiments and tested for correlations. For the

correlation analysis, the rating results of each scene were averaged by category over

all subjects.

6.3 Results

No significant differences were found between the mean ratings of the two experi-

ments (see Figure 7 left). If anything, a slight non-significant tendency (p=0.22) was

found that scenes were perceived as more interesting in Experiment 2. The pattern

of correlations between mean isovist measurands and rated experiential qualities of

the scenes in Experiment 2 was very similar to Experiment 1 (cf. Figure 6). Anal-

ogously, the ratings of the both sessions were all positively correlated (see Figure 7

right), the correlation coefficient r varied from .49 (beauty) to .88 (spaciousness and

complexity). The overall variance between the scenes was almost identical in both

experiments (cf. Figure 8 right). The variance within the scenes was very similar

between the two conditions except of spaciousness (Figure 8 left): In Experiment 2

spaciousness ratings differed more between subjects than in Experiment 1 (p=.01,

not corrected for multiple comparisons).

—————— insert figure 7&8 about here ——————————

17

6.4 Discussion

The high correlations between ratings of Experiment 1 and Experiment 2 together

with the lack of significant absolute sample differences demonstrated that the aver-

age appraisals were very similar in both experiments. The potential slight tendency

observed in Experiment 2 to rate the scenes generally more interesting might be ex-

plained by the shorter exposure time in this experiment, a factor that is known to

affect arousal ratings (cf. e.g., Franz, 2005, pp. 164-166). Apart from that, this over-

all outcome suggests that the navigation task including free exploration in Exper-

iment 1 had very little influence on the rating task. Therefore, the negative corre-

lation between task difficulty and pleasingness might be rather interpreted within

a broader context of general preferences for environments that are clear and easily

legible (Kaplan, 1988a; Nasar, 1998), a relation which also makes sense from the ini-

tially reviewed evolutionary perspective. The same theoretical framework may also

provide an alternative explanation the potential negative influence of ego-motion on

room interestingness: The mystery theory (Kaplan, 1988a) suggesting that spatial sit-

uations that only promise the gain of information when moving (as in Experiment

2) are more interesting than the same spatial situations after actual exploration (as

in Experiment 1). An analysis comparing the rating variance within and between

the scenes could provide for an alternative explanation of the rather low correla-

tion in the beauty rating category (r=.49, p=.06) between the experiments: In both

experiments the rating variance within the scenes was remarkably similar over all

categories (Figure 8 left), while the variance between the scenes varied depending

on the rating category (Figure 8 right). The differences of the mean ratings between

the scenes were lowest in the beauty rating category, in other words, all scenes were

perceived as being similarly beautiful. Hence, in the beauty category individual

differences between the subjects had a much stronger influence on the correlation

between the experiments than in the other ratings, and the apparent effect 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 differences

between the scenes, and were not an artifact caused by the navigation task. Alto-

gether, remarkable similarities between the experiential qualities rated from a fixed

position (Experiment 2) and after free navigation (Experiment 1) were found.

18

7 Experiment 3

7.1 Objective

Experiment 1 demonstrated that subjects’ experience and behavior in two specific

navigation tasks, namely finding the positions that maximized and minimized the

visible area within the 16 virtual environments, was correlated with the isovist de-

rived measurand jaggedness. A significant share of both effects could be tentatively

explained ascribing the relations to influences of visual or configurational complex-

ity. The aim of this experiment was to test for similar influences of visuo-spatial

properties of environments on a finer scale level of spatial behavior, more precisely

on single movement decisions and locomotion. For this, subjects’ behavior, when

solving the task of finding the best overview place in the different environments,

was recorded and analyzed at the level of trajectories.

7.2 Method

Experimental procedure. The procedure of this experiment was a variation of the

navigation task of Experiment 1 (see Section 5.2). In contrast to the previous experi-

ment, subjects were only asked to find the best overview place and were instructed

to approach this place as directly and quickly as possible in order to provoke a more

direct, goal-directed behavior. Therefore, a complete experimental session took only

about 15 minutes. The experiment used the same setup and stimuli. 16 naive paid

subjects (9 female, 7 male, mostly university students) voluntarily participated in the

experiment.

Variables of Interest. During the experiment, subjects’ trajectories, i.e. their po-

sition and orientation over time, were recorded at a temporal resolution of 5 Hz.

In order to characterize the trajectories as a whole, several global descriptors were

calculated such as mean velocity during navigation, number of stops, time traveled

(see Figure 9 for the complete list of the trajectory derivatives). In order to reduce

the influence of individual differences between subjects, the trajectory data were z-

transformed per subject. In addition to the trajectory derivatives, subjects’ perfor-

mance in finding the best overview place was evaluated as described in Experiment

1 (see Section 5.2). These behavioral measures were correlated to the mean isovist

measurands of the 16 virtual indoor scenes (cf. Section 4.3).

