Accident Analysis and Prevention 73 (2014) 274287

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Accident Analysis and Prevention

journal homepage: www.elsevier.com/locate/aap

A model to identify high crash road segments with the dynamic

segmentation method
Amin Mirza Boroujerdian a, *, Mahmoud Saffarzadeh a , Hassan Youse b,c ,
Hassan Ghassemian d
a
Faculty of Civil & Environmental Engineering, Tarbiat Modares University, Tehran, Iran
b
School of Civil Engineering, Faculty of Engineering, Tehran University, Tehran, Iran
c
Institute of Structural Mechanics (ISM), Bauhaus-University Weimar, 1599423 Weimar, Germany
d
Faculty of Electrical & Computer Engineering, Tarbiat Modares University, Tehran, Iran

A R T I C L E I N F O A B S T R A C T

Article history: Currently, high social and economic costs in addition to physical and mental consequences put road
Received 20 November 2013 safety among most important issues. This paper aims at presenting a novel approach, capable of
Received in revised form 6 September 2014 identifying the location as well as the length of high crash road segments. It focuses on the location of
Accepted 11 September 2014
accidents occurred along the road and their effective regions. In other words, due to applicability and
Available online 27 September 2014
budget limitations in improving safety of road segments, it is not possible to recognize all high crash road
segments. Therefore, it is of utmost importance to identify high crash road segments and their real length
Keyword:
to be able to prioritize the safety improvement in roads. In this paper, after evaluating deciencies of the
High crash road segment
Segmentation
current road segmentation models, different kinds of errors caused by these methods are addressed. One
Prioritization of the main deciencies of these models is that they can not identify the length of high crash road
Wavelet theory segments. In this paper, identifying the length of high crash road segments (corresponding to the
Multiple resolutions arrangement of accidents along the road) is achieved by converting accident data to the road response
signal of through trafc with a dynamic model based on the wavelet theory. The signicant advantage of
the presented method is multi-scale segmentation. In other words, this model identies high crash road
segments with different lengths and also it can recognize small segments within long segments. Applying
the presented model into a real case for identifying 1020 percent of high crash road segment showed an
improvement of 2538 percent in relative to the existing methods.
2014 Elsevier Ltd. All rights reserved.

1. Introduction review, some of the current segmentation methods are as the

following:
Accident prevention is the most effective method to improve
the safety of road networks. Due to wide-spread and complex 2. Current segmentation methods
nature of accident causes, identifying high crash road segments
and proposing countermeasures are difcult to analyze. In order to Identifying high crash road segments is a very critical stage in
evaluate the high accident-proneness of a road, it is required to road safety studies. Using segmentation, one can assign accidents
divide this road into certain segments and then predict the to specic road segments and identify high crash road segments.
accident risk probability by collecting and studying physical and The previous researches in segmentation show that for
trafc characteristics of the road. The process of safety assessment identifying high crash road segments in many countries the rst
gets more costly and time consuming as the number of segments step involves dividing the road of interest into equal length
increase. Additionally, it is probable that inaccurate evaluation segments and then studying the accidents in each segment using
arises as the number of segments increases. In the literature one of the identication methods of high crash road segments.
Although, the segment lengths are dened differently in different
countries, the length for evaluating a specic road is unique.
Kononov and Allery (2003) studied the level of road safety
* Corresponding author. Tel.: +98 21 82884367; fax: +98 21 82884915.
service. In their study after separating some parts of the road, they
E-mail addresses: ambrouj@yahoo.com, boroujerdian@modares.ac.ir
(A.M. Boroujerdian), saffar_m@modares.ac.ir (M. Saffarzadeh), hyose@ut.ac.ir divided the road into 2 mile segments to identify high crash road
(H. Youse), ghassemi@modares.ac.ir (H. Ghassemian). segments (Kononov and Allery, 2003). According to Federal

http://dx.doi.org/10.1016/j.aap.2014.09.014
0001-4575/ 2014 Elsevier Ltd. All rights reserved.
 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287 275

