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Cognitive measurements of graph aesthetics
Colin Ware
1
Helen Purchase
2
Linda Colpoys
2
Matthew McGill
2
Data Visualization Research Lab, Durham, U.S.A.;
School of Computer Science and Electrical
Engineering, The University of Queensland, St
Lucia, 4072, Brisbane, Australia
Correspondence:
Colin Ware, Data Visualization Research Lab,
Center for Coastal and Ocean Mapping,
University of New Hampshire, 24 Colovos
Road, Durham, NH 03824, U.S.A.
Tel: 603 862 1138; Fax: 603 862 0839;
E-mail: colinw@cisunix.unh.edu
Abstract
A large class of diagrams can be informally characterized as node–link
diagrams. Typically nodes represent entities, and links represent relationships
between them. The discipline of graph drawing is concerned with methods
for drawing abstract versions of such diagrams. At the foundation of the disci-
pline are a set of graph aesthetics (rules for graph layout) that, it is assumed,
will produce graphs that can be clearly understood. Examples of aesthetics
include minimizing edge crossings and minimizing the sum of the lengths of
the edges. However, with a few notable exceptions, these aesthetics are taken
as axiomatic, and have not been empirically tested. We argue that human
pattern perception can tell us much that is relevant to the study of graph
aesthetics including providing a more detailed understanding of aesthetics
and suggesting new ones. In particular, we find the importance of good conti-
nuity (ie keeping multi-edge paths as straight as possible) has been neglected.
We introduce a methodology for evaluating the cognitive cost of graph
aesthetics and we apply it to the task of finding the shortest paths in spring
layout graphs. The results suggest that after the length of the path the two
most important factors are continuity and edge crossings, and we provide
cognitive cost estimates for these parameters. Another important factor is the
number of branches emanating from nodes on the path.
Information Visualization (2002) 00, 00 – 00. doi:10.1057/palgrave.ivs.9500013
Keywords: Graph layout; aesthetics; cognitive modeling; network visualization
Introduction
Many diagrams use boxes or circles to show entities and linking lines
drawn between them to represent relationships between the entities. An
example is a software structure chart where subroutines are shown as boxes
and the linking lines show which subroutines call each other. Other exam-
ples of node-link diagrams include organization charts, data flow diagrams,
flow charts and the set of diagrams encompassed by the unified modeling
language (UML).
1
Graphs are abstractions of node–link diagrams studied by mathemati-
cians, and the discipline of graph drawing has developed to investigate
methods for laying out graphs according to a set of aesthetic principles
that are assumed to improve readability.
2
Many of the principles and meth-
ods of graph drawing can be applied to the broad area of drawing effective
node–link diagrams and thus have the potential for wide ranging applic-
ability.
Some commonly applied graph layout aesthetics are the minimization
of edge crossings, displaying symmetry of graph structure, minimizing
bends in edges. However, despite the considerable effort that has gone into
constructing algorithms to optimize according to these aesthetics, surpris-
ingly little work has gone into the empirical validation of these aesthetic
principles. A notable exception is the pioneering work of Purchase
3
which
compared task performance on five pairs of graphs that were designed to
differ according to the aesthetic principles of edge bends, edge crosses,
maximizing the minimum angle, orthogonality and symmetry. This study
Received 2 January 2002
Revised 1 April 2002
Accepted 11 April 2002
Information Visualization (2002) 00, 00–00
ª
2002 Palgrave Macmillan Ltd. All rights reserved 1473 – 8716 $15.00
www.palgrave-journals.com/ivs
IVS 011_02
concluded that edge crossings was ‘by far the most impor-
tant aesthetic’ when compared with the other four
aesthetic criteria. However, the crossings conclusion itself
was based on only two hand drawn graphs, one with
many crossings and one with few. A visible inspection
suggests a number of confounding factors: in the version
with more crossings the geometric path lengths appear to
have been longer, there is a less even distribution of
nodes, and the paths appear to be less continuous than
the alternative (ie: their angular deviation from a straight
line is greater than the version with less crossings).
The results of the initial Purchase study suggest that
there is scope for more experimental work in this area.
Experiments that are more controlled, and which consid-
er a greater range of aesthetics within the same graph
drawings (rather than merely between two drawings
representing the extremes of each aesthetic) are more
likely to indicate the relative importance of the differing
aesthetics.
Perceptual and cognitive issues in graph aesthetics
Much of what we know about human pattern perception
originates with the early work of the Gestalt psycholo-
gists.
