[lecture notes in computer science] spatial information theory volume 6899 ||

Lecture Notes in Computer Science 6899Commenced Publication in 1973Founding and Former Series Editors:Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen

Editorial Board

David HutchisonLancaster University, UK

Takeo KanadeCarnegie Mellon University, Pittsburgh, PA, USA

Josef KittlerUniversity of Surrey, Guildford, UK

Jon M. KleinbergCornell University, Ithaca, NY, USA

Alfred KobsaUniversity of California, Irvine, CA, USA

Friedemann MatternETH Zurich, Switzerland

John C. MitchellStanford University, CA, USA

Moni NaorWeizmann Institute of Science, Rehovot, Israel

Oscar NierstraszUniversity of Bern, Switzerland

C. Pandu RanganIndian Institute of Technology, Madras, India

Bernhard SteffenTU Dortmund University, Germany

Madhu SudanMicrosoft Research, Cambridge, MA, USA

Demetri TerzopoulosUniversity of California, Los Angeles, CA, USA

Doug TygarUniversity of California, Berkeley, CA, USA

Gerhard WeikumMax Planck Institute for Informatics, Saarbruecken, Germany

Max Egenhofer Nicholas GiudiceReinhard Moratz Michael Worboys (Eds.)

SpatialInformation Theory

10th International Conference, COSIT 2011Belfast, ME, USA, September 12-16, 2011Proceedings

1 3

Volume Editors

Max EgenhoferNicholas GiudiceReinhard MoratzMichael WorboysUniversity of MaineOrono, ME 04469, USAE-mail: {max, giudice, moratz, worboys}@spatial.maine.edu

ISSN 0302-9743 e-ISSN 1611-3349ISBN 978-3-642-23195-7 e-ISBN 978-3-642-23196-4DOI 10.1007/978-3-642-23196-4Springer Heidelberg Dordrecht London New York

Library of Congress Control Number: 2011934621

CR Subject Classification (1998): E.1, H.2.8, J.2, I.5.3, I.2, F.1

LNCS Sublibrary: SL 1 Theoretical Computer Science and General Issues

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Preface

The Conference on Spatial Information TheoryCOSITwas established in1993 as a biennial interdisciplinary conference. The COSIT conference seriesfocuses on innovation in spatial information theory across the disciplines. Itcaters to researchers in such fields as anthropology, artificial intelligence, cog-nitive neuroscience, computer science, geography, linguistics, mathematics, psy-chology, and spatial cognition who are concerned with models of space and time.Of particular interest are perspectives that cut across multiple domains or thosethat leverage established methods common in one field so that new insights aboutspace are gained in another field or discipline.

COSIT 2011 marked the 10th time that COSIT convened. The 2011 confer-ence was held September 12-16, 2011 at the Hutchinson Center in Belfast, Maine,on the Penobscot Bay. Late September was an excellent time to enjoy the stun-ning beauty of Maines coast since fall is New Englands most picturesque timeof year. The foliage brings a crisp chill and vibrant leaf colorations.

All COSIT submissions were fully refereed by three or four members of theProgram Committee, who were asked to write substantial appraisals analyzingthe submissions relevance to the conference, their intellectual merit, their scien-tific significance, novelty, relation to previously published literature, and clarityof presentation. Out of the 55 submissions, the Program Committee selected 23papers for oral presentation.

The three keynote speakers for COSIT 2011 were Ernest Davis, Departmentof Computer Science, New York University, Nora Newcombe, Department ofPsychology at Temple University and Spatial Intelligence and Learning Center(SILC), and Thomas Wolbers, Centre for Cognitive and Neural Systems, Uni-versity of Edinburgh. In addition to the technical program, COSIT 2011 had aposter session, four workshops, two tutorials, and a doctoral colloquium.

We thank the many people who made COSIT 2011 such a success: all thosewho submitted work and participated at the meeting, the reviewers, the ProgramCommittee, the local Organizing Committee, and the staff of the HutchinsonCenter.

September 2011 Max EgenhoferNicholas GiudiceReinhard Moratz

Mike Worboys

Organization

General Chairs

Nicholas Giudice University of Maine, USAMike Worboys University of Maine, USA

Program Chairs

Max Egenhofer University of Maine, USAReinhard Moratz University of Maine, USA

Steering Committee

Christophe Claramunt Naval Academy Research Institute, FranceAnthony Cohn University of Leeds, UKMichel Denis LIMSI-CNRS, Paris, FranceMatt Duckham University of Melbourne, AustraliaMax Egenhofer University of Maine, USAAndrew Frank Technical University Vienna, AustriaChristian Freksa University of Bremen, GermanyStephen Hirtle University of Pittsburgh, USAWerner Kuhn University of Munster, GermanyBenjamin Kuipers University of Michigan, USADavid Mark SUNY Buffalo, USADan Montello UCSB, USAKathleen Stewart University of Iowa, USASabine Timpf University of Augsburg, GermanyBarbara Tversky Stanford University, USAStephan Winter University of Melbourne, AustraliaMichael Worboys University of Maine, USA

Program Committee

Pragya AgarwalBrandon BennettMoulin BernardSven BertelMichela Bertolotto

Mehul BhattThomas BittnerGilberto CamaraChristophe ClaramuntEliseo Clementini

VIII Organization

Helen CouclelisLeila De FlorianiMatt DuckhamGeoffrey EdwardsCarola EschenbachSara FabrikantAndrew FrankChristian FreksaMark GaheganAntony GaltonStephen HirtleChristopher JonesMarinos KavourasAlexander KlippelChristian KrayBarry KronenfeldWerner KuhnLars KulikDamir MedakDaniel R. Montello

Nora NewcombeMartin RaubalJochen RenzKai-Florian RichterAndrea RodriguezChristoph SchliederAngela SchweringJohn StellKathleen StewartSabine TimpfBarbara TverskyDavid UttalNico Van De WegheJan Oliver WallgrunRobert WeibelStephan WinterThomas WolbersDiedrich WolterMay Yuan

Table of Contents

Maps and Navigation

How Do Decision Time and Realism Affect Map-Based DecisionMaking? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Jan Wilkening and Sara Irina Fabrikant

Towards Cognitively Plausible Spatial Representations for Sketch MapAlignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Malumbo Chipofya, Jia Wang, and Angela Schwering

Scalable Navigation Support for Crowds: Personalized Guidance viaAugmented Signage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Fathi Hamhoum and Christian Kray

Information on the Consequence of a Move and Its Use for RouteImprovisation Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Takeshi Shirabe

The Effect of Activity on Relevance and Granularity for Navigation . . . . 73Stephen C. Hirtle, Sabine Timpf, and Thora Tenbrink

I Can Tell by the Way You Use Your Walk: Real-Time Classification ofWayfinding Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Makoto Takemiya and Toru Ishikawa

Spatial Change

From Video to RCC8: Exploiting a Distance Based Semantics toStabilise the Interpretation of Mereotopological Relations . . . . . . . . . . . . . 110

Muralikrishna Sridhar, Anthony G. Cohn, and David C. Hogg

Decentralized Reasoning about Gradual Changes of TopologicalRelationships between Continuously Evolving Regions . . . . . . . . . . . . . . . . 126

Lin-Jie Guan and Matt Duckham

Spatio-temporal Evolution as Bigraph Dynamics . . . . . . . . . . . . . . . . . . . . . 148John Stell, Geraldine Del Mondo, Remy Thibaud, andChristophe Claramunt

Spatial Reasoning

On Optimal Arrangements of Binary Sensors . . . . . . . . . . . . . . . . . . . . . . . . 168Parvin Asadzadeh, Lars Kulik, Egemen Tanin, and Anthony Wirth