Highway Administration report, the length of high crash road least 4 accidents occur in 3 years in a length of less than 100 m. In
segments is equal to 0.3 miles in road segmentation (Federal this method, the template (100 m or 1000 m) is used for
Highway Administration, 1981). According to Texas Transportation segmentation (Elvik, 2008).
Institution the length of high crash road segments should be at In Iran, the road is divided into 1 km segments and then the
least 0.1 miles (Bonneson and Zimmerman, 2006). In Ohio, accidents in each year are counted. Table 1 summarizes the
Segmentation method is applied differently. According to this common denition of high crash road segments in each country
method, segmentation is a procedure in which a road is divided (Elvik, 2008).
into segments with the same characteristics. In this research, the However, in addition to various lengths of high crash road
length of road segments is equal to 0.25 miles. Also, each segment segments in different methods, another difference between the
should not be too long or too short. Depending on conditions, the segmentation methods is the denition of starting point. There are
segments of less than 0.25 miles and 0.250.5 miles are dened in basically three starting point denition: (1) some xed and
the list of segments (Pant et al., 2003). A different method for road successive segments are dened from the beginning of the road (2)
segmentation is proposed by Torke. According to this method, the the segments are moved in half of the length of xed segments and
road is divided into 0.2 km segments which may be continued then the accidents in the new segments are studied so that analysis
along the highway or included in the other segments or errors in this method may be reduced (3) high crash road segments
intersections (Troche, 2007). are identied by oating the xed template segment along the
In a project undertaken by the European researchers, the road. The last denition is the most accurate.
current methods of high crash road segment management and
road network safety analysis are evaluated (Elvik, 2008). In 3. Evaluation of current segmentation methods
Austria, a xed segment of 2.5 km moves along the road as a
template. The segments which are dened along this template The current segmentation methods fall into two categories:
and meet the specic criteria of high accident-proneness level are static and dynamic segmentation methods. In static segmentation
dened as high crash road segments (Troche, 2007). High crash methods the length of each segment is xed; high crash road
road segment in Denmark is dened by dividing road systems into segments are identied by dividing the road into segments with
different kinds of road segments and intersections (Vistisen, specic lengths, and by counting the accidents in these segments
2002). A test based on the Poisson distribution is done to identify according to the denition of high crash road segments. Then the
high crash road segments. The minimum number of accidents segments with high priority are identied in terms of high
that is considered for a high crash road segment is 4 accidents in a accident-proneness. With regards to accident distribution along
period of 5 years. Accordingly, segmentation is achieved to the road and their causes, it can be concluded that the risk index or
identify high crash road segments using the dened template. The probability of accident occurrence along the road may vary due to
length of this template depends on the number of normal interaction between safety factors of the road, vehicles, and
accidents in each segment (Vistisen, 2002). In Belgium, based on humans. For example, the friction coefcient may not be suitable
police report, every segment in which three or more accidents along the road and lead to an accident occurrence at time intervals
occur during 3 years is dened as a high crash road segment. In in a year or the accidents may occur in part of a road due to
this method, a 100 miles template is used to identify high crash inadequate sight distance such as in a road curve. Considering the
road segments. Therefore, the segments with the maximum aforementioned examples, it is concluded that the length of high
length of 100 miles and 3 accidents are recorded (Geurts, 2006). crash road segments may vary along the road depending on the
In Romania, there are two denitions to identify high crash road extent of accident causes. Also, using the static segmentation
segments: (1) with the exclusion of the residential areas, a high methods may lead to some errors in results analysis and high crash
crash road segment is a location in which at least 4 accidents road segment identication or may even fail to identify some high
occur in 3 years in a length of less than 1000 m (2) in residential crash road segments. Three main deciencies of static segmenta-
areas, a segment is identied as a high crash road segment if at tion methods are as follows:

Table 1
Denition of high crash road segments in some countries (Elvik, 2008).

Country Denition
Germany - 300 m road segments
- More than 3 accidents during 1 year and more than 5 accidents during 3 years

United Kingdom - 300 meters road segments

- The location in which the total number of accidents is more than 12 during 3 years.

Portugal - The segments with the length of 200 m

- More than 5 accidents during one year

Spain - 1 km segments
- More than 5 injury accidents or 2 fatal accidents during 1 year
- More than 10 injury accidents or 5 fatal accidents during 3 years

Norway - 100 meter road segments and more than 4 fatal accidents during one year

Czech Republic - A road segment of 250 meters

- At least 3 injury accidents during one year or 3 similar injury accidents during 3 years
- At least 5 similar accidents during 1 year

Netherland - At least 10 total accidents or at least 5 accidents with certain specications

 276 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287
[(Fig._1)TD$IG]
Static Segmentation Method

9 8 5 5

1 14 2 10
Dynamic Segmentation Method

Fig. 1. The number of accidents counted by two segmentation methods.