2,4
They produced a set of gestalt laws that
determine whether we see something as a ‘figure’ as
opposed to ‘ground’. One gestalt law that is especially
relevant to graph drawing is the principle of good conti-
nuation as illustrated in Figure 1. This suggests that we
will more easily see smooth continuous contours than
jagged ones. It also suggests that we will be able to inter-
pret Manhattan layout graphs (with only vertical and
horizontal lines) less easily than graphs that use smoothly
curved lines, because the continuous lines are more likely
to ‘pop out’ as perceptually complete objects.
5
More recent results from neurophysiology bear on the
issue of edge crossings in graphs. Rapid early-stage neural
processing is thought to underlie the tendency of certain
simple forms to ‘pop out’ from their surroundings.
6
At
the early stage of visual processing every part of the visual
field is processed in parallel with a set of orientation
tuned neurons that respond preferentially to bars with
particular orientations. These detectors are only coarsely
tuned, roughly within +308.
7
This suggests that when
edges cross at acute angles, they will be more likely to
cause visual confusion when rapid interpretation is
important, than when they cross close to 908. See Figure
2.
Cell assemblies are responsible for capturing entire
contours, and recent research has cast light on how they
may function, thereby giving the principle of good conti-
nuation a more robust empirical and theoretical
foundation. A set of experiments by Field et al
8
quantified
the good continuation principle, and their stimulus
design is illustrated in Figure 3. These studies showed that
when contour segments are aligned along a smooth curve
they are easier to see than when they are not, and the
ease with which the contour can be seen is a direct func-
tion of the continuity of the path. According to the
emerging theory, points detected along a curved edge
are linked together by a neural mechanism that allows
edges as a whole to be perceived through a set of local
rules that link the output of independent feature detec-
tors.
8
Whether individual cell tuning properties or cell
assemblies can best account for how easily people can
perceive paths in graphs is beyond current theory, but it
is likely that both levels of analysis are important.
Good continuation has two direct applications to
graph drawing. First, it suggests that a path will be more
readily perceived if the nodes are not in a zigzag pattern,
but form a smooth continuous sequence. This point is
illustrated in Figure 4. Good continuation also suggests
that curved lines can be used to make certain paths more
apparent (as illustrated in Figure 5) although this is not
the focus of our present study.
Our present study was motivated by two primary
concerns: we wished to follow up the earlier work of
Purchase using a more refined procedure to determine
the relative importance of different aesthetics. In particu-
lar we were interested in the problem of path continuity
(Figures 4 and 5). In many cases edge crossings can only
be reduced at the cost of constructing a more indirect
or less continuous path. If this were the case then algo-
rithms should be constructed that take both factors into
account.
The second goal was to place the value of graph
aesthetics on a firmer empirical foundation, by develop-
ing and applying a methodology for measuring the
cognitive cost of graph aesthetics. By using a large
number of trials and varying a set of interesting para-
meters we hoped to be able to deduce the relative
cognitive cost of different factors in graph layout (eg edge
crossings, path continuity, geometric line length).
Perceptual and cognitive modeling The discipline of
human-computer interaction (HCI) has developed simple
cognitive models of common computer interaction tasks,
such as selection of objects using a mouse.
10
For example,
Fitt’s law
11
has been adopted to describe how long it takes
to make a visually guided hand movement (using a
computer mouse) as a function of how small the target
is and how far the distance to be moved.
Figure 1 The pattern on the left (a) is perceived as a curved line
overlapping a rectangle (b) rather than as shown in (c).
Cognitive measurements of graph aesthetics Colin Ware et al
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The general strategy for building simple perceptual or
cognitive models is applicable to the problems of graph
aesthetics. If we consider a task such as determining
the shortest path between two nodes, we can measure
how the time to perform such a task depends on
various factors, such as the length of the path, the
continuity of the path and the number of edge cross-
ings on the path. If such an approach can produce
robust and reproducible results, we can estimate the
cognitive cost of, for example, the number of edges
leaving intermediate nodes, each crossing, and the
angle of the edge crossings. The result could then be
used to develop optimal layouts to support a set of
tasks that are anticipated in the use of a node–line
diagram.