X Table of Contents

A Hybrid Geometric-Qualitative Spatial Reasoning System and ItsApplication in GIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

Giorgio De Felice, Paolo Fogliaroni, and Jan Oliver Wallgrun

CLP(QS): A Declarative Spatial Reasoning Framework . . . . . . . . . . . . . . . 210Mehul Bhatt, Jae Hee Lee, and Carl Schultz

Spatial Cognition and Social Aspects of Space

The Social Connection in Mental Representations of Space:Explicit and Implicit Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

Holly A. Taylor, Qi Wang, Stephanie A. Gagnon,Keith B. Maddox, and Tad T. Brunye

Revisiting the Plasticity of Human Spatial Cognition . . . . . . . . . . . . . . . . . 245Linda Abarbanell, Rachel Montana, and Peggy Li

Linguistic and Cultural Universality of the Concept ofSense-of-Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

Daniel R. Montello and Danqing Xiao

Towards a Formalization of Social Spaces for Socially Aware Robots . . . . 283Felix Lindner and Carola Eschenbach

Perception and Spatial Semantics

Finite Relativist Geometry Grounded in Perceptual Operations . . . . . . . . 304Simon Scheider and Werner Kuhn

Linking Spatial Haptic Perception to Linguistic Representations:Assisting Utterances for Tactile-Map Explorations . . . . . . . . . . . . . . . . . . . . 328

Kris Lohmann, Carola Eschenbach, and Christopher Habel

Analyzing the Spatial-Semantic Interaction of Points of Interest inVolunteered Geographic Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350

Christoph Mulligann, Krzysztof Janowicz, Mao Ye, andWang-Chien Lee

Space and Language

A Model of Spatial Reference Frames in Language . . . . . . . . . . . . . . . . . . . 371Thora Tenbrink and Werner Kuhn

Universality, Language-Variability and Individuality: DefiningLinguistic Building Blocks for Spatial Relations . . . . . . . . . . . . . . . . . . . . . . 391

Kristin Stock and Claudia Cialone

Table of Contents XI

The Semantics of Farsi be: Applying the Principled Polysemy Model . . . . 413Narges Mahpeykar and Andrea Tyler

On the Explicit and Implicit Spatiotemporal Architecture of Narrativesof Personal Experience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434

Blake Stephen Howald and E. Graham Katz

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

M. Egenhofer et al. (Eds.): COSIT 2011, LNCS 6899, pp. 119, 2011. Springer-Verlag Berlin Heidelberg 2011

How Do Decision Time and Realism Affect Map-Based Decision Making?

Jan Wilkening and Sara Irina Fabrikant

Geographic Information Visualization & Analysis Group (GIVA), Department of Geography,

University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland {jan.wilkening,sara.fabrikant}@geo.uzh.ch

Abstract. We commonly make decisions based on different kinds of maps, and under varying time constraints. The accuracy of these decisions often can decide even over life and death. In this study, we investigate how varying time constraints and different map types can influence peoples visuo-spatial decision making, specifically for a complex slope detection task involving three spatial dimensions. We find that participants response accuracy and response confidence do not decrease linearly, as hypothesized, when given less response time. Assessing collected responses within the signal detection theory framework, we find that different inference error types occur with different map types. Finally, we replicate previous findings suggesting that while people might prefer more realistic looking maps, they do not necessarily perform better with them.

Keywords: time pressure, slope maps, shaded relief maps, empirical map evaluation.

1 Introduction

Many people have used maps for spatio-temporal decision-making under varying time constraints. For instance, commuters must choose alternative driving routes with road maps, depending on rapidly changing traffic situations. Hikers might need to rapidly select a different trail using a topographic map, when the weather suddenly deteriorates in the mountains, or a sailor might have to quickly consult a nautical chart when navigating in an area with sudden wind and water level changes. Time available for such kinds of map-based decisions can vary enormously. Sometimes the decision time window might consist merely of a few seconds, and the decision might decide over life and death. With increasing human mobility, and respective increased availability of mobile map devices, it seems crucial to investigate how decision time constraints and display types might affect the quality of map-based decision making under rapidly changing conditions. We have been investigating this rather under researched issue with a series of prior controlled experiments, which we review with other relevant research in the related work section.

In this study, involving a map-based slope detection task under varying time pressure scenarios, we specifically investigate decision-making within a three-dimensional context

2 J. Wilkening and S.I. Fabrikant

and different display types, and analyze collected responses (i.e., accuracy) within the signal detection theory framework.

2 Related Work

Our research program lies at the intersection of time pressure and decision-making research, mainly carried out in psychology and economics, including empirical map design research in cartography. In the following, we review related work from these cognate research fields.

2.1 Decision Making under Time Pressure

Many external factors and cognitive biases impair optimal human decision-making (Simon, 1959; Payne, 1982; Gigerenzer, 2002). The effect of time constraints on decision making has been evaluated systematically by cognitive, developmental, and personality psychologists, as well as by human resources researchers, or economists (see Frster et al., 2003 for an extensive review). It is widely accepted that decision time influences the quality of decisions (Svenson et al., 1990), and that the negative effect of time pressure on decision making is robust and consistent (Pew, 1969; Ahituv et al., 1998).

Two concepts from the psychological literature on time pressure and decision-making seem relevant for our study: Firstly, the speed-accuracy trade-off concept (Wickelgren, 1977) suggests that time pressure can reduce the overall quality of a decision, and, secondly, the speed-confidence trade-off (Smith et al., 1982) suggests that the confidence with which people make decisions might decrease with increasing time pressure. The characteristics of the speed-accuracy trade-off depend on task complexity: The more complex a task, the more likely the occurrence of the speed-accuracy trade-off (Johnson et al., 1993).

However, there are also instances when time pressure has a beneficial effect on decision-making. For example, in a long-term time pressure study with NASA scientists and engineers Andrews and Farris (1972) found that decision performance actually increased with increased time pressure, but only to a certain tipping point. Beyond that point, decision performance decreased again. Peters et al. (1984) replicated these findings in a related study involving commercial bankers as decision makers. Hwang (1994) argues that perhaps the best way to describe the interaction between decision performance and time pressure is not a linear relationship, but an inverted U-shaped curve: Increasing time pressure leads to better performance up to a certain point, beyond that point more time pressure reduces, rather than increases, performance. (Hwang, 1994, p. 198).

A still open question remains whether map-based decisions follow a linear speed-accuracy trade-off relation, or an inverted U-shaped curve as found in previous research outside of GIScience, which would imply that time pressure could also have a positive effect on map-based decisions. At this point, it is also unclear how map design and task complexity might interact with map-based decision making under time pressure.

In empirical cartographic research, response time is typically employed as a dependent variable (i.e., efficiency measure) to evaluate cartographic design

How Do Decision Time and Realism Affect Map-Based Decision Making? 3

principles (Lloyd and Bunch, 2003; Garlandini and Fabrikant, 2009; Dillemuth, 2009). However, little work has been done until now to study the effect of time pressure (i.e., as a controlled, independent variable or factor) on map based decision-making. Baus, Krger and Wahlster (2002) suggest to consider time pressure when designing displays of mobile devices for pedestrian navigation. They argue that changing travelling speeds during navigation create varying time pressure situations, which in turn should lead to different user requirements for navigation displays. They contend that different content should be displayed on a map used in different time pressure conditions. In another study involving user motivation in navigation, Srinivas and Hirtle (2010) offered a reward to one participant group as an incentive for faster task completion, while the other control group was not given any incentive to reduce task completion time. Indeed, the more motivated participants completed the routes significantly faster than the participants in the control group.