a Probability of omitting some road segments with high accident incrementally with a specic step. This method is a bit similar to
density;In this method, the boundary of some segments may fall the dynamic segmentation method, but the new proposed model
in the middle of a high accident density region. In this case, half in this research, in addition to solving all of the aforementioned
of the accidents are located within one segment and half in the problems in this section, is able to develop some new analytical
other. Therefore, with depreciation of the accident density in capabilities which are mentioned in the next sections.
these two segments, the high crash road segments may not be
identied and thus the analysis may not be accurate. The 4. The algorithm of wavelet theory
deciency is illustrated in Fig. 1.As it is indicated in Fig. 1, the
number of accidents does not exceed 10 in any segments with In this research, the data is processed after specifying the
the static segmentation method, but by applying the dynamic accident locations along the road based on the accident data
method (based on the accident density), some segments with reported by the police. Then considering the relative accident
more than 10 accidents are identied. locations (accident widespread or density) the road segments are
b Not identifying the segments in different levels.If there is one identied based on the accident-proneness. In this method, the
general problem or there are several local problems along the appropriate models are used for analyzing the accident data by
specic length of the road, the current methods are not able to changing them to discrete and analyzable data through wavelet
identify this problem. The problem is shown in Fig. 2.Regarding theory. In this method, the accident density in each segment of a
the distribution of accidents along the road, it can be concluded road is considered as the local response of that segment to the
that a specic cause may be the main cause of high accident- passing trafc. Furthermore, the length of accident-prone segment
proneness in the longer length of the road while the severity of is measured based on accident distribution.
that cause may be greater in the shorter length of that road. One of the common signal processing tools is the Fourier
Therefore, in this location, the probability of accident occurrence transform. There, it is assumed that a smooth function can be
is greater than in the other locations of the road. The current decomposed to innite harmonic waves of innite support. Hence,
segmentation models may not be able to identify this location. frequency content of the function can easily be captured regarding
c Mismatch between the specied length of segments with the the harmonic waves. This transform provides only information
current static segmentation methods and the length of the real about the frequency content; the positions (time) of the frequen-
high crash road segments.If the length of high crash road cies are omitted.
segments is more or less than the length of each specied If a process is stationary, then the Fourier transform is enough
segment, the suitable length of each segment can not be to study the data. In case of non-stationary data (data with
identied by the current method. The high crash road segment transient features during forming), however, recognizing both the
length should be dened with regards to the proportional frequency content and corresponding spatial positions are impor-
distribution of accident causes along the road. When evaluating tant. One of the non-stationary processes is road accident data,
road safety, assuming xed lengths of segments may lead to where the accident frequency and corresponding spatial position
errors identifying high crash road segments. are equally important. In these cases, the features obtained by the
famous Fourier transform are no longer useful.
Considering the given explanations and examples, it is Some researches on a non-stationary data simultaneously with
concluded that most of the current methods for identifying high spatio-frequency spaces have been undertaken. The well-known
crash road segments have serious deciencies. However, after one is the windowed Fourier transform; in this research, the data is
reviewing the studies in several countries, the segmentation locally studied by means of the Fourier transform. To meet the
method was improved to decrease the mentioned deciencies. purpose, the data is observed by a spatially compact support
Therefore, instead of simple segmentation, a xed length template window (with constant width in spatial domain) and the data of
is created based on the length of the road and moves along the road corresponding range is used for the Fourier transform. The
[(Fig._2)TD$IG]
Static Segmentation Method

3 7 9 4

8
3 20
Dynamic Segmentation Method

Fig. 2. The number of accidents counted by two segmentation methods.

 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287 277
[(Fig._3)TD$IG]
b) is evaluated. By changing the scale values, the transform process
is repeated again. Finally the initial data {x,f(x)} is mapped to space
{a,b,WC f(a,b)} , a 3D surface; there spatio-frequency features are
presented simultaneously. In this theory to capture high frequency
and smooth features, scales of small and large values are used,
respectively.
In the following the Mexican hat wavelet is illustrated in
Fig. 3, and is dened as (Lcwalle, 1995):
2 x2
cx pp4 1  x2 e 2 (4)
3 p

Fig. 3. Mexican hat wavelet. where it satises the conditions:

Z
resulting frequency content, then, is considered to associate with ca;b xdx 0 (5a)
the window center. This locally watching-transforming process is
continuously repeated throughout the data, and nally the spatio-
Z h i2
frequency features of the data are captured. In this transform, the
ca;b x dx 1 (5b)
window width (support) is assumed to be constant. In brief, the
transform can be expressed as (Youse and Noorzad, 2004): The condition (5a) means that the scaled wavelets have zero
Z 1 average, or in other words they measure variations (details) of
WFTb; w f xgx  beiwx dx (1) data; the condition (5b) shows that the scaled wavelets have unit
1
energy (for such condition, a scaled wavelet is normalized as
where f(x) and g(x) are the data and compact support window,
Eq. (3)), hence by multiplying them to a function, energy of the
respectively. The parameter b denotes the center of the window g
function does not change during the wavelet transform (see
(x) in spatial domain.
Eq. (2)) (energy preserving transform).
The window Fourier transform is inefcient in case of data
From Fig. 3 it is clear that the region of positive C (x) values
having features of different frequency contents with different
equals to 2a; this property will be used in this work to identify
supports (in spatial domain); it can not detect all the features
accident zones: variation of accident with different frequencies,
simultaneously. This is because, the window has constant support
both low and high frequency zones, simultaneously.
size; hence this transform is useful in cases where feature supports
In the following, the performance of the wavelet-based
are approximately equal to the window support size.
approach is conrmed by some simple examples; in which,
To remedy the aforementioned drawback, the wavelet theory is
accident zones can easily be distinguished.
developed (Mallet, 1998; Lcwalle, 1995). Here, the window based
approach is used too, but the size of support is no longer constant;
5. The identication model of high crash road segments
the window denotes with C (x). Regarding the window support, in
the wavelet theory, there are two kinds of window functions: (1)
Mathematical models can be used for analyzing logical
completely compact support windows: in this case the window
concepts in nature. Nowadays, different kinds of theories and
width is spatially limited (it has non-zero values only in a compact
models are proposed to analyze accidents and identify high crash
range), like the Mexican hat wavelets (Mallet, 1998; Lcwalle, 1995);
road segments each of which has their own advantages and
(2) windows with innite width: in this case however values of the
disadvantages. This research aims at nding a suitable mathemat-
window vanish rapidly from center of wavelet function, like the
ical model that reduces the aforementioned errors of current
Newland wavelet family (Mallet, 1998). In both cases, the wavelet
R1 models used in application studies. According to the data
functions have nite energy; i.e.,: 1 cx2 dx < C where C is a
nite positive constant. [(Fig._4)TD$IG]
The support size of a scaled wavelet function varies regarding
frequency content of data; the windows of narrow support are Collecting accident data along the road including location of accident occurrence
used in high frequency zones, while the ones with wide supports
are employed in smooth portions. Converting Discrete Spatially Non-uniform data to a Spatially Uniform One
The continuous wavelet transform then can be dened as:
Z 1
1  xb
W c f a; b p f xc dx (2) Analysis of Produced Signal using Wavelet Theory
jaj 1 a
where f(x) is the data; C (x) denotes the wavelet (a small wave: the
window); a is the scale number controlling window width; b Omitting Disturbances from the Accident Signal
represents spatial position where the wavelet is shifted there; the
symbol * shows imaginary conjugate of a function.
Analysis of Wavelet Converting and Identifying the Center and Length of High
The shifted-scaled version of the wavelet C (x) denotes as C a, Crash Road Segments
b(x), and is as follows:

1 xb Dividing the Road into some Segments According to the Accident Probability
ca;b x pc (3)
jaj a

considering above formulation, the shifting and dilatation sizes are Prioritizing High Crash Road Segments Based on the Magnitude of Wavelet
b and a, respectively. Conversion
In the wavelet transforms, by considering a constant scale, the
variable b is continuously varied and the wavelet transform, WC f(a, Fig. 4. The procedure of the identifying model of high crash road segments using
wavelet theory.
278 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287
[(Fig._5)TD$IG]

Fig. 5. The instance of accident arrangement along the road.

distribution of accidents along the road, rstly, it is assumed that uniform grid. The important point is that in such mapping the total
accumulation of accidents along the limited length of the road number of accidents should not be altered. Therefore, here we use
indicates that there is one or several accident causes in that linear interpolation for remapping data of magnitude F located
location. Therefore, in this stage, the goal is to identify the locations between two surrounding grid points. Assume distances of an
of meaningful accident accumulation along the road. When accident from two neighbor points to be: x (from the left grid
considering the variation of real length of high crash road point) and D  x (from the right grid point); here D is distance of
segments, which by denition is proportional to the risk factors uniform grid points from each other (sampling step in spatial
along the road, the model, which denes the initial length of domain) and 0  x  D. Then by using the following simple linear
segmentation according to the distribution of accident locations, is interpolation formula the data is mapped:
more efcient in identifying high crash road segments.    
x X
The structure of the proposed model is shown in Fig. 4. FL 1  FandFR F
D D
6. Collecting the accident data along the road including each where FL and FR are maps of F on the left and right points,
accident location respectively. Please note that at this mapping, total number of
accidents are preserved, since: FL + FR = F.
Determining the location and length of high crash road
segments depends on the determination of the exact location of 8. Analyzing accident signal and identifying high crash road
accident occurrence. Since the duration of data collection affects segments
analysis output, the accident data must be considered during the
entire 35 year period regarding the random nature of crash The segments in which some accidents occur due to some
occurrence and to get a regression to the phenomena. causes could be identied by both dilation and shifting of the
mother wavelet window as described before. Finally the wavelet
7. Converting discrete spatially non-uniform data to a spatially transform values are represented as function of the scale (which
uniform one measures frequency) and spatial position (locations of wavelet
function centers) in a contour plot graph. Here, values of transform
In the above owchart, one point should be explained in more coefcients are in accordance with the accident density and the
details. In this study, the considered wavelet transform works on risk index. This helps to improve safety in such high risk portions.
uniform grids (this kind of wavelet transforms is known as the rst Sometimes, one factor may be the cause of the accidents in a
generation wavelets). In this regard, it is necessary to pre-process longer length of road, while in a smaller segment of this road there
data (which are actually distributed on non-uniform locations). may be accidents with a different cause. Regarding the multiple
This pre-processing is done to remap the irregular data on a analysis capability which is done by changing the window scale in
[(Fig._6)TD$IG]

Fig. 6. The output of wavelet model to analyze the example in Fig. 6 (Boroujerdian, 2011).
 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287 279
[(Fig._7)TD$IG]

Fig. 7. The output of wavelet conversion after removing the effect of scattered data (Boroujerdian, 2011).

