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Intersections of Our World

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There are several situations where the type of a street intersections can become very important, especially in the case of navigation studies. The types of intersections affect the route complexity and this has to be accounted for, e.g., already during the experimental design phase of a navigation study. In this work we introduce a formal definition for intersection types and present a framework that allows for extracting information about the intersections of our planet. We present a case study that demonstrates the importance and necessity of being able to extract this information.
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Intersections of Our World
Paolo Fogliaroni
Vienna University of Technology, Austria
paolo.fogliaroni@geo.tuwien.ac.at
Dominik Bucher
ETH Zurich, Switzerland
dobucher@ethz.ch
Nikola Jankovic
Vienna University of Technology, Austria
nikola.jankovic@geo.tuwien.ac.at
Ioannis Giannopoulos
Vienna University of Technology, Austria
igiannopoulos@geo.tuwien.ac.at
Abstract
There are several situations where the type of a street intersections can become very important,
especially in the case of navigation studies. The types of intersections affect the route complexity
and this has to be accounted for, e.g., already during the experimental design phase of a navigation
study. In this work we introduce a formal definition for intersection types and present a framework
that allows for extracting information about the intersections of our planet. We present a case
study that demonstrates the importance and necessity of being able to extract this information.
2012 ACM Subject Classification Information systems Geographic information systems, In-
formation systems Data analytics
Keywords and phrases intersection types, navigation, experimental design
Digital Object Identifier 10.4230/LIPIcs.GIScience.2018.3
1 Introduction
The street network of a city is a physical artifact embedded in the natural world. Most of the
times, it consists of highways (i.e., streets meant for cars only), roads (meant for cars and
pedestrians) and pathways (only for pedestrians). Sometimes these networks are following
strict human design guidelines and sometimes they are bounded by natural constraints. Along
with historical rationales, these constraints are the primary reasons that not all parts of a
city follow a gridded design structure (e.g., curvilinear). This means that beside commonly
encountered 3- and 4-way intersections, also more complex ones can exist.
But what are the main implications of this diversity of streets and intersections, and why
is it important to know how a city, a country or even a continent are structured? What can
we learn from this information and how can this information be useful?
In the following we will exemplify our work focusing on the area of navigation studies and
experimental design. Independently of the research discipline, when planning an experiment
there is a certain process that is followed in order to come up with a correct design. At the
very beginning, information for the various relevant variables is collected that eventually will
help to make the right choices.
In the case of navigation experiments, the relevant variables concern the subjects (e.g.,
gender or age), the type of navigation aid [
13
] and the timing of instructions [
12
], if any,
©Paolo Fogliaroni, Dominik Bucher, Nikola Jankovic, and Ioannis Giannopoulos;
licensed under Creative Commons License CC-BY
10th International Conference on Geographic Information Science (GIScience 2018).
Editors: Stephan Winter, Amy Griffin, and Monika Sester; Article No. 3; pp. 3:1–3:15
Leibniz International Proceedings in Informatics
Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany
3:2 Intersections of Our World
and the environment (e.g., the route). When it comes to the environment, the relevant
factors that have to be considered are numerous [
15
] and decisions can be made by taking
into account possible interactions between the relevant subjects and the environment –
e.g., previous experience of the subjects with the environment. Besides factors such as
architectural differentiation and environmental landmarks [
30
], the types of intersections are
highly relevant since they contribute to the complexity of a wayfinding decision [
15
]. A typical
question during the design process is how the decision points along the designated route
should be selected in terms of number of choices. How many and what kind of crossroads
should the route encompass? Of course, the number of crossroads and their shape (e.g., T-
or Y-intersections) on an experimental route is strongly related to the underlying research
questions.
The aim of this work is to help answering this type of questions. We computed the
number and type of all intersections on Earth and developed a web application that can be
easily used to extract this precomputed information for any area in the world. Of course this
work is not limited to navigation and experimental design. Next to researchers of various
disciplines, industries related to the areas of transportation and urban planning can use our
work for their decision making processes. For instance, by comparing the intersections of a
street network between two areas, interesting correlations with other phenomena could be
made, allowing to draw conclusions regarding the impact of the intersection types.
As a data source for our work we resorted to OpenStreetMap (OSM), that is one of the
most commonly used source of volunteered geographical information (VGI). While approach
we present does not require any particular form of road network data, the wide and free
availability as well as the generally good quality of OSM [
16
] make it an adequate choice for
intersection analysis. OSM data was analyzed in a multitude of studies before, not only in
terms of quality and completeness [
18
], but also as a data source for answering questions
about various environments [
9
], to determine the distribution of landmarks and points of
interest [
31
,
28
,
3
], to build recommender systems [
4
] or as contextual enhancement for other
types of data, such as Twitter posts [17].