19

7.3 Results

Subjects’ mean performance in finding the best overview place was again very

strongly correlated with mean jaggedness (r=-.73, p

well as the similar correlation patterns for mean jaggedness and mean number of

vertices can be interpreted in a coherent way: Results of the rating task of Experi-

ment 1 suggest that the isovist measurands jaggedness and number of vertices can

be seen as measures describing different aspects of perceptual complexity of an en-

vironment (see Sections 5.3 and 5.4). The scale independent measurand jaggedness

could capture primarily information density, whereas the number of vertices rather

describes the overall amount of information. It seems plausible that in environments

featuring high perceptual complexity subjects on average not only perform worse,

but also behave differently. In this case they apparently needed more time and nav-

igated longer distances until choosing the best overview position. The decrease in

angular velocity during rotations in environments with high jaggedness or number

of vertices measures as well as the increase in overall turning angle point in the same

direction: In more complex environments subjects need more time to pick up task-

relevant information and therefore turn more slowly during navigation.

The increase in navigation speed in more complex environments is counterintuitive

at first glance. If subjects turned more slowly in complex environments, one would

expect them to also navigate more slowly. This result, however, can be tentatively

explained by assuming an influence of the experiment instructions: subjects were

asked to approach the position allowing for the best overview as quickly and directly

as possible. The increase in navigation speed could therefore reflect a compensation

for the increase in time and traveled distance subjects need to solve the task in more

complex environments.

7.5 Transferability of findings

As regards the general implications of these empirical observations, one might raise

the objection that the recorded behavior was strongly influenced by the specific task,

the way of interaction, and perceptual conditions of the virtual reality setting. For

example, it is known that space perception is distorted by both a narrow vertical

FOV and by a mismatch between the actual and rendered FOV (e.g., Psotka, Lewis,

& King, 1998; Arthur, 2000; Creem-Regehr, Willemsen, Gooch, & Thompson, 2005).

Both of these effects were present in the experimental setup used for this study.

While this consideration certainly suggests cautiousness with respect to direct trans-

lations, it seems nevertheless unlikely that the observed effects were basically ar-

tifacts. For instance, subjects reached very good performance levels (above 90%)

21

when faced with the tasks of finding the best overview or best hiding place. This re-

sult demonstrates that, despite the mismatches between the actual and the rendered

FOV, subjects could perceive and use the relevant spatial information very well. Fur-

thermore, to successfully master these navigation tasks a certain pattern of informa-

tion pick up, integration, and comparison over time has to be accomplished. For

example, in order to find the best overview or hiding place in an environment con-

sisting of multiple subspaces, these subspaces have to be explored, their sizes have

to be memorized and compared, and their spatial dimensions have to be related to

each other. This holds true for the real world as well as for any VR-setting.

In this study all trials were equally affected by the constant experimental conditions,

it therefore seems well justifiable to ascribe the observed differences mainly to the

spatial and configurational differences of the stimuli. Moreover, since the observed

relations are also well interpretable and fit to existing general theories, they should

be considered as more than qualified hypotheses on likely environmental influences

on real world behavior. To the authors’ view, it seems well justifiable to assume

a high level of correspondences between realworld and virtual behavior with re-

spect to the relative directions and magnitudes of the observed effects, because un-

der both conditions behavior is dependent on the perceptual and navigation context

provided by the environments. Nevertheless, a direct transfer of all the recorded

behavior patterns at the level of trajectories to a real world scenario seems inappro-

priate. Overall turning angle, for example, appears to be a behavior that is strongly

influenced by the specific VR setting with its comparably small field of view. In order

to get an overview of the environment, subjects would do fast gaze shifts including

head movements. In the current study they had to perform relatively slow rotations.

Nonetheless, the authors are convinced that the strong positive correlation between

overall turning angle and perceptual complexity primarily mirrors the increased dif-

ficulty to acquire and integrate task relevant information in complex environments,

a factor that would be equally present in real world scenarios. Thus, an increased

perceptual complexity could result in an increase of eye- and head movements in

the real world.

Altogether, the results are first evidence that isovists and their derivatives have pre-

dictive power not only for overall performance in the task tested (see also Experi-

ment 1), but also for spatial behavior at the level of trajectories. While actual real

world predictions would certainly require comparative analyses addressing the spe-

cific differences, the general analytical approach promises novel insights into the

22

perceptual basis of locomotion and could on the long run offer qualified hypotheses

for people’s movement decisions.

8 Conclusions

The experiments presented in this study investigated interrelations between spatial

properties of environments on the one hand and spatial experience as well as nav-

igation behavior on the other hand. Taken together, the experiments could demon-

strate strong influences of the environment on all experimental tasks. Beyond this

qualitative statement, the technique of isovist analysis allowed the identification and

quantitative description of environmental factors that were systematically related to

the recorded behavior. For both experiential qualities and navigation performance,

already single isovist measurands were sufficient to explain a substantial share of

the variance in the mean behavioral data. The method of averaging isovist measur-

ands over the entire indoor environments rendered meaningful and discriminatory

global characteristic values. An additional indication for the behavioral relevance of

isovists can be derived from subjects’ remarkably good performance in the naviga-

tion task, demonstrating that basic characteristics of isovists such as area were well

perceptible.