each point of the road, it is possible to identify a high crash road In the proposed example in Fig. 5, the length of road where the
segment with a limited length of that segment. accidents happen is 26,000 m and corresponds to the arrangement
As it was mentioned in the previous section, different windows in this gure. The horizontal axis represents the number of
can be used to analyze a signal based on the wavelet theory. This samples or the ratio of length of the road to the length of sampling
wavelet could be used to identify high crash road segments with unit (length of sampling unit is 100 m) and the vertical axis
regard to the characteristics of Mexican hat analytical window. represents the number of accidents in each sampling unit.
Using the Mexican hat window enables the analyzer to identify The denition of the horizontal axis in Figs. 5 and 6 is the same
the center of the high crash road segments and the effective region. and shows the length of the road and the vertical axis represents
In this method, the locations which are identied as the peaks in the wavelet scale. Therefore, the value of x in the extreme points in
the wavelet theory analysis diagram are the center of high crash Fig. 6 represents the situation of points along the road and the
road segment. Since the sign of accident data is positive, the value of y represents the scale in which the wavelet transform
maximum wavelet transform value occurs in the scale where the value is at maximum and the contour line passed from point y
local information of interest lies within the positive extent of the represents the wavelet transform size at that point. As Fig. 5 shows,
wavelet window. Therefore, the length of the high crash road wherever the accident happens in Fig. 5, its effect can be
segment could be identied by doubling the scale of the wavelet recognized. The centers of high crash road segments are the
transform size in the center of the high crash road segment. This contour line peaks in Fig. 6 and the size of the peaks represents the
capability will be evaluated using an example in the following: length of high crash road segments. However, there is a problem in
In the example shown in Fig. 5, the capabilities of the proposed this analysis with existing extra data caused by scattered accidents.
model are introduced by reconstruction of accident data in a Identifying high crash road segments as the output of wavelet
manner similar to what happens in a real road. transform is performed after de-noising and analysis of the new
The manual analysis of the example can be done to show that a signal. De-noising is discussed in the next section.
general evaluation using the capabilities of the proposed model is
possible. 9. De-noising
Some issues should be taken into account when developing this
example; the issues include: high crash road segments with In this method, the analysis output is de-noised by calculating
different lengths, high crash road segments with limited length the amount of wavelet transform of the high accident-proneness
along the longer segments, and scattered accident data which does threshold (for e.g., one accident along the sampling stage) and by
not show accident causes in the road and may be due to irrelevant omitting some areas with a wavelet transform that is less than the
causes of road characteristics. The accident arrangement of the amount of wavelet transform of the high accident-proneness
previous example and the output of the wavelet analysis method threshold.
are shown in Figs. 5 and 6 respectively. This model can be evaluated Considering that the applied wavelet in this analysis is Mexican
by comparing these two gures. hat its function is formulated as follows:
 280 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287
[(Fig._8)TD$IG]

Fig. 8. Segmentation of the road through the output of corrected wavelet conversion (Boroujerdian, 2011).

2 x2
cx pp4 1  x2 e 2 (Repetition 4) transform that are more than the threshold value for identifying
3 p high crash road segments are shown in Fig. 7.
The wavelet transform of data including one accident is calculated As the above gure shows, the noises have been removed in
as follows: Fig. 7b as compared with Fig. 7a. It should be considered that the
p
Z   Z x values of wavelet transform are divided into a. This performance
1 xb b0 1
W a;b p c dxdx ! W cr p c dxdx will be discussed in the next sections.
a a a a
Z  
1 x0 1 2 10. Dening the length of high crash road segments
p p  pp (6)
a a a 34 p
In Fig. 8, the road is divided into segments based on the output
In the above equation, d(x) shows the delta function whose of wavelet transform without the scattered accidents. In this gure,
characteristics are dened based on the following equations: the high crash road segments are identied by the dynamic
 segmentation method based on the location of each accident. For
dx 0 x 6 0 (7)
dx 1 x 0 better analysis, the axes which specify the center of high crash road
segments are labeled with numbers and the specied segments in
this example have been shown in two separate rows to represent
Z
1 the multi-scale property for recognizing high crash road segments
dxdx 1 (8) with different length. The aforementioned scales are labeled large-
1 scale segmentation (LS) and small-scale segmentation (SS). As it
was discussed in the previous sections, the center and length of
high crash road segments are identied by the line which passes
Z
through the peak of the wavelet transform surface and the peak
f xdx  x0 dx f x0 (9)
scale size respectively.
Since the least value of a is equal to 1, the least value of wavelet The SS and LS sections reveals themselves as local peaks in the
transform is 1.73 based on the Eq. (7). The values of wavelet wavelet transform representation (b,a,W(a,b)) with effective length
2a; where a denotes the scale of the wavelet function (see Fig. 3); in
 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287 281
[(Fig._9)TD$IG]

Fig. 9. Articial peaks in the Mexican hat wavelet transform for a constant function with bounded spatial support.

the length 2a, the Mexican hat wavelet is positive. The SS and LS inappropriate due to a general cause (such as a nonstandard
sections locate around small and large a values, respectively. friction coefcient in the long segment of a road) and when more
Smaller a value is a more localized feature. accidents occur along this segment or along one or more shorter
In this regard, the axes 3, 4, 6, 8, 9, 10, 12, and 13 specify the parts of the road due to another cause (such as an unsuitable curve
locations of high crash road segments with limited length (with radius). These kinds of segments could be identied by the
slightly different support lengths: 2a). As it can be seen in the multiple clarity application which is involved in this method. As it
arrangement of accidents, many accidents have happened along can be seen in Fig. 8, the axes 1, 2, 3, 5 and 13 indicate the high crash
the short length next to these axes. These segments may be located road segments with different lengths where the occurring
within the connes of other longer high crash road segments. This accidents are more than the threshold value of high accident-
situation may happen in real roads when the road safety is proneness. The model is sensitive to axis 9, which is a long segment
[(Fig._10)TD$IG]

Fig. 10. Segmentation of the road through the output of corrected wavelet conversion (Boroujerdian, 2011).
282 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287
[(Fig._1)TD$IG]

Fig. 11. The arrangement of recorded accidents in more than 50 km of ShahroodSabzevar road (Boroujerdian, 2011).