In terms of intersection analysis, most previous work focuses around the automatic
detection of roads and intersections from other sources of data, such as GPS traces [
10
,
7
]
or satellite imagery [
6
]. A variety of techniques exist, where intersection types are either
implicitly learned using machine learning techniques (such as neural networks for satellite
image analysis) [
27
,
32
], or considered directly within the model [
25
]. To the best of our
knowledge, in all of the automated detection methods the individual intersections are not
classified in any way except based on the number of roads that lead up to them.
Intersections also play a central role in many routing applications [
24
]. Not only do red
lights (commonly occurring at intersections) influence the driving time, behavior, and related
emissions [
23
,
2
], but even the difference between a right or left turn at an intersection
incurs different penalties to route computations [
20
]. In addition, vehicular ad hoc networks
(VANETs, which are used for inter-car communications) optimally also take intersections
into consideration, as they provide data exchange points for cars driving on different routes
and cars are likely to stop there [5, 1].
2 Types of Intersections
While the terms junction and intersection are commonly used interchangeably to refer street
joints and crossings, they have slightly different meanings, with the term intersection referring
to a specific type of junctions. According to the Oxford Dictionary, a junction is a place
P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:3
(a) T-intersection. (b) Y-intersection. (c) Cross-intersection. (d) X-intersection.
Figure 1 The most common types of prototypical named intersections.
where two or more roads or railway lines meet, while an intersection is a point at which two
or more things intersect, especially a road junction.
The term junction unambiguously relates to the mobility infrastructure domain and
denotes roads coming together but does not specify the exact nature of their connection
(intersect, touch, meet at a square, etc.). Conversely, the term intersection has a broader
scope – as it can refer to several domains. Yet, when it comes to the mobility infrastructure
domain it clearly refers to the cases where two or more roads intersect with each other.
Intersections are mostly studied in the areas of Architecture, Civil and Traffic Engineering,
as well as Urban Planning. Studies in these domains are concerned with intersection design and
construction to optimize traffic load, road safety, and traveling time (e.g., [
29
]). Intersections
are typically split into two main categories: at-grade and grade-separated (see, e.g., [
8
]).
At-grade intersections consist of roads located at the same level (grade), while the roads
creating a grade-separated intersection are at different levels (grades) and pass above or
below each other. Grade-separated intersections are mostly used in highways and motorways,
as they allow for a faster and smoother merging of car traffic but are not well suited for
pedestrian navigation.
Both categories can be more finely classified. Grade-separated intersections can be
divided into interchanges and grade-separations without ramps. Subcategories of at-grade
intersections include proper intersections,roundabouts, and staggered (or offset) intersections,
among others. Proper intersections are the most prototypical type of intersection for the
layman: several road segments converge to meet at the same point. Roundabouts are circular
intersections that cars can enter and exit smoothly and in which road traffic flows in a single
direction. In Staggered intersections several (minor) roads meet a main road at a slight
distance apart such that they do not all come together at the same point.
In the scope of this work we only take into consideration proper intersections and,
marginally, staggered intersections (that we regard as a composition of proper intersections).
The analysis of more more complex types of intersections such as, e.g., roundabouts will be
investigated in future work.
In the following we will introduce relevant terminology and discuss properties of proper
intersections. The most straightforward property to classify intersections is the number
n
of street segments stemming out of it. We call such street segments the branches of the
intersection. An intersection
I
with
n
branches is called an
n
-way intersection and we denote
it by
In
. Obviously, we need at least two street segments to meet in order to form an
intersection. In this work we focus on the intersections which call for navigational decision
making: given one street segment that is used to approach an intersection, there have to be
at least two more street segments that can be used to leave that intersection (i.e., n3).
A second discriminant that we use to classify an intersection is its shape. That is, the
angular arrangement of its branches. Typically, this is done by comparing the intersections
at hand to some others that are generally accepted as prototypical ones [
33
,
22
,
26
,
14
]. The
GIScience 2018
3:4 Intersections of Our World
most common ones are reported in Figure 1: they are called T- and Y-intersections for
n
= 3;
cross- and X-intersections for
n
= 4. Every intersection with more than four branches (
n >
4)
is typically referred to as a star-intersection.
There is evidence that these named intersection types are used very naturally by people
when communicating route instructions verbally [
33
,
22
] or schematically [
33
,
26
,
14
]. However,
they suffer from two major drawbacks. First, these namings only exist for intersections with a
small number of branches (
n
4). Second, they are often not precisely defined: for example,
while most people would agree that a cross-intersection splits a revolution into four right
angles, there might be a large disagreement on the skewness of an X-intersection.