Experimental determination of perceptual and cognitive
costs
In order to estimate the cognitive cost of various graph
layout aesthetics we developed an experiment to measure
the time to perceive the shortest path between two speci-
fied nodes in a spring layout graph. The method involved
generating a large number of graphs each with a unique
shortest path between two specified nodes, in which
the following factors varied:
Continuity (‘path bendiness’) (con) We defined continua-
tion at a node as the angular deviation from a straight
line of the two edges on the shortest path which emanate
from the node. To get the total path continuity the angu-
lar deviations were simply summed at all nodes on the
path. By this metric a straight path has a low value.
Number of crossings (cr) and average crossing angles
(aca) We recorded the number of edge crossings on
the shortest path, as well as the angle of each edge cross-
ing (from which we derived the average cosine crossing
angle). We expected that acute angles would be more
disruptive than more perpendicular angles.
Number of branches (br) For each of the intermediate
nodes on the shortest path, we recorded the number of
edges leaving the node which were not part of the short-
est path itself (ie the degree of the node 72). Every
branch on a path represents a possible alternative path
that might be considered in determining the shortest
path. Thus, as the total number of branches on the short-
est path increases, we can expect the task to become more
difficult.
Figure 2 The coarse orientation tuning of edge detectors in the
brain suggests that lines that cross at an acute angle as shown
on the left are more likely to be confusion than lines that cross
nearly at 908as shown on the right.
Figure 3 A schematic diagram illustrating the experiments con-
ducted by Field et al.
8
If the elements are aligned as shown in
(a) so that a smooth curve can be drawn between them, then
the curve shown in (b) is perceived. In the actual experiment Gabor
patches were used.
Figure 4 The principle of good continuation suggests that it should
be easier to see the shortest path from x to a than from x to b, de-
spite the fact that in both cases, the shortest path length is 3.
Figure 5 Good continuation suggests that the path from a to b
should be easier to perceive than that from b to c.
Cognitive measurements of graph aesthetics Colin Ware et al
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Shortest path length (spl) We were not interested in the
number of edges in the shortest path as such; however,
in order to generalize the results we thought it desirable
to evaluate the other factors in the context of the length
of the shortest path.
In addition to the primary factors we were also inter-
ested in:
Total geometric line length (tll) The spring layout algo-
rithm we used is designed to produce edges of
approximately constant length. Nevertheless, com-bined
spring forces can cause edges to be shorter or longer than
the designed length. Therefore we were interested in the
actual total geometric length of the shortest path.
Total crossings in the graph (tcr) We recorded the total
number of crossings in the entire graph drawing. We
did not expect this measurement to have any bearing
on the result, but included it as this was the measurement
used by Purchase in the earlier study with which we
wished to compare our results.
Experimental task The subjects were asked to determine
the shortest path length of each graph drawing presented
to them, as produced by the spring layout algorithm. For
any given graph drawing, the shortest path between the
two highlighted nodes was between three and five. The
start and end nodes were both highlighted.
The diagrams Each graph drawing used in the experi-
ment was a simple non-meaningful node–link diagram,
which did not describe a specific domain. The parameters
for all 180 experimental graphs were determined prior to
the experiment, and stored in a file. The drawings them-
selves generated during the experiment itself, using the
stored parameter information. Each trial entailed generat-
ing a graph drawing using spring forces and simulated
annealing.
12
There were 42 nodes in the graph, and the
number of edges on each node was randomly varied
between one and five. The size of the window was 700
pixels square, and physically measured 19.4 by 19.4 cm.
The subjects sat directly in front of the computer screen,
at a distance of 40–50 cm. The spring constant was set so
that the mean of the edge lengths was approximately 50
pixels (this converts to approximately 1.4 cm).
For each trial, the algorithm randomly determined a
start node that had at least two incident edges. It then
used a breadth first search to find a path to another node
such that there was a unique shortest path between the
two nodes of length 3, 4 or 5.
Examples of typical diagrams used in the experiment
can be seen in Figure 6.
Experimental methodology
Experimental documents Subjects were given a set of
experimental materials to familiarize themselves with
the task and the online system. These materials consisted
of a consent form, instructions for the online system, and
a tutorial sheet.
The instruction sheet described the task and the online
system that would be used by the subject. The tutorial
explained graph drawings and the concept of the shortest
path between two nodes, as well as presenting six exam-
ple graph drawings. These drawings had two nodes
highlighted, and the correct answer for the shortest path
question was indicated for each.
The subjects were given 5 min to sign the consent
form, reach through and understand the materials, ask
questions, take notes, or draw diagrams as necessary.