These findings suggest that for further experiments it is worthwhile to translate qual-

itative descriptions and explanatory theories for spatial preferences and behavior

into empirically testable hypotheses that make use of isovist measurands. Of course,

due to the limited number of tested scenes and the specific character of the navi-

gation task, future work has to test the validity of the specific findings both for a

broader range of spatial situations and for different kinds of spatial behavior. It

seems also worthwhile to test the generality of the findings using other more im-

mersive experimental setups or to run comparative studies in realworld environ-

ments. Yet, altogether the outcomes of this study suggest that the taken descrip-

tive approach, analyzing space from an inside beholder-centered perspective, meets

the initially postulated requirements for architectural description systems well. Iso-

vist and visibility graph analysis provides well-formalized, flexibly extendable, and

generically applicable methods to generate meaningful variables that have predic-

tive power for human spatial experience and behavior.

23

9 Acknowledgments

This work was supported by the Deutsche Forschungsgemeinschaft (MA 1038/9-1)

and the Max Planck Institute for Biological Cybernetics, Tübingen.

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27

Figures

(5)

(12)

(14)

(8)

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(2) (3)(1)

(16)(15)

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(9) (11)

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Figure 1:

28

Figure 2:

29

area

perimeter

open edge

closed edge

vertices

observationpoint

Figure 3:

30

pe

rfo

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nce

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finding best overview place finding best hiding place

Figure 4:

31

jaggedness

-1.0

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Figure 5:

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-1.0

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pl be in co cl sprating category

****

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Figure 6:

33

-1.0

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mean scores over all ratings

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rating

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erating category

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7p=0.76 p=0.54 p=0.22 p=0.72 p=0.71 p=0.62

Exp. 1Exp. 2

Figure 7:

34

variance within scenes

pl be in co cl sp 0.0

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std m

ean r

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0.0

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Exp. 1Exp. 2

Exp. 1Exp. 2

**

Figure 8:

35

jaggedness

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Figure 9:

36

Figure captions

Figure 1: Floor plans of the 16 virtual indoor scenes used in the experiments. The

indices are used in the following in order to refer to the individual envi-

ronment. The dot in the center of each room marks the starting position

for the experimental tasks.

Figure 2: Three screenshots of the virtual indoor scenes as experienced by the sub-

jects.

Figure 3: Generating isovists: Left: a hypothetical indoor environment; middle:

the gray area is visible from the person’s observation point within the

environment; right: the resulting isovist and its basic measurands.

Figure 4: Subjects’ average performance per scene; left: finding the position that

minimizes the isovist area (best hiding place), right: finding the position

that maximizes the isovist area (best overview place). The error-bars dis-

play the standard error of the means.

Figure 5: Correlation between subjects’ performance finding the best hiding resp.

overview place and mean isovist measurands area, jaggedness, and num-

ber of vertices.

Figure 6: Linear correlations between the selected isovist measurands and aver-

aged rated experiential qualities of the scenes in Experiment 1. The rating

categories were pleasingness, beauty, interestingness, complexity, clarity,

and spaciousness.

Figure 7: Mean scores over all ratings and correlations between the ratings of Ex-

periment 1 and Experiment 2. The rating categories were pleasingness,

beauty, interestingness, complexity, clarity, and spaciousness.

Figure 8: Bar plots illustrating the variances of the ratings within the scenes (left)

and between the scenes (right) of Experiment 1 (black) and Experiment 2

(green). The rating categories were pleasingness, beauty, interestingness,

complexity, clarity, and spaciousness.

Figure 9: Correlations between trajectory derivatives and the isovist measurands

mean isovist area, mean number of vertices, and mean jaggedness. For the

37

calculation of the trajectory derivatives, only data points after the initial-

ization of the first translation are taken into account. Trajectory deriva-

tives: time ~ overall navigation time, angle ~ sum of turning angles, velang

~ mean angular velocity, vel ~ mean locomotion velocity, dist ~ traveled

distance normalized by room size, stops ~ number of stops per distance,

perf ~ task performance

38

Tables

Category

interestingness boring interesting langweilig interessant

pleasingness unpleasant pleasant unangenehm angenehm

beauty ugly beautiful hässlich schön

spaciousness narrow spacious eng weit

complexity simple complex einfach komplex

clarity unclear clear unübersichtlich übersichtlich

English low extreme

English high extreme

German low extreme

German high extreme

Table 1:

39

Table captions

Table 1: English translations and original terms of the rating categories used in

the semantic differential. The experiments were conducted in German

language.

40