2.2 Map Design Issues in Decision Making

Numerous prior empirical studies in cartography have investigated how map design might influence human visuo-spatial inference and decision making, typically depending on a specific map use task (Fabrikant and Lobben, 2009). For our study on slope detection, research comparing 2D and 3D-looking maps for a task involving three spatial dimensions seems particularly relevant. For example, studying aviator navigation performance, Smallman et al. (2001) have shown that users search time for selecting aircraft which meet certain criteria was significantly faster with 2D maps than with 3D-looking map displays. In related work on the design of cockpit displays, Thomas and Wickens (2006) found no significant performance differences in participants accuracy and response times between 2D co-planar or 3D perspective displays. Coors et al. (2005) evaluated small-screen 3D and 2D mobile navigation aids, and found that the majority of the participants had a positive attitude towards 3D. Participants found that 3D maps were generally a good idea, but also that 2D was already sufficient for mobile navigation. However, participants response times were significantly slower with 3D maps compared to 2D maps. This suggests that 3D displays in the context of navigation might be more suitable when having more time available for decision-making, but less useful under time pressure.

In this context, the potential discrepancy between user preferences and actual task performance is also relevant. For instance, Canham, Smallman and Hegarty (2007) and Hegarty et al. (2009) have shown that users tend to prefer more realistic, 3D-looking weather maps that on the surface seem to contain more information for the decision-making task at hand than more abstract 2D maps. However, while users prefer 3D, these displays do not necessarily seem to positively influence users task performance. In fact, Hegarty and colleagues (2009) found that performance was generally better with the less realistic-looking maps, while users preference ratings indicated just the opposite. They interpret these results as another good, empirically validated illustration of the common-sense notion that what people think they want is not always what is best for them (Fabrikant and Lobben, 2009). According to Hegarty and colleagues, nave cartographers seem to prefer 3D displays to 2D displays, and also seem to prefer more realistic depictions to simpler, more abstract ones. Cartographic design theories and principles, however, aim for reducing graphic


complexity (Bertin, 1967). Similarly, the claims by designers for maximizing the data-ink ratio and for minimizing chart junk (Tufte, 1983), or the empirically validated clutter principle by Rosenholtz and colleagues (2007) also call for more abstraction, and less gratuitous realism to facilitate visuo-spatial decision making. From these related studies, we can derive an initial research hypothesis that users prefer more realistic-looking maps (e.g., satellite image maps) and 3D maps (e.g., shaded relief maps), but might perform better with traditional 2D cartographic maps (i.e., topographic maps).

While on the surface it might seem obvious that certain map types are suitable for certain kinds of tasks, it is less obvious how variations of map display designs might influence the quality of map-based decisions under varying temporal usage constraints.

3 Previous Own Work: Experiments and Expert Interviews

In order to fill the existing research gap between time pressure research and empirical map design and map use studies, we have been conducting a series of controlled experiments on map-based decision making under time pressure. We complemented these studies by expert interviews with professionals in the field of map-based decision-making under time pressure. In the following, we summarize the main findings of this work which set the context for the slope detection experiment reported in Section 4.

In a first experiment on map use preferences for a road selection task under various time pressure conditions, we found that participants preferred realistic-looking orthographic satellite image maps and perspective views with hill shaded relief when they were not under time pressure (Wilkening, 2009). However, these preferred image maps were rated significantly less useful when under time pressure. In contrast, preference ratings for the more abstract looking topographic or road maps (i.e., without hill shading) were not affected by time pressure.

In a second experiment, we assessed users road selection task performance in flat urban terrain. The roads were depicted either on a satellite image map or on a standard road map, under varying time pressure scenarios (Wilkening, 2010). The map display type did not affect participants accuracy scores. However, participants reported a significantly higher confidence in their performance with satellite images compared to the more abstract road maps. This over-confidence in realistic depictions has been discovered in prior work (Hegarty et al., 2009; Smallman and St. John, 2005; Fabrikant and Boughman, 2006).

In our road selection experiment, shorter decision time limits resulted in a significant decrease in participants confidence, but not in accuracy. In other words, while we did find a speed-confidence trade-off effect, we did not find strong evidence for a speed-accuracy trade-off.

After having obtained some first insights on map type preferences and task performance under time pressure by non expert map users, we were interested in interviewing professionals who perform map-based decisions under time pressure on a daily basis, specifically within a more complex three-dimensional context. For this reason we interviewed, amongst others, search and rescue helicopter pilots and


professionally trained mountain guides. Both professional groups mentioned that they were generally satisfied with using the classic 2D topographic map for their routine work. In the age of 3D interactive globe viewers, and location-aware mobile displays, we found that the static, two-dimensional topographic map on paper is still the state-of-the-art for professionals dealing with real world emergency situations under time pressure. One reason could be that the majority of search and rescue personnel have been specifically trained with these maps, can read them well, and thus are generally comfortable with using them. These interviews confirm findings from our first experiment that familiarity (and training) with a display can positively influence usage preference, especially when under time pressure (Wilkening, 2009).

For both helicopter flying and mountaineering activities, accurate slope identification is very important. For example, a helicopter must assess the steepness of the terrain for landing (Bloom, 2007), and for a mountain guide the steepness of a slope needs to be regularly assessed for determining the avalanche potential when on a ski tour during the snow season (Suter, 2007). As the depiction style of the thematically relevant third dimension might be important for these kinds of tasks, we specifically chose a slope detection task for our next experiment, which is described in detail the next sections.

4 Experiment

As mentioned earlier, in own prior work we discovered a significant effect of time pressure on user preferences and response confidence for realistic 3D-looking maps in a 2D task context, while actual performance did not seem to be affected by the verisimilitude of the display. In this study, we are interested how 3D realism might affect participants response accuracy and confidence for a task under time pressure that specifically involves decision-making within a 3D context.

We asked task domain novices, that is, people who might be familiar with maps, but have never used maps for landing a helicopter, to identify locations on various map stimuli where a helicopter could land. The previously interviewed professional helicopter pilots had mentioned inclines of less than 14% (or 8 degrees) for safe helicopter landing. This threshold seems to be a standard in the literature (e.g., Bloom, 2007).

We again selected three time pressure scenarios with time limits what were identified through pilot testing. The experiment follows a within-subject design, where each participant was exposed to all time constraints and display types.

4.1 Participants

Fifty-five (32 male and 23 female) participants took part in this study. Participants were either students or staff at the Department of Geography at the University of Zurich and the Institute of Cartography at the Swiss Federal Institute of Technology in Zurich. The majority of participants stated to be rather familiar with topographic maps (58.2%) and 3D displays (61.8%), while 32.7% reported to be very familiar with topographic maps, and 14.5% to be very familiar with 3D depictions. While our sample represents the more experienced map designer and user, the participants are not experts in the slope detection task domain, and do not represent experts in map-based decision making under time pressure.


4.2 Materials

We created twelve map displays in total, depicting mountainous areas in Switzerland. All maps were of identical size (389x355 pixels), and included a scale bar on the upper right of the display (see Figure 1). The elevation data for the stimuli were derived from the SRTM3 Digital Elevation Model (Jarvis et al., 2008). Slope information could be identified with two pieces of information depicted in the stimulus: the scale bar next to the map and the contour lines in the map. The map scale was held constant at 1:20,000 (run), and the contour line interval was held constant at 100m (rise). The twelve maps represent the elevation data in four different ways:

1. Contour lines only (map a) 2. Contour lines plus light hill shading (map b) 3. Contour lines plus dark hill shading (map c) 4. Contour lines plus colored slope classes (map d)

While all map types are suitable for identifying slope, the depiction methods systematically vary in the degree of the depicted realism (i.e., shaded relief vs. contour line maps), in the apparent visual clutter (i.e., contour line vs. shaded relief maps), and in the information content for detecting slope suitability (slope vs. contour line maps). In other words, the maps are neither computationally nor informationally equivalent (Simon and Larkin, 1987; Fabrikant et al., 2008).