Online task Following the preparation time, subjects
were told to start the custom-built online experimental
system. The graph drawings were presented individually
on the screen and subjects were required to respond by
indicating the length of the shortest path between the
two highlighted nodes. Three adjacent keys on the
keyboard were used for this purpose: they were labeled
3, 4, and 5, the complete range of possible answers.
The subjects were shown 10 blocks of 20 graph draw-
ings each, with the first two blocks being identical to
the final two sets. These first two blocks of diagrams were
used as practice diagrams and were excluded from the
data, as were the first two diagrams in each consecutive
block. These practice diagrams were used to accommo-
date for the learning effect (whereby the subjects’
performance on the task may improve over time, as they
become more competent in the task).
The eight different experimental blocks of graph draw-
ings were presented in random order for each subject,
though the order of the diagrams within the blocks
remained the same. This meant the two practice blocks
at the beginning of the experiment differed for each
subject, as they were always the same as the last two
blocks of diagrams in the experiment.
Each diagram was displayed until the subject either
pressed the space bar in order to see the following
diagram, or pressed one of the labeled numeric keys (3,
4 or 5). There was no time limit on the display of the
diagrams and only once the subjects pressed the space
bar would the next diagram appear. A computer beep
indicated an incorrect response, to encourage the
subjects to perform as best they could, and to identify
subjects who were not taking the task seriously.
In addition, there was a rest period between each block of
graph drawings, allowing the subjects to recover their con-
centration before continuing with the experiment. The
length of this rest break was controlled by the subjects.
Data collection The experimental data collected was the
response time and accuracy of the subjects’ responses to
the experimental diagrams: this information was
recorded by the online system during the experiments.
Elapsed times were measured through system calls with
millisecond nominal resolution. However, temporal reso-
Cognitive measurements of graph aesthetics Colin Ware et al
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Information Visualization
lution could be no better than the 16 millisecond granu-
larity imposed by the monitor refresh rate.
Independently of the experiments, graphical measure-
ments were calculated and recorded for each of the 180
graph drawings used. These included:
.the correct value for the shortest path length (spl): 3, 4
or 5
.the continuity (‘bendiness’) of the shortest path (con):
measured in degrees.
.the number of crossing edges on the shortest path (cr)
.the cosine of the angle at which each crossing edge
crossed the shortest path. The purpose of this was to al-
low us to weight shallow angle crossings higher than
orthogonal crossings. From this we computed the aver-
age cosine crossing angle (aca)
.the total number of crossed edges in the graph drawing
(tcr)
.the number of edges branching from nodes along the
shortest path (br)
.average geometric line length along the shortest path,
per edge (all). This was computed in arbitrary units.
To get centimeters it is necessary to multiply by 1.4.
.total geometric line length of the shortest path (tll):
same units as all
Subjects The 43 subjects were second and third year Com-
puter Science and Information Systems students at the
University of Queensland. The subjects were paid $15 for
their time, and, as an incentivefor them to take the experi-
ment seriously, the best performer was given a CD voucher.
Results
Ninety-three per cent of the subjects’ responses were
correct. The response time data was analyzed using only
the correct trials. Subjects saw 10 blocks of 20 drawings
each. Seven graph drawings were eliminated from the
analysis because of an unexpected perceptual error, where
an edge passing under a node, looked as if it were two
edges attached to that node. Eliminating the practice
graphs (the first two blocks, 40 drawings), and the first
two drawings of each subsequent set (268=16 drawings),
left us with 137 drawings in our experimental set.
Our independent variable was the average response
time over all subjects for each graph drawing (rt), and
our dependent variables were the measured geometric
features of each drawing: spl, con, cr, aca, trc, br, all, tll.
Table 1 shows the linear correlations between the inde-
pendent variables and the average response time. Figure 7
shows selected scatter graphs to demonstrate some of the
most important correlations identified.
Data analysis: linear correlations
The results presented above (Table 1, Figure 7) use linear
correlations, showing the relationships between each
independent variable and the dependent variable of
response time. From these linear correlations we observe
that:
.The two key variables of crossings (cr) and continuity
(con) are almost independent.
.The variability of the data increases with increase in
‘bendiness’: straight paths were generally responded
to between 2 and 5 s while paths with a high measure
of ‘bendiness’ were responded to in between 2 and 14 s.
.A similar effect can be seen with the total geometric
line length of the shortest path: responses to short
paths only varied between 2 and 4 s whereas for long
path the range was between 4 s and about 14 s.