with a xed high accident-proneness level. Thus it is clear that the support (dening on a bounded spatial domain) is considered. In
hazardousness of specied segments depends on the amount of Fig. 9(a), the constant function and the wavelet are shown; the
the indicated wavelet transform and the segment length which is wavelet function locates completely in support of f(x). The
discussed in Section 15. As it can be seen in the output of wavelet corresponding wavelet transform, therefore, is zero; since positive
transform, segment 9 is made up of three distinct high crash road and negative parts of transforms eliminates each other. By
segments of shorter length. approaching the wavelet to the edge of f(x) (end of support), at
The axes 7 and 11 are (small) peaks, which are articially rst, the transform value W(a,b) increases (Fig. 9(b)). This is due to
detected by the wavelet transform. Mathematically, it can be unbalancing of the positivenegative parts of W(a,b). The maxi-
explained by Fig. 9. There, a constant function f(x) with nite mum value is achieved when one negative part of W(a,b) is
[(Fig._12)TD$IG]

Fig. 12. The segmentation of ShahroodSabzevar road (Boroujerdian, 2011).

 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287 283
[(Fig._13)TD$IG]

Fig. 13. The signal wavelet conversion amount of ShahroodSabzevar road accidents.

completely outside the support (Fig. 9(c)). After this point, by With regards to the division of high crash road segments into
further shifting of the wavelet, the W(a,b) value decreases until it LS and SS segments and depending upon the amount of
becomes zero (Fig. 9(d)). By further shifting of the wavelet it maximum accident density index in each segment (Fig. 10;
continues to decrease (Fig. 9(e)) until W(a,b) reaches a minimum here, the numbers in the rectangles are the W(a,b) values), it may
value. Thereafter, negative value of W(a,b) increases until the be concluded that the segments 10, 12, 9, 6, 4 and 8 are the SS
wavelet is completely outside the support of f(x). Beyond this high crash road segments, respectively, in the road of interest and
point, W(a,b) will be zero (Fig. 9(f)). In this regard, the wavelet also the segments 3, 9, 5, 2, 13 and 1 are identied as the LS high
transform detects a maximum value near the edge of f(x) articially crash road segments, respectively, from the most to the least
(Fig. 9(c)). hazardous.

11. The relationship between size of the wavelet transform in

different segments and the probability of accident occurrence 12. Genuine example
in each segment
In this section, the capabilities of the proposed model are
Based on the rules of the wavelet method for analyzing accident evaluated using a genuine example. In this example, the accident
data, it is concluded that for every segment of the road which has a data is collected along the road which is 50 km in length between
higher accident density, the improvement priority of that segment Shahrood and Sabzevar for a duration of 3 years i.e., 20042007
is higher. Therefore, by this method, the length of high crash road (Boroujerdian, 2011).
segments may be identied and its relative prioritization is The gurative pattern of reported accident data in the case
determined. Naturally, if the data is corrected, for example by using study is illustrated in Fig. 11. In this gure, the horizontal and
the equivalent coefcient of accident severity, the effect of accident vertical axes present the length of the road (km) and the number
severity may be taken into account in the analysis. Prioritization by of accidents respectively. As it can be seen in the gure, no
this method may be done provided that the fundamentals of the accident has been reported in the rst 3 km of the road. Also, the
theory used for prioritizing high crash road segments coincides reported accidents in the end of 20 km section of the road under
with the hypothesis of the wavelet transform method. study are scattered. One of the most important characteristics of
As seen in Eq. (10), in order to calculate the wavelet transform these data is that they have accuracy of 1 km; this means that
an accident frequency index around a point is divided by the the least length of identiable high crash road segment is about
second root of the wavelet size scale that matches with the length 1 km. The data is collected for the accidents occurred during
of effective area of this point. 20042007. It is necessary to be rigorous in developing the
Z analysis process for threshold value denition of high crash road
1 xb segment.
W p c dxdx (10)
a a It is expected that the model can remove the effect of scattered
Therefore, a density index is developed by dividing the wavelet data from the analysis and identify the high crash road segments
transform size at each point by the second root of the wavelet scale matched with the length of segment.
size for that point which is applicable for the relative prioritization
of the segments by high accident-proneness probability.
13. Converting the accident signal wavelet and de-noising

Table 2 Accident signal is analyzed by the wavelet transform method

The priority of segments based on crash density. and the results are shown in Fig. 12. As already discussed in the
Segment No. 1 2 3 4 5 6 7 8 9 10 11 12 previous section, by omitting the contour Lines having the amount
Priority 6 5 4 10 8 12 1 9 2 7 11 3
of less than the threshold value, there is a possibility of de-noising
the data for accidents.
284 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287