For these reasons, we introduce the concept of regular intersection, whose branches divide
a revolution into uniform parts. More formally:
IDefinition 1
(Regular
n
-way intersection)
.
Let
b0,· · · , bn1
be the branches of an
n
-way
intersection enumerated in circular order . We define
αi
as the angle formed by the pair
(
bi1, bimod n
)for every
iN
such that 1
in
. We say that a
n
-way intersection is
regular if and only if α1=α2=· · · =αn= 360/n and we denote it by Rn.
In general, to further characterize an
n
-way intersection we compare it to its regular
counterpart, rather than to the aforementioned named intersection types. However, it has
to be noted that regular 3- and 4-way intersections can be interpreted as exact definitions
for Y- and cross-intersections, respectively. The arbitrary skewness of X-intersections makes
them unsuitable to be taken as an objective reference for comparison. T-intersections, on
the other hand, are well defined. For this reason, for 3-way intersections we also perform a
comparison to T- intersections.
Finally, we define the angular distance ∆(
In, Rn
)among a generic
n
-way intersection
In
and its regular counterpart
Rn
as the minimum sum of angles that we have to rotate the
branches of
In
to perfectly match
Rn
, while preserving the circular order of
In
’s branches.
Note that there are
n
1possible rotations that can be performed to match
In
to
Rn
(see
Sec 3.2 for more details).
3 Intersections Framework
In the following, we present our framework that was implemented for the classification
and analysis of intersections. As one of the goals was to make worldwide intersection data
available, the presented framework is based on OpenStreetMap data and is publicly available
1
.
The framework is able to periodically process this data and writes the resulting intersection
measures into a database, where they can be accessed through a web application.
3.1 Data Source
OpenStreetMap (OSM) is arguably one of the largest and most important volunteered
geographic information (VGI) projects. As VGI is often not only the cheapest source of
geographic information, but even the only one available in certain regions [
16
], it is an
agreeable data source for a global intersection analysis. It needs to be noted that even though
OSM data quality can be considered adequate for many purposes, its spatial distribution
is not uniform, but depends on factors such as the information of interest or social events
(e.g., an upcoming Football World Cup) in a region [
18
,
19
,
11
]. However, these quality
1See http://intersection.geo.tuwien.ac.at.
P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:5
Analysis Class
Highway Tag Values Description
Road
living_street,primary,secondary,ter-
tiary,unclassified,residential,ser-
vice,primary_link,secondary_link,ter-
tiary_link
All ways that can be traversed by both
cars and pedestrians, namely all nor-
mal roads.
Path Road highway tag values plus
path,steps,bridleway,footway,track,
pedestrian
All ways that can be used by pedestri-
ans. Including smaller tracks, hiking
routes, etc. where cars cannot drive.
Car Road highway tag values plus
motorway,motorway_link,trunk,
trunk_link
All ways that can be traversed by car.
This additionally includes highways
and motorways, where pedestrian ac-
cess is usually forbidden.
Table 1 Different highway tag values used within the intersection analysis framework.
issues often concern single newly built roads or geographical information unrelated to the
road network, which make up for a negligible amount of data with respect to a regional
intersection analysis.
The three primary data structures of OSM are nodes,ways and relations. Nodes represent
single points in space (i.e., they have a longitude and latitude), such as points of interest or
individual objects. Ways are ordered lists of nodes, and encode linear features (like roads or
rivers) and boundaries of areas (when the first and last node are equal). Finally, relations
describe relationships between multiple elements, e.g., a collection of ways which form a
scenic route, or turn restrictions, which state that you cannot cross from one way into another
at a certain intersection.
All the node, way and relation objects can have an arbitrary number of tags, which have
a simple key
value form (both key and value are arbitrary strings). The tags themselves
are not formally specified, but are chosen based on a consensus in the OSM community. For
example, the very common tag highway is assigned to way objects which can somehow be
used for travel, e.g., for walking or driving. It can take the values described in Table 1
2
.
Note that we distinguish between three analysis classes, one with ways solely accessible
to pedestrians, and another two with ways accessible to cars (including resp. excluding
motorways). To find intersections in the OSM data, it suffices to look at ways that carry a
highway tag, and to determine which nodes are shared among several of these ways.
OSM data is available in different formats. As the whole uncompressed xml planet file is
around 850 GB at the time of this writing, we opted for the protocol buffer binary format
(PBF) instead, which is available as a 40 GB gzipped file
3
and consists of around 4.3 billion
nodes and 470 million ways.