Figure 6 Two of the experimental graph drawings, as viewed by the subjects. In the originals the small nodes were red while the larger
end-point nodes were light blue.
Cognitive measurements of graph aesthetics Colin Ware et al
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Data analysis: multiple regression
However, linear correlations are insufficient for appropri-
ate interpretation, as there are many significant
correlations between the independent variables them-
selves (Table 1). We need to be sure that the internal
relationships between the individual independent vari-
ables are ‘factored out’, so that we can identify the
relative contribution of each variable, independent of
its relationship to the other variables.
We used stepwise multiple regression in two steps. In
the first step, we included only the shortest path length
(spl) into the equation, as we knew that it would have
the greatest effect, and we first wished to remove the
variance in the data that it caused. We did not force the
number of edge crossings (cr) into the equation at this
point (despite the prior work by Purchase which
concluded that crossings was the most important factor)
as we wished to determine whether the number of edge
crossings really was more dominant than the other
factors.
In the second step, we put all the remaining indepen-
dent variables into the equation and performed a
stepwise analysis. Thus, the most significant independent
variable (ie the variable that explains the most of the
variance that has not already been explained by the
previously entered variables) would be used first, then
the next most significant independent variable, etc., with
the relative order of importance indicated by the left-to-
right ordering of the terms in the equation. Any indepen-
dent variables that were not significant at a 0.05
significance level would not appear in the final multiple
regression equation.
Performing a stepwise multiple regression analysis
on the 137 graph drawings, with response time as
the dependent variable, the following equation relates
the response time to the shortest path length, the
continuity of the shortest path, the number of crosses
on the shortest path and the number of additional
branches from the intermediate nodes on the shortest
path. The other independent variables were not signif-
icant.
rt=74.970+1.390 spl+0.01699 con+0.654 cr+0.295 br (1)
When the data has been normalized to eliminate the
constant, the following equation better allows us to see
the relative contributions of the independent variables:
rt=70.414 spl+0.406 con+0.317 cr+0.172 br (2)
An R
2
value can indicate the extent to which the
dependent variable correlates with the independent vari-
ables on the left hand side of the equation. The change in
the R
2
value after each independent variable is included
in the stepwise regression, indicates the relative effect
of each of the variables. R
2
after shortest path length
(spl) is included: 0.542. R
2
after continuity (con) is
included: 0.642 (change=0.100). R
2
after crossings (cr) is
included: 0.760 (change=0.118). R
2
after branches (br) is
included: 0.784 (change=0.024).
Discussion
As a contribution to graph layout research perhaps our
most significant result is the finding that path continuity
is an important factor in perceiving shortest paths.
Considering that path length is an intrinsic property of
a graph, this makes continuity the most important
aesthetic property in the set of graphs that we generated.
Simply put, the results show that 1008of continuity
(bendiness) on a path contribute 1.7 s to finding the
shortest path while each edge crossing contribute
0.65 s. A more general way of stating this is to say that
the cognitive cost of a single crossing is approximately
the same as 388of continuity. The practical consequence
is that it may be worth allowing for an occasional cross-
ing in a graph layout if it reduces the bendiness of
paths. Using this information it should be possible to
construct graph layout algorithms that are more effective
for analytic tasks where path finding is important. More
studies are required to determine the robustness of our
findings of this study for other than spring layout graphs
and for different graph sizes, but the theoretical argu-
ments given in the introduction would lead us to
expect the results to be generalized.
In comparing these results with those of Purchase
3
,it
was found that her measurement of the total number of
edge crossings in the graph drawing is not a significant
indicator of response time. For shortest path tasks, we
Table 1 Linear correlation coefficients between the measured graph drawing properties, including the shortest path
length for the task and the average response time over all subjects. Shaded cells indicate results that are statistically
significant
spl con cr aca tcr br all tll rt
spl 1 0.484 0.191 0.134 0.059 0.379 0.064 0.930 0.736
con 1 0.019 0.082 0.125 0.119 770.294 0.331 0.633
cr 1 0.141 0.347 0.267 0.428 0.332 0.449
aca 1 0.064 0.208 0.099 0.167 0.148
tcr 1 0.116 0.011 0.066 0.216
br 1 0.353 0.475 0.462
all 1 0.419 0.050
tll 1 0.623
rt 1
Cognitive measurements of graph aesthetics Colin Ware et al
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have shown here that it is the number of edges that cross
the shortest path itself that is important, rather than the
total number of edges crossing in the drawing. The results
of the Purchase experiment, were, however, not purely
based on a shortest path task: the task of identifying
the nodes and edges which, when removed, would cause
two nodes to be disconnected, were also included in her
performance data. The effect of the total number of cross-
ings in the whole graph drawing may have been more
important in these latter two tasks than in the shortest
path task.