Map (a) in Figure 1, containing only contour lines, represents the most abstract of the tested map types, and with the least amount of information (i.e., implicit slope information). Maps (b) and (c) additionally contain a shaded relief (i.e., explicit relative slope information), thus more information than map (a). Users can obtain slope information not only (implicitly) from the distance between the contour lines (a), but also from the relative darkness of the pixels (maps b+c). The steeper the slope, the darker is the appearance of the relief. To investigate the potential effect of the graphic quality of the hill shading, we created a lighter version (b) and a darker version (c) of the hill shaded relief maps. We employed the hill shade function available with the 3D Analyst Toolbox in ESRIs ArcGIS. The light source for the hill shading was set to a 45 angle for the lighter relief (map b) and to a 22 angle for the dark relief (map c), respectively.

Based on Simon and Larkin (1987), we hypothesize that the more implicit the depiction of the task relevant information (i.e., map a), and the higher the amount of task irrelevant information (i.e., maps b+c) the more reasoning effort is needed when making decisions with these maps.

While our interviewed map-based decision-making professionals did not use slope maps (map d) for their daily work, they considered them as nice-to-have, so we included them in our study. The slope maps contain most task-relevant information in our tested maps. They show slope information explicitly in the map, and the respective information is explained in the accompanying legend, thus, should be easiest to use for task domain novices. Slope was calculated in ESRIs ArcGIS and depicted in a diverging color scheme, employing the traffic light metaphor (green = go, red = stop). Slopes that are flat enough for a helicopter to land (i.e., below 14% steepness) are depicted with green shades, while slopes that are too steep for landing (i.e., above 14%) are shown in magenta shades (Figure 1d). We define amount of


realism as a degree of verisimilitude with the real world (Zanola et al., 2009). We thus contend that shaded relief maps (b+c in Figure 1) look more realistic than a contour map (Figure 1a), because contours cannot be seen in the real world.

Fig. 1. Reduced examples of employed map stimuli: only contour line map (a), light hill shaded relief map (b), dark hill shaded relief map (c), and slope map (d)

Finally, the four tested map types also vary in graphic quality, or negatively put, in their degree of visual clutter. In Rosenholtz et al. (2007)s terminology, clutter relates to the degree of perceptual organization of information in a display. The more organized a display, the less visual clutter (detracting information) it contains for a given task. We quantitatively assessed this purely bottom-up vision concept in our test displays by means of the Subband Entropy clutter measure, proposed by Rosenholtz and colleagues. This measure, also empirically validated with map displays, is based on the notion of clutter as related to the efficiency with which the image can be encoded and inversely related to the amount of redundancy and grouping in the image (Rosenholtz et al., 2007, p. 18). Subband entropy seems to be a good predictor for human map-reading performance under time pressure. The higher the subband entropy measure for a display (i.e., the more clutter), the less computationally efficient the extraction of information encoded in the image (Simon and Larkin 1987). To exemplify this measure, we computed subband entropy for the four stimuli shown in Figure 1, and find most clutter in the slope map (3.75), followed by the dark hill shaded relief (3.31), the light hill shaded relief (3.27), and lastly, the contour map (3.25). While the slope map is graphically more cluttered than the others (e.g., it includes an additional visual variable color), it shows the task relevant information


explicitly (i.e., in the legend), thus despite perceptual clutter one would expect this map to need less reasoning effort to extract the task relevant information. The investigated factors are summarized in Table 1 below.

Table 1. Comparison of the map types used in the slope detection experiment. The amount of information is indicated with + (low) to +++ (very high).

contour map shaded relief maps slope mapdegree of realism (+) (++) (+)

depiction type (elevation information)

lines of equal elevation (absolute)


&shaded relief

(relative)


&slope classes

(absolute)slope information type

(amount)implicit

(+)implicit

(++)explicit (+++)

visual clutter (Subband Entropy)

(+) (++) (+++)

reasoning effort (+++) (++) (+)

The locations participants had to assess for potential helicopter landing were represented with black labels (numbers) on a yellow background to maximize saliency. Each stimulus contained six such locations for assessment. No other pieces of information (such as labels of place names) were contained in the map. We ran a saliency model (Itti and Koch, 2001) on our test stimuli, to make sure that the saliency of the decision points was not significantly influenced by the tested map types.

4.3 Procedure

The experiment took place in a lab equipped with standard personal computers connected to the Internet. The experiment was carried out digitally in a web browser displayed on a 17-inch computer screen set to 1280x768 pixel screen resolution. After filling out a background questionnaire, participants were then asked to safely land a helicopter on slopes not steeper than 14%. To assure that participants all had the necessary background to complete the task, they were first introduced to the slope concept and how slope can be calculated. They were shown how slope can be identified in a contour line map using the elevation information displayed with labels on the contour lines, and the ground distance information contained in the map scale bar. No other task relevant information was given to the participants. Participants were then asked to solve two warm-up tasks, which were identical to the actual experiment, which is described below.

Then, they were shown the sequence of twelve maps described in the previous section. The order of the stimuli was systematically rotated to prevent learning biases due to potential ordering effects. For each map, participants had to select one or more locations that were flat enough for a helicopter to land, by clicking the respective checkbox below the map. For each map, six locations had to be assessed. The number of correct locations varied randomly from 1 to 5 per map. Overall, 50% of the labeled slopes were too steep to land a helicopter.


Subjects had to solve the slope detection task under all three time constraint conditions, including 20s (most severe), 40s (moderate), and 60s (least severe) time limits and for all map display types described earlier. After completing each task, participants were asked to rate their confidence of response on a scale from 1 not confident at all to 4 very confident. Participants were not under time pressure when asked to rate their response confidence. Responses were collected digitally and included participants accuracy (percentage of correct answers) as well as (self-reported) confidence as success measures. After completing the digital portion of the experiment, participants were debriefed, and given a meal voucher for the university cafeteria in return for their participation. The experiment took approximately 15 minutes to complete.

4.4 Signal Detection Analysis

The conceptual framework of signal detection theory (SDT), which was originally developed for research on visual perception (Tanner and Swets, 1954), can generally be employed for decision-making under uncertainty, and especially when decisions have to be made based on two or more alternatives. The benefits of using this framework for our research context is that response accuracy can be assessed with more analytical depth than just comparing correct and false answers. In SDT correct answers are coined hits or correct rejects, and errors are called misses or false alarms, respectively. This analysis framework can especially help us to identify which kinds of errors participants might make, due to varying time constraints and map display types, and thus if errors might follow a particular pattern.

Applying this concept to our slope detection experiment, correctly selected locations per question are classified as hits (14%, see Table 2 below). Participant answers that are incorrect are classified as either misses or false alarms, respectively. A miss indicates a location that was not selected, even though it is correct (14%). In other words, a miss is an overestimation of slope, while a false alarm represents the underestimation of a slope. Table 2 illustrates how we classify four possible types of responses within the data analysis framework of Signal Detection Theory.