3.2 Data Processing
After uncompressing the PBF file, we first search for nodes that should be considered
intersections. As stated above, this corresponds to nodes which have more than two branches
(
n
3). For each way in the OSM dataset that has one of the appropriate highway tag values
2
For a detailed description of the individual values, and also additional ones that are not used in this
framework, please consult the OSM documentation under wiki.openstreetmap.org/wiki/Key:highway.
3For details see wiki.openstreetmap.org/wiki/PBF_Format.
GIScience 2018
3:6 Intersections of Our World
I
b
b
b
b
(a)
Original 4-way intersection
Iwith branches b0-b3.
Rn
(b)
Overlay of perfect 4-way in-
tersection R4.
Rn
0
(c)
Angles between original and
perfect intersection.
Figure 2
Computation of ∆(
In, Rn
), the sum of all angles that each branch
bi
has to be rotated
in order to produce a regular
n
-way intersection. Note that it suffices to align the regular intersection
with each branch (as is done for b0in (c)), and take the minimal of all possible alignments.
(cf. Table 1), we iterate through all the nodes making up this way, and build a mapping that
stores all neighboring nodes of each node. To be able to distinguish the different analysis
classes later on, the highway tag value is additionally stored for each neighboring node.
In essence, we define intersections as a function mapping a center node
p
to a number
n
of adjacent nodes
pp,i
, where for each
pp,i
in addition the highway tag value
th,i
of the
connecting way is stored:
In:p7→ {(pp,i, th,i )|0i<n}(1)
As this is done for all nodes in the OSM dataset (irrespectively of
n
), in a second iteration, a
final set of intersections
{I0, ..., Ik}
has to be built by removing all nodes that dissatisfy the
minimal number of branches condition (i.e.,
|I
(
p
)
|<
3). This set of intersections contains all
the relevant OSM nodes for the purposes of the here presented framework. To compare each
intersection to its regular counterpart (in the case of a 3-way intersection additionally to a
perfect T-intersection), it is required to compute all angles between the different roads in a
next step.
Thus, for the remaining intersections, a second pass through the OSM data collects the
coordinates of the center node
p
itself, as well as the coordinates of all the neighboring
nodes
pp,i
that can be reached by traversing its branches
bi
. Using these coordinates, it is
possible to compute all angles between the branches and the meridian passing through the
center node. Figure 2 depicts a hypothetical 4-way intersection in black and, beneath it, the
regular 4-way intersection, where the angles between branches are always 90
. In order to
compute the angular distance ∆(
In, Rn
)to the regular intersection, we rotate the regular
intersection
n
times, so that it always aligns perfectly with one of the branches
bi
. Figure 2c
shows one of the four possible alignments for a 4-way intersection. For each non-aligned
branch,
αi
denotes the required rotation to reach an alignment with the next “free” branch
of the regular intersection (in this respect, “free” simply means that no two branches of the
original intersection may be rotated to the same branch of the regular intersection). For any
alignment with a branch of the regular intersection, a
0
is computed as the sum of all
αi
.
The final takes the value of the minimal
0
over all
n
possible alignments. Note that this
is a globally minimal , even if arbitrary rotations of the regular intersection were allowed
(and not just “snapping” to branches of the original intersection), as rotating the regular
intersection monotonically increases or decreases , until another alignment is reached. As
such, all minima and maxima of must occur at an alignment with the regular intersection.
P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:7
All the intersections with their coordinates, the number of branches, as well as the
computed ∆(
In, Rn
)are finally written to a PostGIS database
4
. Since it is required to know
the analysis class of each intersection, an additional database field denotes if an intersection
is valid for road,path, and car, or only any subset thereof.
3.3 Data Service
We provide public access to the intersection data computed with our framework through a
web application that is accessible at intersection.geo.tuwien.ac.at.
The interface provides a map canvas with OSM as a basemap that can be used to freely
browse the whole globe. With the current release of the application, the user is provided
with a selection menu from where she can specify the type of intersections of interest (column
“Analysis Class” in Table 1). We plan to extend this in future releases to allow the selection
of combinations of the base intersection types.
We offer three possibilities to specify the region of interest: polygon drawing, viewport,
and name search. In the first case, the user can specify a region by drawing a polygon on the
map. With the canvas selection, the viewport currently shown on the map canvas is used to
perform the database query. Finally, it is possible to look for named entities via a search box
that provides a live interface to an OSM Nominatim
5
server. After typing in the name of
the searched feature, the user can ask the interface to draw the corresponding polygon on
the map. Given the huge amount of intersection data available, we decided to limit the area
of the search region to not overload the server. In future releases this limitation might be
removed. Also, in order to promote interoperability, we plan to include the possibility of
specifying custom geometries expressed in different type formats (e.g., KML, geoJSON, etc.).