Table 3 them the segments 2 and 10 have larger lengths. In order to display
The number of accidents by different segmentations (Boroujerdian, 2011).
the segments more clearly, the results are shown in two axes.
km The number of Fixed segmentation Dynamic As it is illustrated, around the axis 1, considering the
accident per segmentation approximation of these three segments with high number of
kilometers
accidents, the dynamic segmentation model denes the length of
2 km 3 km 5 km 2 km SS LS
segment segment segment segment
segment so that it includes these three segments. Also, around the
(oating) axis 4, there is a similar situation and the corresponding model to
1 0 0 0 46 0 0 0
the location of accidents denes the length of the segment.
2 0 0 Apparently, the minimum length of segment which is identiable
3 0 25 in this method is the same as the length of sampling step which is
4 25 66 46 66 142 dened in many SS high crash road segments. Fig. 12 illustrates the
5 21 41
segmentation of ShahroodSabzevar road.
6 20 96 20
7 14 49 56 49 14 Approximation of the many occurred accidents may indicate
8 35 35 that the there might be a special cause along particular part of the
9 7 27 7 7 road, thus the problem can be solved along the segments 2 and 10.
10 20 40 36 36
11 16 20 62 76
Table 4
12 4 28 4
The accident density in different segments (Boroujerdian, 2011).
13 24 28 42 24
14 4 4 4 km Fixed segmentation Dynamic
15 14 22 22 14 segmentation
16 8 61 76 14
17 6 53 53 2 km 3 km 5 km 2 km segment SS LS
18 47 47 227 segment segment segment (oating)
19 1 15 50 1 15 1 0.0 0.0 9.2 0 0.0 0.0
20 14 49 2 0
21 35 42 113 35 3 12.5
22 7 57 7 7 4 22.0 23 22.0 20.3
23 41 50 50 41 5 20.5
24 9 9 6 19/2 20
25 21 33 39 33 21 7 24.5 18.7 24.5 14.0
26 12 61 18 8 35.0
27 6 40 40 9 13.5 7 7.0
28 34 43 34 10 13.3 18 18.0
29 5 9 9 17 17 11 10.0 12.4 10.9
30 4 12 14 4.0
31 1 2 5 6 1 13 14.0 14.0 24.0
32 1 4 14 4 4.0
33 3 3 15 11.0 11 14.0
34 0 1 1 16 20.3 15.2 7.0
35 1 1 17 26.5 26.5
36 0 0 0 18 47.0 20.6
37 0 0 0 19 7.5 16.7 1 7.5
38 0 0 20 24.5
39 0 0 21 21.0 22.6 35.0
40 0 1 1 22 19.0 7 7.0
41 1 1 1 23 25.0 25 41.0
42 0 0 24 9.0
43 0 0 0 25 16.5 13.0 16.5 21.0
44 0 0 26 12.2 9.0
45 0 0 27 20.0 20
46 0 1 1 0 28 14.3 34.0
47 0 1 29 4.5 4.5 0.7 0.7
48 1 1 30
49 0 0 0 31 1.0 1.7 1.2 1
50 0 0 32 2
51 0 33 1.5
34 0.3 0.5
35 0.5
36 0.0 0
37 0.0 0.0
With regards to the step length of this information which is 38 0
39 0.0
1 km, the threshold value of wavelet transform has been calculated
40 0.3 0.5
based on 10 accidents per kilometer. Clearly, accident-proneness 41 0.5 0.2
threshold can be dened in each area based on the safety policies 42 0
of local road organizations. 43 0.0 0.0
44 0
45 0.0
14. Road segmentation using the wavelet transform output
46 0.3 0.2 0
47 0.5
In this section, high crash road segments are identied using 48 0.5
the modied wavelet transform surface of the segments. 49 0.0 0.0
As shown in Fig. 12, twelve high crash road segments were 50 0
51
identied with different lengths in the example, which among
 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287 285

Table 5
Comparing the statistical index segmentation by static and dynamic segmentation methods (Boroujerdian, 2011).

Fixed segmentation Dynamic segmentation

2 km segment (oating) 5 km segment 3 km segment 2 km segment LS SS

The number of identied segments 30 11 17 26 5 21
The maximum density 26.5 22.6 22.0 26.5 21.8 47.0
The total segments density 250.5 92.4 154 231 55.1 354.9
The variance of segments density 94.4 64.5 73.0 86.3 91.3 177.3

15. Prioritizing high crash road segments by the wavelet method that the total length of them is equal to the maximum
transform of safety improvable length considering the economic limitations.
Considering the conditions, the best segmentation style is the one
Since the amount of wavelet transform illustrated in counter that recognizes the maximum total number of accidents in the
form of Fig. 13 indicates the accident density index along the road, specied segments.
the priority of segments may be identied using it. It must be noted To compare xed and dynamic segmentation methods, the
that the priority of SS and LS high crash road segments can be previous road is divided into xed segments of 2, 3 and 5 km in
compared to each other. Table 2 shows the result of prioritization. length and also into oating segment of 2 km in length. Then the
number of accidents is recognized along the segments by each
16. Dynamic segmentation model evaluation method. After that, the accident density of all segments is
calculated by both xed and dynamic segmentation method.
Two mathematical and economic factors are used to study the The number of accidents along the road is shown in Table 3.
validity of segmentation model. These two factors are dened The calculated accident density in each segment is based on the
before the analysis. As length of high crash road segments is proposed example in Table 3 which is shown in Table 4. The
dened according to the accidents arrangement in this research, so maximum density, total accident density and the variance of
the best segmentation procedure is to divide the road in a way that accident density in the segments dened by each segmentation
the difference in accidents number in adjacent segments is at method are indicated in Table 4. Identifying the segments with
maximum. This means maximizing the accident density along more maximum accident density by a segmentation method
some of high crash road segments and minimizing the accident indicates identifying the highest crash road segment along the
density along the other segments. Thus, more variance of accidents road of interest by that method comparing to the other methods. If
density along the segments indicates that the segmentation the total accident density in a segmentation style is more than the
process has been performed well. others it means that the dened length of segments by this style is
The other parameter to compare various types of segmentation more compatible with the real length of high crash road segments
method is to calculate the number of accidents in the segments of the road. Finally, the segmentation style which has more
with higher priority in the length unit. First of all, considering variance of accident density comparing to the others is better than
budget limitations, it is assumed that safety improvement is the others (Boroujerdian, 2011).
possible in the shorter length of the road. Therefore, some As it can be seen in Table 5, considering each of the three
segments with high priority (with maximum accident density introduced indices, the dynamic segmentation method is more
along the segment) are chosen through every segmentation suitable. Considering the characteristics of xed segmentation