Table 2. Classification of correct and false answers according to Signal Detection Theory

RealityParticipants decisions Slope too steep (> 14%) Slope flat enough ( 14%) correct reject (true) miss (false)Slope flat enough (


5.1 Time Pressure Effect

Overall participants average response accuracy and confidence ratings shown in Figure 2 reveal a surprising and counterintuitive pattern. Participants are most accurate with the moderate time limit of 40s (M=82.8%, SD=11.4%), followed by the most generous time limit with 60s (M=72.2%, SD=15.2%), and lastly, as expected, the most severe time limit of 20s (M=66.7%, SD=20.4%). Similarly, participants self-reported confidence is also highest for the moderate 40s time limit (M=2.86, SD=0.44), followed by the least severe 60s limit (M=2.73, SD=0.15) and, lowest, again as expected, for the most severe 20s limit (M=2.67, SD=0.20). The performance increase from the 20s time limit to the 40s limit, and the performance decrease from the 40s to the 60s time limit are all significant for both accuracy and confidence (p< .001).

Fig. 2. Average accuracy and confidence per time pressure limit. Error bars: 2 Standard Error (SE).


5.2 Map Type Effect

As expected, participants accuracy was significantly better with the slope map (M=83.6%, SD=14.8%) compared to all other maps, as shown in Figure 3. However, accuracy was not better as predicted, but even worse with the shaded relief maps compared to all other maps. Participants mean accuracy for the light hill shaded relief map is 73.1% (SD=16.8%), and with 65.4% (SD=18.5%) it is lowest overall for the dark hill shaded relief map. Surprisingly, participants perform even worse with the hill shaded relief maps that look more realistic, and contain more information than the most abstract contour map (M=73.5%, SD=13%). The difference between the contour map and the light hill shaded relief map is significant (p< .01), as well as the difference between the slope map and all other maps (p< .001).

As can be seen in Figure 3, in congruence with the accuracy response pattern, participants confidence ratings are also highest for the slope map (M=3.13,

Fig. 3. Accuracy and confidence ratings for tested map display types ( 2 SE)


SD=0.55), and higher for the contour maps (M=2.67, SD=0.47), compared to the lowest scoring hill shaded relief maps (dark: M=2.64, SD=0.47 and light: M=2.52, SD=0.47). Surprisingly again, participants have significantly higher confidence in their performance with the contour map, compared to the light hill shaded relief map (p< .05) that contains more information.

The power of signal detection theory lets us analyze response accuracy in more detail. Overall, regardless of map type, misses (i.e., slope overestimation) occur more frequently than false alarms. Misses occur also more frequently than false alarms, independent of the tested time limits. The correct rejection is overall the more frequent correct answer than the hit, also for all map types and all temporal conditions. As expected, the number of false alarms (i.e., slope underestimation) shown in Figure 4 is significantly higher for the light hill shaded relief map (M=2.00, SD=1.75) than for the dark hill shaded relief map (M=1.18, SD=1.23). In contrast, the number of misses (i.e., slope overestimation) is, again as expected, higher with the darker hill shaded relief map (M=2.67, SD=1.77) compared to the light shaded relief (M=2.05, SD=1.69).

As shown in Figure 4, SDT provides additional insights on what kinds of decision errors might have specifically contributed to the unexpectedly low accuracy for the shaded relief maps. Similar to the other map types, participants seem to overestimate the steepness of the slopes more frequently with the dark hill shaded relief maps (i.e., higher number of misses) compared to the light shaded relief maps. Hence, a map with a lighter shaded relief might help reduce this potential source of error. However, one can also see in Figure 4 that one drawback of light hill shaded relief maps might be their relatively high rate of false alarms.

Fig. 4. Misses and false alarms with shaded relief maps ( 2 SE). The maximum number of possible errors is 9 per map type.

5.3 Interaction of Map Type and Time Pressure

We now turn to the research question how map types might support participants in their decision-making under varying time pressure scenarios. Participants gave most


accurate answers with the (explicit) slope map under all time constraint conditions (see Figure 5). In the most severe time limit condition (20s), participants scored better with the most abstract contour map (M=71.2%, SD=30.5%), containing least amount of information, compared to the more realistic looking shaded relief maps (dark: M=63.9%, SD=27.9% and light: M=53.3%, SD=40.1%). For this shortest time limit, the overall differences between tested map types are significant (p< .01 for both shaded relief maps). Accuracy scores generally increase from the most severe (20s) to the moderate (40s) time limit condition. The accuracy differences between maps are not significant in the moderate condition. Overall, accuracy scores drop again for the highest scoring slope and contour maps under the least severe time constraint condition (60s), while accuracy scores for the hill shaded relief maps do not change much for the 40s and 60s limit conditions. In other words, participants accuracy with hill shaded relief maps only reaches the higher level of the other more abstract map types when participants are not under severe time pressure.

Fig. 5. Participant average accuracy per map display type and time limit

A very similar response pattern can be observed in Figure 6, when looking at participants confidence ratings. Again, mirroring accuracy scores, participants are most confident in their responses with the slope map, regardless of the given time limit. Participants confidence is also consistently high with the contour line map.

The difference between the average confidence ratings for the slope map and the shaded relief maps is only significant at the 20s time limit. For this shortest time limit, the average confidence rating with the contour map is 2.58 (SD=0.08) and 2.30 (SD=0.07) with the shaded relief map. The rating difference between the contour map and both hill shaded relief maps is significant (p< .001).

Only in the moderate time limit condition (40s), confidence ratings for the hill shaded relief maps are higher than for the contour map. This is in contrast to participants accuracy scores shown in Figure 5 earlier, where participant performance is better with the contour map that the shaded relief maps.


Fig. 6. Participant average confidence per map display and time limit

6 Discussion

Summarizing our results, we find that indeed, response accuracy and confidence ratings are worst when under highest time pressure, but best when participants are under a moderate response time limit. Both scores decrease significantly when participants have more decision time available. These results, which seem somewhat counterintuitive, do resemble the previously discovered inverted U-shaped response curve found by Hwang (1994), but not related to map-based decision making.

Based on Johnson et al.s (1993) and Hwangs (1994) research results reviewed earlier, changes in speed-accuracy and speed-confidence trade-offs might be a consequence of task difficulty. As both response accuracy and confidence decreased with a time limit more severe than 40s, this slope detection task might have become significantly more difficult when participants had less than 40s to respond. As a result, we do find a clear speed-accuracy and speed-confidence trade-off effect. Participant performance did not further increase from the moderate to the least severe time limit, thus the slope detection task is not getting easier with more available decision time beyond the 40s time limit. In this study, the tipping point to which time pressure actually increases performance seems to be in the vicinity of 40s decision time. This pattern is in contrast to our previous road selection task study, where we did not find a time pressure effect on response accuracy, even with overall shorter decision time limits, down to even 10s decision time. One could argue that the road selection task on flat terrain is significantly less complex than a 3D slope detection task, and thus speed-accuracy and speed-confidence trade-offs are generally harder to find. This difference in task complexity might be one of the main reasons for the non-repeatability of the results of Experiment I.

Regarding the decision performance differences due to different the map types, surprisingly, participants accuracy and response confidence was unexpectedly low with the shaded relief maps. This result supports prior work by Hegarty and colleagues (Hegarty et al., 2008; Hegarty et al., 2009), who have shown that more


realistic, 3D-looking displays while often preferred by nave users, do not necessarily increase performance. While three-dimensional shaded reliefs provide more task-relevant (but implicit) information, compared to the more abstract contour map, this more on information does not lead to more effective (accurate) or efficient (faster) decision-making. One reason for this is might, arguably, be that the implicit thematically relevant information is not presented in a cognitively and perceptually adequate and inspired way (Swienty et al., 2008; Fabrikant et al., 2010). While the hill shaded relief maps might contain more explicit task-related information than the contour maps, they are also more cluttered (Rosenholtz et al., 2007), and thus might require more time for participants to visually parse. As Tufte (1983) would put it, the task-relevant data to graphic ink ratio in the visuo-spatial display is not optimized for the task at hand. On the other hand, while the slope maps exhibit the highest clutter values of the tested displays (see Table 1), the task-relevant data to graphic ink-ratio is indeed optimized for the task at hand. In fact, running a saliency model (Itti and Koch, 2001) on the stimuli, we find only one significant difference between the slope map and the other three tested map types (see Figure 1). The area along the bottom edge of the maps, where the density of the elevation contours is highest (i.e., the steepest area in the map), the slope map also shows darkest magenta shades between the contour lines. Moreover, the visual variable color hue seems not to have much influence on this saliency map pattern, as running the saliency model on a gray scale version of the slope maps (i.e., removing color hue) yields an identical saliency map pattern. Another possibility why the more abstract maps could have performed better under time pressure is that our 3D maps with high graphic density might have a general relative disadvantage when shown at smaller screen sizes with lower spatial display resolution than the 2D maps.