The intersection type and the region specified are used to submit a query that returns
a statistical summary for intersections of the given type in the provided region. This
summary contains the number of occurrences for each
n
-way intersection, the average
from the corresponding regular intersection – for 3-ways, also the average from the regular
T intersection. Besides the statistical summary the user is also provided with a link to
download the whole intersection data set for the specified region and type as a CSV file.
At the time of writing the CSV file only contains information about the intersection
points that were computed from OSM nodes. Beside the geometric information (reported in
WKT) each point is associated the following attributes: the number of branches and the type
of intersection, and the angular distance to the corresponding regular intersection.
Note that the intersection classes defined in Table 1 are not disjoint. This results in
the same intersection occurring up to three times in our database, once for each category.
Imagine the case of an intersection where both roads and paths converge. For example, we
may have 3 roads and 1 path. This intersection appears twice in our dataset: as a path and as
a road. Since roads are accessible by both pedestrians and cars but paths are only accessible
by cars, we have a 4-way path intersection and a 3-way road intersection. A similar concept
applies to the categories of road and car intersections. The relation of the number of ways
(denoted as
nclass
) between the intersections that overlap is
ncar nroad
and
npath nroad
.
In our database we also keep trace of the ways that form intersection branches: their
geometry (also converted to OGC standard), the original OSM highway tag, and a relation to
the intersections that they generate. This information is not accessible through the current
version of the application, but will be made available in future releases.
4PostgreSQL 9.6 with PostGIS 2.3.2, the processing application is implemented in Rust 1.23.0.
5Nominatim is a search engine for OSM data, see wiki.openstreetmap.org/wiki/Nominatim.
GIScience 2018
3:8 Intersections of Our World
Figure 3
Distribution of the intersections as
the number of branches nvaries.
Detroit Melbourne Vienna Zürich
3-way 46.76% 84.49% 75.16% 78.88%
4-way 52.84% 15.20% 23.74% 20.13%
5-way 0.36% 0.29% 0.93% 0.82%
6-way 0.04% 0.02% 0.13% 0.14%
7-way 0.002% 0.002% 0.02% 0.02%
8-way 0.002% - 0.01% 0.004%
10-way - - - 0.004%
Total 40929 191508 75644 26286
Table 2
Distribution of intersections over
number of ways for the four cities.
4 Use Case: Detroit, Melbourne, Vienna, and Zürich
In this section we present and discuss intersection data obtained with our framework for
four exemplary cities and showcase how this data can be used during the design process
of navigational experiments. In Section 4.1 we compare the four different cities, while in
Section 4.2 we focus on local differences within a single city.
4.1 Comparative Study
We used our framework to extract intersection data for Detroit (USA), Melbourne (Australia),
Vienna (Austria), and Zürich (Switzerland). While the framework allows for extracting
intersection data concerning different types of streets (cf. Section 3.1), for this case study we
focus on paths and roads (i.e., set of all walkable streets).
Table 2 reports the distribution (as percentages) of intersections as the number of branches
n
varies. From this data we can derive several interesting insights. First and foremost it has
to be noted that for all the cities in exam almost the entirety of intersections are 3-ways
and 4-ways. This becomes even more evident by looking at the graphical representation
of the data reported in Figure 3. While this fact may seem trivial, it is still surprising the
cumulative percentage that these two intersection categories reach together – ranging from
98
.
9% for Vienna to 99
.
7% for Melbourne. This pattern seems to recur everywhere in the
world. Indeed, we found it in many other cities (Athens, Rome, Kathmandu, Washington
DC, Paris, and London, among others) that we analyzed with our framework in a preliminary
analysis for this work. This pattern consistently (only with minor differences) repeats across
different cities, independently of their very heterogeneous morphology, history, and age.
The second insight that we can derive from this data relates to the ratio between the
number of 3-way and 4-way intersections. In this respect, we notice that Melbourne, Vienna,
and Zürich present a very similar trend with the majority of intersections being 3-ways,
although with slightly different ratios between the number of 3- and 4-ways: approx. 5.5
for Melbourne, 3.2 for Vienna, and 3.9 for Zürich. Conversely, Detroit shows the opposite
trend, with the number of 4-ways slightly bigger than that of 3-ways. This may indicate, for
example, a more blocked structure of the city.