Perhaps the result that is most difficult to explain is the
negative intercept for the regression equation (1). A
simple extrapolation from this would imply that with
very short straight paths the task can be accomplished
in negative time. Of course, all of our results were posi-
tive. A possible explanation is that short straight paths
can be perceived in roughly constant time and that it is
only when the path length exceeds 3 that a significant
cognitive cost is incurred. This is made more plausible
by research that has shown that we can count visual
objects up to three ‘at a glance’, that is, in constant
time.
13
Thus the cognitive cost of counting nodes is
incurred only after the length of a path exceeds three.
We believe that a major part of their contribution in
this study is the methodology itself. In many visualiza-
tion problems there are similar tradeoffs between
different optimization criteria. The same experimental
methodology described here can be applied to any
display problem that has similar characteristics and a
Figure 7 Scatter plots showing the linear correlations between some of the measured graph drawing properties, and the average response
time for each graph drawing over all subjects (time is measured in seconds).
Cognitive measurements of graph aesthetics Colin Ware et al
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well-defined elementary task. For example, it is common
practice to display vector fields using particle traces, but
the optimal way of doing this is unknown. As with graph
layout there are many free display parameters to be opti-
mized: the length of the particle traces, their density, and
their sizes can all be manipulated. Several tasks are avail-
able for optimization: one is the perception of vector field
strength, another is the prediction of advection (ie where
in the field a dropped particle would end up.)
Two areas of future work can stem from this research:
firstly the data presented here needs validating to deter-
mine whether it truly can be used as a predictive model
for shortest path tasks in graph drawing. Secondly, the
methodology can be applied to a variety of other simple
visual tasks for which the cognitive cost of differing
visual features would be of interest.
Acknowledgments
We are grateful to the students from the School of Informa-
tion Technology and Electrical Engineering at the University
of Queensland, who willingly took part in the experiments,
and to Julie McCreddon and Maureen Tingley for advice
on the statistical analysis. Discussions with Sue Whitesides
at McGill University were instrumental in shaping this study.
The Australian Research Council partly funded this research,
and partial funding for Colin Ware came from the U.S.
National Science Foundation. Ethical clearance for this study
was granted by the University of Queensland, 2001.
References
1 RumbauchJ,JacobsonI,BoochG.The Unified Modeling Language
Reference Manual. Addison Wesley Longman, Inc.: Reading, Mass.
1999.
2 Battista GD, Eades P, Tamassia R, Tollis IG. Graph Drawing:
Algorithms for the Visualization of Graphs.. Prentice Hall, 1999.
3 Purchase H. Which aesthetic has the greatest effect on human
understanding. In: Battista G (Ed). Graph Drawing 97, 1353 of
Lecture Notes in Computer Science. Springer Verlag: 1997 284–
290.
4 Koffka K. Principles of Gestalt Psychology. Harcort Brace: New York.
1935.
5 Ware C. Information Visualization: Perception for Design. Morgan
Kaufman. 1999.
6 Triesman A, Gormican S. Feature analysis in early vision: Evidence
from search asymmetries. Psychological Review, 1988;95:15 – 48.
7 Blake R, Holopogan K. Orientation selectivity in cats and humans
assessed by masking. Vision Research 1985;23:1459 – 1467.
8 Field D, Hayes A, Hess FR. Contour integration by the human visual
system: Evidence for a local ‘‘association field’’. Vision Research
1993;33:173 – 193.
9 Parent P, Zucker S. Trace interference, curvature consistency and
curve detection. IEEE Transactions on Pattern Analysis and Machine
Intelligence 1989;6:661 – 675.
10 Card S, Moran TP, Newell A. The Psychology of Human-Computer
Interaction. Lawrence Erlbaum Associates: New Jersey, 1983.
11 Fitts PM. The information capacity of the human motor system in
controlling the amplitude of movements. Journal of Experimental
Psychology 1954;47:381 – 391.
12 Davidson R, Harel D. Drawing graphs nicely using simulated
annealing. ACM Trans. on Graphics 1996; 15: 301 – 331.
13 Dehaene S. The Number Sense: How the Mind Creates Mathematics.
Oxford Press: New York, 1997.
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