However, participants do perform better with the shaded relief maps compared to the more abstract contour line map when they have more decision time available, and also seem to be more confident in their responses when under less time pressure. In this case, participant performance and confidence seem to reflect participant preferences, when we compare results from this study with the results from a prior map use preference experiment (see previous work Section 3), in which more realistic 3D looking satellite image maps obtained higher preference ratings when participants have more decision time available. In other words, we did not find strong evidence for a nave realism effect (Smallman and St. John, 2005), or over-confidence in realistic-looking maps in this experiment, as low accuracy scores co-occurred with equally low confidence ratings for the tested shaded relief maps. This could be due to the fact that our participant sample consisted mainly of cartographic (design) professionals, and thus not nave cartographers.

Not surprisingly, the 2D slope maps, containing most of the thematically relevant information, outperformed all other map types with respect to effectiveness (i.e., accuracy) and efficiency (i.e., under all time limits), including participant confidence. In this case, in contrast to the shaded relief maps, the information increase had a positive effect on response accuracy and confidence, even though perceptually these maps appeared to be most cluttered (see Table 1). Reasons for this could be that the slope map already explicitly contains an intrinsic reasoning step (i.e., slope computation). This more on thematically relevant information is communicated in a cognitively adequate (explicit), and perceptually salient way, using empirically


validated cartographic design principles (Fabrikant, Rebich-Hespanha and Hegarty 2010). In other words, participants can perform well and be confident in their decisions even with an abstract (but computationally efficient) depiction method, but only when thematically relevant information is communicated explicitly and rendered in a perceptually salient manner. It would be thus interesting to further investigate how different ways of representing slope information might affect the outcomes of map-based decision making tasks under time pressure. Although slope maps are not commonly known or used by map-based decision-making experts under time pressure, or the general public, our expert interviewees did find them useful, and had no problem in detecting the relevant information without any training.

7 Summary and Outlook

In this study, we investigated how display types might affect peoples decision making when solving a complex slope detection task under varying time pressure conditions. Replicating previous work (Andrews and Farris, 1972; Hwang, 1994) we discovered an inverted U-shaped accuracy response curve which implies that moderate time pressure can have a positive effect on map-based decision-making, but only up to a certain tipping point, which seems to be around 40s in our study. Moreover, confirming long-standing (but rarely empirically validated) cartographic design theory (Bertin, 1967), we found that more abstract, but well designed contour and slope maps outperform more preferred realistic, 3D-looking hill shaded relief maps for the 3D slope detection task in our study. This might suggest that the benefit of explicitly communicating thematic relevant information, even in a graphically abstract way (i.e., higher cognitive cost), is greater for efficient and effective map-based decision-making, than adding preferred and attractive, but visually more cluttered realism (i.e., higher perceptual cost). Low participant performance with shaded relief mapseven lower than the more abstract contour maps, containing even less informationsuggest that visual realism might negatively influence decision-making, especially when under time pressure.

Future experiments in varying map-based decision making contexts with different task complexity levels should be conducted to further investigate the generalizability of these somewhat counterintuitive findings, involving 1) performance decreases with more available decision time, and 2) surprisingly poor performance with shaded relief maps. For example, one could vary display sizes and the ways of representing slope information, in order to investigate the robustness of our findings.

It is unclear at this point how performance is affected by user background and training. In future related studies, participants with less cartography training could be tested in similar time pressure contexts, in order to compare previous results by Hegarty and colleagues (2009), who have found higher preferences for 3D maps among nave cartographers.

Finally, we also encourage like minded researchers in GIScience and cartography to more often try to analyze response accuracy with the signal detection approach and to explore in which context misses or false alarms are the dominant types of errors, and how individual and group differences might influence hit and false alarm rates. For example, we found a higher number of misses compared to the number of false


alarms in our experiment. One explanation for this play-safe strategy in this safety-critical task context could be that our participants, not trained in helicopter landing, might have rather preferred to miss a suitable landing spot, than landing on unsuitable terrain, with potentially life-threatening consequences (e.g., see the work of Hofer and Schwaninger (2005) relating to baggage screening tasks).

Future empirical map design and map use studies could thus focus more on the question of what kinds of errors might result in low accuracy rates, and this might in turn lead to more focused map design guidelines.

Acknowledgements. We would especially like to thank all our participants who were willing to participate in this study. We are also indebted to Christian Hberling from the Institute of Cartography at the Swiss Federal Institute of Technology Zurich, who gave us the opportunity to conduct our experiments in his cartography classes. Finally, we are grateful to our interviewees at Protection & Rescue (Schutz & Rettung) and Swiss Air Rescue (Rega) in Zurich, and at the Institute for Snow and Avalanche Research (SLF) in Davos, Switzerland, for sharing their expert insights on map-based decision making under time pressure.

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Towards Cognitively Plausible Spatial Representations for Sketch Map Alignment

Malumbo Chipofya, Jia Wang, and Angela Schwering

Institute for Geoinformatics, University of Muenster, Germany {mchipofya,jia.wang,schwering}@uni-muenster.de

Abstract. Over the past years user-generated content has gained increasing importance in the area of geographic information science. Private citizens collect environmental data of their neighborhoods and publish it on the web. The wide success of volunteered geographic information relies on the simplicity of such systems. We propose to use sketch maps as a visual user interface, because sketch maps are intuitive, easy to produce for humans and commonly used in human-to-human communication. Sketch maps reflect users spatial knowledge that is based on observations rather than on measurements. However, sketch maps, often considered as externalizations of cognitive maps, are distorted, schematized, incomplete, and generalized. Processing spatial information from sketch maps must therefore account for these cognitive aspects. In this paper, we suggest a set of qualitative spatial aspects that should be captured in representations of sketch maps and give empirical evidence that these spatial aspects are robust against typical schematizations and distortions in human spatial knowledge. We propose several existing qualitative spatial calculi to formally represent the spatial aspects, suggest appropriate methods for applying them, and evaluate the proposed representations for alignment of sketch maps and metric maps.

Keywords: cognitive qualitative representation, sketch map, qualitative spatial reasoning, sketch alignment.

1 Introduction

Sketch maps are an intuitive way to express human spatial knowledge about the environment. They contain objects which represent real world geographic features, relations between these objects, and oftentimes symbolic and textual annotations [4]. These elements enable us to use sketch maps to communicate about our environments and to reason about our actions in those environments. In this way, sketch maps provide an intuitive user interaction modality for some geospatial computer applications [9]. Especially with the advent of Volunteered Geographic Information (VGI) [13], sketch maps may be the key to removing some of the barriers imposed by the technical requirements of traditional Geographic Information Systems (GIS) as noted by [27]. Sketch maps, however, do not have a georeferenced coordinate system. Therefore, in order to allow users to contribute and query geographic information using sketch maps, an automated system must be able to analyze them and establish correct

Towards Cognitively Plausible Spatial Representations for Sketch Map Alignment 21

correspondences between elements of a sketch map and elements of other spatial data sources [35], be they sketch maps or metric maps. The analysis involves extracting and characterizing useful information, such as depicted objects, from a sketch map and establishing correspondences involves describing the relationship between elements of the sketch map and elements of the other data source. This is also known as alignment if the spatial relations among the elements are of primary interest.