In the following we analyze the further discriminant introduced in this work to classify
intersections: the similarity to regular intersections (see Definition 1). As discussed in
Sections 2 and 3.2, we measure this by the angular distance ∆(
In, Rn
)between a generic
n
-way intersection
In
and the corresponding regular intersection
Rn
. For the case of 3-ways,
P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:9
City Min P25 P50 P75 Max
Det 0% 0.58% 1.96% 15.98% 99.99%
Mel 0% 1.03% 4.31% 21.59% 99.65%
Vie 0% 1.51% 6.08% 22.16% 99.87%
Zur 0% 2.09% 7.54% 23.48% 99.76%
-range: [0°,180°]
(a) 3-way to regular T, delta percentiles.
City Min P25 P50 P75 Max
Det 0% 0.23% 0.59% 2.11% 50.00%
Mel 0% 0.63% 2.37% 8.05% 83.69%
Vie 0% 0.91% 3.17% 9.69% 85.81%
Zur 0% 1.44% 4.45% 11.41% 64.12%
-range: [0°,360°]
(b) 4-way to regular 4-way, delta percentiles.
Table 3
Distribution of 3-way (4a) and 4-way (4b) intersections for the four cities (normalized).
we compare against regular T intersection instead. Moreover, given that for the cities in
exam 3-ways and 4-ways combined cover almost the totality of the number of intersections,
we will only focus on those.
Tables 4a and 4b report descriptive statistics for 3-ways and 4-ways, respectively. The
numbers reported are percentages referring to the value range that the angular distances can
take on. This is called -range and denotes the difference between the minimum (
min
) and
maximum (
max
) angular distances from a generic intersection to its regular counterpart.
Obviously, the minimum is always zero (
min
= 0
°
), which corresponds to a perfect match
with the regular intersection. Conversely,
max
depends on the number of branches (
n
) of the
intersection at hand and corresponds to the angular distance of the (theoretical) worst-case
scenario where all the branches of an intersection collapse on top of each other:
max =
bn1
2c
X
i=1
(2) + ((n1) mod 2) π(2)
For an understanding of this formula imagine to align any branch of the regular intersection
to the first branch of the
n
-way at hand. Subsequently, take a pair of unmatched branches
from the generic intersection and rotate them (one clockwise and the other counterclockwise)
by
α
=
360
n
to match the first pair of unmatched branches of the regular intersection. Now
repeat for the second pair of unmatched branches. In this case, we will have to rotate 2
α
in
order to find the first pair of unmatched branches of the regular intersection. Generalizing
this operation we obtain the formula in Equation 2. For 3-ways and 4-ways we have -ranges
equal to [0
°,
240
°
]and [0
°,
360
°
], respectively. The -range for 3-ways when compared against
the regular T intersection is equal to [0°,180°].
Figures 4a and 4b plot in greater details the distribution of 3-ways and 4-ways as the
angular distance varies over the -ranges for the regular T intersection and the regular
4-way, respectively. The figures show that the majority of the intersections are very similar
to their regular counterparts (which aligns nicely with Klippel’s set of wayfinding choremes
[
22
,
21
]), with Detroit and Zürich representing extreme cases. The intersections of Detroit
are the most regular, with approximately 70% of its 3-ways and 90% of its 4-ways showing
an angular distance below 10% to the regular T intersection (i.e., 18
°
) and the regular 4-way
(i.e., 36
°
), respectively. Conversely, Zürich is the least regular, with approximately 55% of
its 3-ways and 70% of its 4-ways showing an angular distance below 10% to the regular T
intersection (i.e., 18
°
) and the regular 4-way (i.e., 36
°
), respectively. Melbourne and Vienna
are located in between these extremes, with Melbourne being slightly more regular than
Vienna with respect to both 3-ways and 4-ways.
These findings can be used, for example, during the design of navigational experiments
to select paths that adhere to the structure of the city where the experiments are to be
GIScience 2018
3:10 Intersections of Our World
(a) 3-way to regular T intersection. (b) 4-way to regular 4-way intersection.
Figure 4
Dsistribution of the angular distance () for 3-ways
(a)
and 4-ways
(b)
with respect
to the regular T intersection and the regular 4-way intersection, respectively. The angular distance
(on the x-axis) is reported as a percentage of the different -ranges for 3-ways (i.e., 0
°
180
°
) and
4-ways (i.e., 0
°
360
°
). The percentage on the y-axis refers to the number of intersections in each
bin with respect to the total number of intersections of that type (i.e., 3-way and 4-way). The
smaller the value of , the higher the similarity to the corresponding regular intersection.
performed. In this way, we can avoid to select some atypical path that may lead to biased
results. Assume that for our hypothetical navigational experiment we need a path that
comprises 10 intersections. If we were to conduct the experiment with a path matching the
characteristics of Detroit, we should select a path in the real world or in a virtual environment
that encompasses, e.g., five 3-way and five 4-way intersections. Of the selected 3-ways (resp.
