man Institute for Standardization , 1998) from Ger-
many and ABNT NBR 9050:2004 (ABNT (Brazil-
ian Association of Technical Standards), 2004) from
Brazil. Other studies as Kasemsuppakorn and
Karimi (Kasemsuppakorn and Karimi, 2009) investi-
gated the most relevant aspects regarding wheelchair
accessibility, for each segment of the route network
(i.e. length, width, slope, sidewalk surface, steps,
sidewalk conditions and sidewalk traffic). More-
over, some studies consider not only barriers but also
provide information about relevant locations (called
Points of Interest - POI) as restaurants, bus stops, ac-
cessible toilets, and police departments (e.g. Menkens
et al. (Menkens et al., 2011), and Wheelmap
9
).
Sumida et al. (Sumida et al., 2012) argues that bar-
riers information should be collected through actual
measurement data and adapted an electric wheelchair
for collecting data as the force necessary to move the
wheelchair and the passage width. Other studies use
data provided by the routing service users (e.g. Open-
RouteService, and Menkens et al. (Menkens et al.,
2011)), volunteers (e.g. OpenRouteService; Menkens
et al. (Menkens et al., 2011); Kulakov et al. (Kulakov
et al., 2015)), authorities (e.g. Kulakov et al. (Ku-
lakov et al., 2015)). Consequently, the collected data
is usually limited to a city or a district. An exception
is the Wheelmap project
9
that provides resources for
crowd sourcing information based on OpenStreetMap
data.
The lack of public available information regarding
accessibility of urban spaces (e.g., streets, sidewalks,
curbs, and type of surface) contribute to the fact that
most of studies on accessible routing are constrained
to cities or districts. Some initiatives as Wheelmap
explore the aspects of crowds for collecting relevant
information regarding POI. Currently, to our knowl-
edge, none of such initiatives are widely adopted in
Curitiba (e.g. there are only about 10 POI registered
in Wheelmap, most of them are accessible bus stops).
Routing estimation is another challenging task. In
order to improve the results of routing estimation,
some services provide additional parameters (e.g.,
maximum inclination, type of surface, maximum curb
height
6
), personalized estimation according to the
users’ profile (e.g. Menkens et al. (Menkens et al.,
2011)). As already noted by A. M. Bishop within
the Routino application, routing planning can use
graph algorithms (e.g. Dijkstra and A*) for calculat-
ing the shortest/least-cost path. Some of those stud-
ies adapt these algorithms aiming at improving per-
formance in terms of execution time (e.g. the con-
cepts of super-segments and super-nodes from A. M.
Bishop
7
). Others claim that there is no clear answer
9
http://wheelmap.org/en. Last Visited 24/08/2015.
as to shortest path algorithm which runs fastest on
real road networks (due to real time computation, the
large network size, and the resulting intensive com-
puting) (Zhan, 1997). Among other critical factors
for route planning we can mention: (1) types of bar-
riers considered for collecting and estimating routes,
(2) data sources for maps information and barriers,
and (3) approaches for route planning.
3 OUR METHOD
Problem Formulation. For GIS applications, the
shortest path based on a road is a basic operation.
In practice, however, users are always interested in
several constraints (such as the combination of spatial
and textual information). From GIS and map analysis
perspective, the routing problem can be described as
a three steps process: the calculation of discrete cost,
accumulated cost and steepest path (Berry, 1993).
The idea is, using base maps (such as roads), create
other derived maps (to calculate information that is
too difficult to collect, such as curb ramps) in order
to finally create cost/avoidance maps which translate
this information into decision criteria. Within this per-
spective, map layers are thematic representations of
geographic information, as shown in Figure 1. In par-
ticular, base maps can be represented by streets, street
blocks (Figure 5) and sidewalks, among others.
The derived maps, composed by large polygon
subdivisions, are often simplified in order to reduce
the total number of vertices which defines it (known
as the map simplification problem (Estkowski and
Mitchell, 2001)). The calibration of the individual
cost maps is an important and sensitive step in the sit-
ing process. Since the computer has no idea of the rel-
ative preferences this step requires human judgment.
As an example, you might be interested in identify-
ing the most preferred route for a wheelchair user that
minimizes its visual exposure to huge avenues, and
maximizes the visual exposure to bus stops.
From the geometry perspective, streets are one or
more single lines (which can also be represented by
one ore more edges in a graph), which thereby are
composed by points (which can also be represented
by a vertice in a graph). Blocks (Figure 5) can be
decomposed by the respective lines, and lines can be
decomposed by respective points (Figure 6).
Formally, a GIS database contains a set of geome-
tries which can be resumed as a set P of points on a
network G = (V, E), where V represents vertices and
E represents edges. The network is a directed con-
nected graph. A point p ∈ P locates on an edge e ∈ E.
The distance between any two points (or vertices) can
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