For a system to perform the tasks described above it must have models that support cognitively plausible sketch map representations. Because human spatial thinking is inherently qualitative [12], such representations may also be expected to be qualitative in nature. Indeed many approaches to sketch map representation [9, 11, 16, 28] attempt to capture some qualitative aspects of the sketch maps by abstracting away from the geometric information. Qualitative representation of spatial knowledge involves representing only the relevant distinctions in a spatial configuration. For example, orientations with a predominantly northerly heading can all be regarded as belonging to the qualitative orientation North. Qualitative representations together with logical and algebraic mechanisms for performing some useful computations on them form what are known as qualitative calculi [8] and their study as Qualitative Spatial Reasoning (QSR).

It has been noted that the most useful aspects of space from a QSR perspective are topology, orientation, and distance [25]. However the cognitive reality of sketch maps requires consideration of the reliability of every aspect of space used. For instance, it is known that sketch maps have inconsistent scale and perspective [4]. This is in part due to omissions, simplifications, exaggerations and other types of distortions introduced at the different stages of observation, perception and memorization of spatial information [33, 34]. These factors must therefore be taken into account.

This paper proposes a set of formal qualitative spatial representations for sketch maps that minimizes the effects of cognitive distortions during alignment. Each representation captures an aspect of sketch maps that is likely to be represented correctly with respect to a metric city map. Only sketch maps of urban areas were considered in the studies reported in this paper. The next section briefly reviews sketch map representation and alignment methods. In section 3 results of an empirical study into criteria for obtaining a cognitively plausible sketch map alignment are presented. Based on the identified criteria five qualitative calculi have been used to formalize the spatial configuration information of objects in sketch maps. The resulting representations are discussed in section 4 and an evaluation of their application on three sample sketch maps is discussed in section 5. Section 6 concludes the paper with a summary and outlook on future work.

2 Background

2.1 Alignment of Spatial Information from Sketch Maps

Alignment of spatial information requires identifying two spatial configurations or so called scenes [23] that are similar. The central question in spatial scene similarity is how to establish the associations between the elements of one scene and those of another scene. Here, we describe two approaches developed recently. Both were proposed for alignment of spatial sketches or sketch maps with metric maps.

22 M. Chipofya, J. Wang, and A. Schwering

Spatial scene similarity [22, 23] applies spatial alignment as part of a query procedure. They seek to align the structure of a query scene with that of another scene. A spatial scene query comprises a set of spatial objects and relations between the objects. A query is formulated as a spatial constraint satisfaction problem (CSP). The evaluation of the query then involves finding configurations in the database that satisfy all the constraints of the query. This is achieved by constructing an association graph which consists of a set of pairs of variables (objects in the query and database). The set of pairs are the nodes of the association graph, while the set of combined constraints become the edges of the graph. The final solutions to the query comprise all maximal complete subgraphs (maximal cliques) of the association graphs.

Qualitative Matching is a similar approach suggested in Wallgrn et al. [35]. It represents a sketch map as a set of qualitative constraint networks (QCN) aspect by aspect. Each QCN is based on a specific qualitative spatial calculus. A matching problem is then defined as follows: for each possible pairing of nodes from one QCN with those from the other, find all consistent combined QCNs that satisfy the constraints from both original QCNs.

2.2 Formal Representation of Sketch Maps

Both of the above methods can be used to align sketch maps over several aspects of space and suitable representations of the sketches are required for the alignments to be performed. In [9] Egenhofer used topological and directional relations in sketches to formulate geospatial queries for real spatial databases. Additional semantics of the spatial relations in the sketch can be obtained by a quantification of the extents to which pairs of objects interact with respect to each given relation [10].

Forbus et al. [11] consider a sketch as being composed of logical units called glyphs. A glyph has two components, the geometry, which is what the user draws, and a conceptual entity which refers to the concept implied by the geometry. The model considers three main types of spatial relations: positional relations given by cardinal directions (South, East, North, and West), adjacency relations captured by the Voronoi diagram of the outer contours of the glyphs, and topological relations computed between bounding boxes of the glyphs. This information can then be used, for a specific domain, to infer other information such as visibility (camouflaged or contrasted from background). In Kopczynski and Sester [16] concepts such as street or park represent objects in the sketch map. Objects and spatial relations are embedded in a conceptual graph structure and used to generate spatial queries.

2.3 Cognitive Aspects of Spatial Knowledge

All the above cited methods attempt to capture some abstract, qualitative aspects of the sketch maps by abstracting away from the geometric information. However, they ignore the influences from human spatial cognition on sketch maps, and as a result fail to explicitly account for schematizations and distortions from cognitive errors [33, 34]. In general, sketch maps are characterized by inconsistent spatial scale and perspective and contain schematizations and distortions from human spatial cognition.

The following gives an overview of important findings about how humans observe and perceive their environments: people make systematic errors in judging orientation of spatial objects that are located in different geographical or political units [29];


distortions due to perspective and due to landmarks are common in spatial judgments, e.g., distances between near spatial objects are considered relatively longer that distances between far away objects [14]; ordinary buildings are judged closer to landmarks than the other way around [18, 26]; routes are judged longer with more turns, more landmarks [31] or more intersections; spatial information is simplified in the cognition process: angles tend to be perceived more rectangular [15] and curved features are perceived straighter [6, 19]. While sketch maps are used for representing spatial information from human memories, such cognitive errors appear very often and have negative influences on sketch map accuracy [36] making direct sketch map alignment unreliable. In addition, omission of information and inclusion of extra information in the form of symbols and annotations occurs quite often [32] and contributes to the difficulty of automating sketch map alignment.

Thus, a cognitively plausible representation for sketch maps is necessary. The abovementioned representations of sketch maps do not provide empirical evidence for the qualitative or quantitative aspects reflected in the representations and also do not evaluate the cognitive adequacy of the chosen representational formalisms. In contrast, the representation proposed in this paper is motivated by cognitive insights into human spatial cognition and thinking obtained in the empirical study described below.

3 Empirical Study: Criteria for Sketch Map Alignment

To succeed in aligning a sketch map and its corresponding metric map, relevant sketch aspects for alignment are required. A list of such sketch aspects might constitute sufficient criteria for performing sketch map alignment with some success. To this end, an empirical study1 was conducted to investigate relevant aspects of sketch maps. The study was divided into two phases: first, during the experiment, participants were asked to draw three locations from their memory on the paper; second, sketch maps were compared with metric maps while six sketch aspects were analyzed. In the end, a list of sketch aspects was concluded as the criteria for sketch map alignment and used to develop suitable formal representations for the task.

3.1 Experiment

Participants. There were in total 25 university students joined the experiment with the age range between 19 and 29 (average age of 23 years with a standard deviation of 2.4 years). Among these 25 participants, 14 are male and 11 are female. All the participants joined the experiment gratuitously and assured to have no specific knowledge in cartography and geography and also no particular advanced skills in art. Though none of the participants are residents of the locations, all of them are familiar with the areas sketched by frequent visit by foot or vehicle. During the experiment, participants were asked to produce sketch maps with as much detail as possible but only from memory. There was no time limit during the sketching task, since this might pressure the participants and could influence the final sketch map quality.