4-ways), three (resp. five) should present a maximum angular distance of 18
°
(resp. 36
°
)
from the regular T intersection (resp. the regular 4-way). Conversely, if we were to conduct
the same experiment with a path matching the characteristics of Zürich, our path should
encompass eight 3-way and two 4-way intersections. Of the selected 3-ways (resp. 4-ways),
four (resp. six) should present a maximum angular distance of 18
°
(resp. 36
°
) from the
regular T intersection (resp. the regular 4-way).
Moreover, the availability of intersection data for the entire world easily supports compar-
ative analysis that so far was difficult to control. Imagine to run the same spatial experiment
in different cities or areas of the globe. The availability of this data may allow for comparing
the different paths and, consequently, for relating and gaining insights on the possibly different
experimental results obtained in different locations.
4.2 Local Differences
In this section we discuss local differences within the city of Vienna. We used our framework
to run analysis on all 23 districts (DIST) and focus on the two with the highest variation,
district 8 and 10.
Table 5 reports the distribution (as percentage) of the intersections as the number of
branches
n
varies. This allows for easily comparing the statistics of the selected districts
against the statistics extracted for whole Vienna. Both the selected districts adhere to
P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:11
Figure 5
Distribution of the intersections
as the number of branches nvaries.
Vienna DIST 8 DIST 10
3-way 75.16% 53.97% 76.46%
4-way 23.74% 44.63% 22.44%
5-way 0.93% 1.4% 1%
6-way 0.13% - 0.07%
7-way 0.02% - 0.03%
8-way 0.01% - -
Total 75644 428 7121
Table 5
Distribution of intersections over
number of ways for whole Vienna and the 2
districts in exam.
the overall distribution pattern that we discussed in Section 4.1, with almost the entirety
of intersections distributed between 3-ways and 4-ways. The graphical representation of
the data (see Figure 5) allows for glimpsing different local patterns for the two districts.
Specifically, district 10 exhibits a distribution almost identical to whole Vienna. In contrast,
district 8 exposes different distributions, with approximately 20% less 3-ways (resp. 20%
more 4-ways) than whole Vienna.
The distribution of 3-way and 4-way intersections can be seen in Figures 6a and 6b as
their normalized angular distance varies in the corresponding -ranges – i.e., [0
°,
180
°
]and
[0
°,
360
°
], respectively. As for 3-ways, district 8 is the most dissimilar with respect to Vienna,
while district 10 exhibits only a small deviation from the distribution of the whole city. The
same pattern emerges also for 4-ways.
Assume that we want to replicate in Vienna the navigational experiment discussed at
the end of Section 4.1 for which we need to select a path encompassing 10 intersections. If
we were to conduct the experiment in district 10, according to the intersection distribution
reported in Figure 5, approximately 76% (resp. 22%) of these intersections should be 3-ways
(resp. 4-ways). Say, for example, that we choose a path consisting of eight 3-ways and two
4-ways. According to the distribution of s in Figures 6a and 6b, of the selected 3-ways
(resp. 4-ways), five (resp. 2) should present a maximum angular distance of 18
°
(resp. 36
°
)
from the regular T intersection (resp. the regular 4-way).
If the experiment was to be conducted in district 8 we could either decide to stick to
the statistics of whole Vienna or to the statistics of the district. In the first case we would
end up with a selection similar to that of district 10. In the second case we would have to
choose differently. If we opt for the first alternative the findings that relate to the structure
of intersections could be considered as a step towards generalization to whole Vienna but
might apply more loosely to district 8. More generally, the statistical data provided by
our framework can be used to find out areas all over the world that expose an intersection
structure similar to that of a given area where, e.g., we performed an experiment. This
information can be used to replicate the experiment in any of these areas and identify
which of the insights we derive from the experiment results are invariant with respect to the
intersection structure of the path.
GIScience 2018
3:12 Intersections of Our World
(a) 3-way to regular T intersection. (b) 4-way to regular 4-way intersection.
Figure 6
Bar plot visualization of the distribution of the angular distance () for 3-ways
(a)
and
4-ways
(b)
with respect to the regular T intersection and the regular 4-way intersection, respectively.
See Figure 4 for reading instructions.