[(Fig._14)TD$IG]
120

110

100
( Sn/nt ) Percentage of Accident

90

80

70

60

50
2
Fixed Segmentation (2km)
40
3
Fixed Segmentation (3km)
30
5
Fixed Segmentation (5km)
20
2
Floating Segmentation(2km)
10
Dynamic Segmentation
0
0 10 20 30 40 50 60 70 80 90 100
( SL/Lt) Percentage of Road Length

Fig. 14. Comparing the accidents per the percentage of road length (Boroujerdian, 2011).
286 A.M. Boroujerdian et al. / Accident Analysis and Prevention 73 (2014) 274287

Table 6
The percentage of counted accidents of high crash road segments by selecting the 15 percent of road length
for safety improvement (Boroujerdian, 2011).

Percentage of covered accidents Segmentation method

34 Fixed segmentation (segments length is 5 km)
36 Fixed segmentation (segments length is 3 km)
41 Fixed segmentation (segments length is 2 km)
42 Floating segmentation (segments length is 2 km)
54 Dynamic segmentation

method, it usually compares with the dynamic SS segmentation It is concluded that the studied hypothesis in this paper is a
model. As seen, none of the methods has identied the density suitable replacement for the current segmentation models.
equal to 47 except dynamic segmentation method. This indicates
there is a high number of accident along the shorter length of the 17. Conclusion
road. Therefore, due to not xed length of high crash road
segments in dynamic method, the segment length in this part of The brief output of this research is categorized as the following:
the road is dened almost the same as the real length of high crash
road segment in this area while the density in the xed - The length of high crash road segments can be identied
segmentation methods with different length is about half of the matches with the accident arrangement along the road by
density of dynamic segmentation method. dynamic segmentation model.
Generally, total density of segments in different methods - Identifying high crash road segments and their priorities can be
indicates that the segments length matches with the accident achieved simultaneously by dynamic segmentation method.
arrangement. This index is 354.8 by dynamic SS segmentation - Dynamic segmentation model leads to improvement of budget
method that is much higher than the other methods. At last, assignment process for road repair and maintenance and also
variance index that indicates the variation of accident density in may optimize the budget assignment process. The amount of
different segments is 177.3 by dynamic segmentation which means improvement is studied in a test in which the number of
the dynamic segmentation model is more suitable than the xed accidents is identied in the segments with higher priority and
segmentation model (Boroujerdian, 2011). specied length based on different models. The diagram which
As already mentioned another method is used to evaluate the compares them indicates that the dynamic segmentation model
validity of the proposed model for applicable comparison of considers 4065 percent of accidents for safety improvement
segmentation methods that is based on the limitation index of of 1020 percent of the road length, while this amount is
road repair and maintenance costs for road safety improvement. 2952 percent of accidents when using the oating segmenta-
In order to suit the purpose, the segments of interest are ordered tion method. Therefore, the results of identifying high crash
by different methods based on their priority (accident density road segments by dynamic segmentation model are improved
along the segment). Then, the number of accidents is calculated by 2538 percent comparing to the oating segmentation
in the specied part of the road by different segmentation method.
styles. Fig. 14 describes the relationship between aggregate - The wavelet conversion signal analysis method can be used in
percentages of accidents and the percentage of studied length in dynamic segmentation method.
each method. - It is possible to identify high crash road segments with shorter
Considering the budget limitation for road repair and mainte- lengths along a high crash road segment by dynamic segmenta-
nance, the segmentation which can identify the most accident tion method.
number in the shortest length of road, is the best segmentation - Mexican hat window can be used as wavelet for identifying high
method. crash road segments by wavelet conversion method.
According to Table 6, it is concluded that when there is budget - For de-noising the signals the amounts of wavelet transform
limitation for safety improvement, by improving 15 percent of the coefcient which are less than the amount of wavelet
road length, 54 percent of accidents along the road can be conversion related to the threshold value of high accident-
considered along the specied segments, if the dynamic segmen- proneness can be omitted from the output.
tation method is used. This is 42 percent when using the oating - The nal accident cause may be taken into account in the
segmentation method with the segments of 2 km in length prioritization process by caused-based prioritization model.
(Boroujerdian, 2011). - Identifying high crash road segments with higher priority is
As seen in Fig. 14, for preventing the 70 percent of accidents, the implemented by the caused-based model from aspect of
total length of segments involving these accidents is different in accident aggregation.
different methods. For example, the length of the road that - By using the caused-based prioritization model, high crash road
includes these accidents is 21 percent of total length of the road segments can be identied as well as the accident cause.
when using dynamic segmentation method, 27 percent when
using the oating segmentation method (the segment length is
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