1 This experiment was conducted in the Spatial Intelligence Lab at the Institute for

Geoinformatics, University of Muenster. For a detailed description of the experiment we refer the reader to [5].


Materials. Each participant was given a piece of DIN-A4 sized sheet of paper and a black pen. Rules and other assisting drawing and measuring tools were not allowed. Before participants producing sketch maps, a sample sketch map was shown to give an example of how a sketch map could look like.

Locations. There were three locations that participants were asked to sketch. All locations were urban areas with paved and built up regions. Besides straight and curved main streets, side streets and various types of buildings as shops and restaurants, the locations also contain natural areas as lakes or grasslands. The area of location I is a part of the inner city of Brueggen with landmarks such as lakes like Laarer See and steep hill as the sketching boundary; the area of location II is along the route which is across the pedestrian zone of Brueggen from the south to the north; the area of location III is in the city of Muenster which has the Ludgeri-Kreisel as its center and with a radius of approximately 1km. Location I and III are with the similar size of 1.5km2 and they were sketched as survey maps. Location II has a route with an overall length of 700m and was sketched as a route map. The time that participants spent and the sketch maps that we received are shown in Table 1.

Table 1. Time that participants spent and the sketch maps received in the experiment

Location I Location II Location III Time Ave (StdDev) 21.7min (11.4) 16.3min (9.9) 14.8min (4.6) Total sketch maps analysed 12 12 5

3.2 Methodology of Sketch Map Comparison

Sketch maps of each location were analyzed and compared with the corresponding metric map2. Six sketch aspects were analyzed during the comparison procedure. These sketch aspects were derived from the former studies of sketch map analysis and comparison [36], and they are related to sketched objects such as landmarks and street segments as well as binary relations sketched such as the topological, directional and order relations of sketched objects. In the context of sketch maps, sketched objects and sketched relations refer to:

Objects Sketched. Landmarks are defined as subjective points of interests, which are the most memorable spatial elements to the participants [5]. So, landmarks could be any spatial objects people draw except for streets. Street network refers to a collection of street segments that connect pairs of junctions. A street segment is a piece of a street which is a linear feature for the means of travelling by foot, bike or vehicle whereas a junction is a specific location with which one or more street segments connect. Furthermore, the city block is defined separately out of the street network. A city block is a part of a street network and it provides more possibilities during sketch map alignment. It can be defined as either an open or a closed area that are surrounded by connected street segments.

Relations Sketched. During sketch map comparison, topological relations were calculated between a landmark and a city block. The street network orientation refers 2 The Deutsch Grundkarte 1:5000 (DGK 5) was used as the metric map source.


to directional relations of pairs of adjacent street segments. Order relations refer to two kinds of relations: one is the order of landmarks along a linear reference frame, which can be a street or a path-extent like water body; the other is the cyclic order of the adjacent landmarks around a junction.

In detail, the six sketch aspects are: topology of street network, street network orientation, order relations of landmarks along a street, order relations of landmarks around a junction, topology of city blocks and containment of landmarks in a city block.

3.3 Resulting Alignment Criteria

The valid sketch maps of three locations were analyzed manually. All the calculations were conducted between adjacent spatial objects. We got a larger set of sketch aspects, which might be the criteria for alignment. Among them, the six sketch aspects that we defined are with the highest accuracy rate (see Table 2).

Topology of street network represents the pattern of interconnection of street segments and junctions of a street network. The street network sketched is usually simplified and incomplete while it is much more complicated in the reality. This sketch aspect was calculated in the extracted street network graph with nodes representing junctions and edges representing street segments. Despite the missing and extra junctions and street segments, the connectivity of street segment and junctions sketched was with 100% accuracy for all three locations.

Street network orientation was calculated between a reference street segment and its adjacent street segments, i.e., the adjacent street segments and the reference street segment share the same junctions. A qualitative orientation model that divides the space into two regions, which are right and left, was applied in the calculation. This directional model is built in a way that it has its reference orientation line formed by a pair of two points, which are the start point3 and the end point4 derived from of the pair of two junctions of the reference street segment. The oriented reference line is always pointing from the start point to the end point. In our case, accuracy rate of direction relations was calculated separately of participants depending on what street segments they drew.

Table 2. Results of sketch map comparison

Accuracy rate Location I Location II Location III Street network topology 100% 100% 100% Street network orientation 100% 100% 100% Order along a route 100% 94% 100% Order around a junction 100% - - City block topology 100% 100% 100% City block containment 100% 99% 100%

- To calculate order of landmarks around a junction, at least two adjacent landmarks being around a junction is required. Location II and III do not fit this basic requirement.

3 The definition of the start and end points is not arbitrary. In route map, for each street

segment, the start point is close to the origin while the end point is close to the destination. In survey map, the definition is varied depending on the calculation.


The order of landmarks along a street shows high similarity with the metric maps. For both location I and III, 100% of all the landmarks sketched along the selected streets were placed in a correct order. For location II, along the route sketched, 94% of all the landmarks were correctly placed. In our case, missing landmarks were exclusive in the calculation of order relations.

During the experiment, we found that most of the landmarks were sketched either along the main streets or around junctions. Order relations of landmarks around junctions could also provide possibility for sketch map alignment. Location I was analyzed for this order relation and showed 100% match with its corresponding metric map.

The topology of city blocks is also represented in a high accuracy for all three locations. City blocks appear quite often while sketching. Although no participant sketched the complete street network, for the sketched street network, nearly 100% of the city blocks were represented by correctly connected junctions and street segments.

In the end, the containment of landmarks in city blocks also shows its reliability for sketch map alignment. For containment analysis, the experiment locations were split up into city blocks that have their scales varied among participants. Though small-scale city blocks formed by side streets were not sketched by all the participants, landmarks were still correctly placed in the relatively large-scale city blocks formed by aggregated street segments. For location I and III, 100% of the landmarks were placed correctly in the city blocks, and for location II, this accuracy rate is 99%.The results show that all the above six sketch aspects always show high similarity (>90%) with the corresponding aspects in metric maps. Also they appear quite often in sketch maps. The six sketch aspects were proofed in this empirical study that participants seldom made mistakes while sketching these aspects and they can be reliable criteria for sketch map alignment.

4 Formal Representations of Sketch Maps for Alignment

In order to reason about sketch maps, spatial information corresponding to the six criteria described above is represented using formal qualitative spatial calculi developed by the QSR community. A quick look at the six criteria indicates that the street network is of primary importance because all the other criteria depend on it. So the first step is to characterize the street network topology and relative orientations of street segments. Formal representations for the remaining four criteria are based on this characterization of the street network as a collection of street segments with some of their end-points coinciding at junctions to form a network topology. Wherever necessary, the end-points of a street segment will be distinguished as the start-point and end-point with regard to one of its two orientations.

4.1 Street Network Topology

The topology of street network can be captured using the connectivity information of the corresponding graph as is usually done in GIS [17]. However, a more explicit structure, DRA7 which is a coarsened version of the dipole relation algebra (DRA) of Moratz et al. [20], was introduced in Wallgrn et al. [35] and captures the topology of sets of oriented line segments. The oriented line segments are also known as dipoles


[20]. A dipole is an ordered pair of points in 2 which can be written as a = (as, ae), where as and ae are the start- and end-point of a respectively. A basic DRA relation between two dipoles A and B is represented by a 4-tuple of facts sBeBsAeA where sB is the position of the start-point of dipole B with respect to dipole A. The other three elements of the relation eB, sA, and eA are defined analogously. For DRA7 the possible positions of the start-/end-point of one dipole with respect to another dipole are s (coincides with the start-point

[lecture notes in computer science] spatial information theory volume 6899 ||

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