5 Discussion and Conclusion
The framework presented in this work can be considered as an important asset during the
design of spatial experiments and to perform spatial analysis. As shown through the case
study in Section 4, the framework can be easily used to partially validate a selected route with
respect to generalization issues. Since local differences can be found in an urban environment
that do not adhere to the overall structure of a city, a country, or even a continent, the choice
of a route has to be considered very carefully. Furthermore, by identifying similarities of
the selected route at different scales (i.e., from district up to continent scale), one can go a
step further and carefully interpret the findings of the experiment (at least those related to
features of the intersection distributions) and draw conclusions concerning the reproducibility
and comparison with experiments performed in different areas. Of course looking only at the
intersections of a route is not sufficient, but necessary. This work can be considered as a
further step towards interpreting the results of an experiment concerning generalizability
aspects.
Next to the scenario used throughout this paper to exemplify how the results of this
work can be utilized, this type of quantitative data can also be useful for a multitude of
other purposes. For instance, machine learning approaches could profit from this framework,
generating relevant features that can help to describe the spatial phenomena of interest.
Another example would include work in the area of transportation, trying to model the access
and demand or relevant work in the area of urban planing. Furthermore this framework
could also easily be used as part of city modeling softwares, e.g., Esri CityEngine
6
, helping
to automatically generate look-alike urban environments.
In this paper we presented the raw intersection data that we generated from OSM data
through the procedure described in Section 3.2 and show an example of how this data can
be used for the design and comparison of navigational experiments. However, according
to the specific experiment at hand it might be necessary to clean the raw data in order to
accommodate geometrical and perceptual aspects. We identified two cases where the raw
data may need to be cleaned before usage. Both cases concern scenarios where two or more
6See http://www.esri.com/software/cityengine.
P. Fogliaroni, D. Bucher, N. Jankovic, and I. Giannopoulos 3:13
intersections are located very close to each other. If the intersections under consideration
are of the same type, this may denote a mapping issue: due to accuracy problems a single
intersection in the real world is actually reported as several in OSM. Alternatively, the
intersections might actually be correctly reported in OSM, but we may have a perception
issue: although we physically have several intersections, they are so close to each other that
a person could perceive them as a single intersection.
The other scenario concerns the case where intersections of different types are very close
to each other. Specifically, we identified a somewhat problematic pattern where a road
intersection is surrounded by a set of path intersections representing sidewalks and zebra
stripes. In such situations, we actually have a single intersection in the real world that is
identified as several by our framework. This issue is due to the fact that in OSM, sidewalks
can either be mapped as separate ways or denoted with an apposite tag on the corresponding
road. This means that we cannot know in advance how many times this scenario appears in
our data. For this reason we performed a simple buffer and cluster analysis on Vienna to find
out the amount of groups of intersections in our data that should actually be considered as a
single intersection. We used buffer of different sizes (ranging from 1m to 10m) to identify
clusters corresponding to both scenarios: intersections of same type and one road surrounded
by path intersections. For the first scenario we found that the number of clusters ranges
from 0.04% to 4.8% (resp. from 0.2% to 12.4%) of the road (reps. path) intersections, as we
increase the buffer radius from 1m to 10m. For the road-to-path scenario, the number of
clusters ranges 0 to 5.7% of the road and path intersections.
Finally, it has to be noted that the implementation of our framework does not compute
the data on the fly from OSM data. Rather, a snapshot of the OSM database is taken and
intersection data is generated from there. This means that the data provided on the website
might not be completely actual, although we do not expect huge discrepancies.
6 Outlook
Since in our work we focused on regular intersections, we omitted analyses of roundabouts.
In the underlying OSM data, roundabouts are modeled as multiple 3-way intersections.
Although this might look correct at a first glance, one can argue that roundabouts form a
category of its own, or even an n-way intersection, with n equals the number of ingoing and
outgoing branches. As this is an open question that needs further investigation and probably
a user study to understand how humans perceive roundabouts, we will focus on this problem
in the future. Since this framework is not only indented to be used for experimental design, a
possible solution could be to transfer the choice to the users of this framework, by providing
multiple options on how to handle roundabouts during runtime.
Also, in this work we did not perform any scale-based aggregation of the street geometries
(e.g., aggregating two lanes of a street into a single line). Therefore, the results presented in
this paper are at the finest level of details allowed by data source. Street aggregation will
also yield a reduction in the number of detected intersections as well as a simplification of
the resulting intersection network. Future work along this direction may potentially lead to
a hierarchical organization of the data that, in turn, may allow for further types of uses and
analyses of the intersection data.
In future work we will also focus deeper on network patterns. For instance, what is the
most common sequence of intersections for a given length (number of intersections)? What is
the typical distance between intersections or intersection types (segment length)? Being able
to extract this type of information will further improve the goals set in this paper, allowing
to draw even better conclusions and automatically create even more realistic look-alike cities.
GIScience 2018
3:14 Intersections of Our World
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