Automatic Identification of Roadway Horizontal Alignment Information Using Geographic Information System Data: CurvS Tool

Abstract

This paper introduces CurvS, a web-based tool for researchers and analysts that automatically extracts, visualizes, and analyzes roadway horizontal alignment information using readily available geographic information system roadway centerline data. The functionalities of CurvS are presented along with a brief background on its methodology. The validation of its estimation results are presented using actual horizontal alignment data from two different roadway types: Route 83, a two-lane two-way rural roadway in New Jersey and I-80, a freeway segment in Nevada. Different metrics are used for validation. These are identification rates of curved and tangent sections, overlap ratio of curved and tangent sections between estimated and actual horizontal alignment data, and percent fit of curve radii. The validation results show that CurvS is able to identify all the curves on these two roadways, and the estimated section lengths are significantly close to the actual alignment data, especially for the I-80 freeway segment, where 90% of curved length and 94% of tangent section length are correctly matched. Even when curves have small central angles, such as the ones in Route 83, CurvS’s estimations covers 71% of curved length and 96% of tangent section length.

The average crash rate for horizontal curves is nearly three times higher than that of other road sections ( 1 ). To alleviate this risk and deploy proper safety countermeasures one needs to locate these sections and obtain their respective geometric properties. Yet, more often than not this information is not readily available in states’ roadway inventory databases. The necessity of horizontal alignment dataset and the difficulties in obtaining it have become more apparent especially since the publication of the Highway Safety Manual (HSM) in 2010, after which there has been an increased interest by many states’ department of transportation (DOT) in the calibration of safety performance functions (SPFs) provided in the manual. The locations of horizontal curves, their radii and length are required to calculate the crash modification factor (CMF) used in the HSM’s crash prediction model for two-lane two-way rural roadways and freeways.

The available methods for collecting and extracting horizontal alignment data include field surveys, Global Positioning Systems (GPS) methods, light detection and ranging (LiDAR), satellite imagery, manual extraction via online mapping services, automated image processing, Geographic Information System (GIS) methods, and as-built plan sheets ( 2 , 4 ).

Although the most accurate horizontal curvature data can be obtained by field surveys or data extraction from as-built plans, these methods are impractical when the analysis scope is large, as it usually is with the SPF calibration process. Mobile asset vehicles (MAVs) are often used to extract roadway alignment data for such purposes. These vehicles are equipped with a variety of technologies including high-resolution video cameras, scanners, Ball Bank Indicator (BBI), GPS systems, LiDAR technology, and distance measurement instruments ( 5 – 12 ). However, in addition to being time consuming, labor intensive, and expensive, requiring comprehensive post-processing of collected data, this method has its shortcomings as discussed in Findley et al. ( 8 ), in which curvature data collected by three different commercial vendors utilizing MAV are found to have contrasting results.

A similar but less costly option is proposed by Wood and Zhang ( 13 ), in which they presented a novel approach to automatically identify and measure horizontal curves using smartphone sensor data including the GPS, accelerometer, and gyroscope readings. This approach is proposed as a low-cost mobile road inventory system for two-lane horizontal curves based on off-the-shelf smartphones. The proposed approach uses Butterworth low-pass filtering to reduce sensor noise, extended Kalman filtering to improve GPS accuracy, and K-means clustering to identify curve locations. Only simple curves with radii less than 5,730 ft are used for validation. The estimated curve radii of 21 curves are compared with the design radii. The results indicate that this approach can measure the radius of sharp horizontal curves with a satisfactory degree of accuracy. However, this approach requires, preferably multiple, runs through survey locations, and it is time and labor intensive and not applicable for a large-scale horizontal curvature extraction.

Other methods include processing of high-resolution photos ( 14 ) and still images from digital cameras ( 15 ). These methods, however, are also not applicable to a large-scale curvature extraction process.

Another method, utilized by many studies ( 16 – 18 ), is manual extraction of horizontal curvature information from satellite images using web-based mapping tools, such as Google Earth™. However, extracting this information, especially for a multitude of roadways, demands a significant amount of time, and the quality of the extracted data is often questionable. For example, Bartin et al. tested the sensitivity of manually extracted curvature data on an 8-mi-long rural two-lane two-way roadway using 15 different analysts ( 19 ). The number of detected curves varied between 10 and 23 curves between trials, with an average of 17.0 curves.

The key conclusion drawn from the review of these methods is that curvature data obtained from the available methods differ significantly and that, for the purpose of calculating CMF for horizontal curvature, a quick and reliable method is needed.

Among the available methods, GIS-based ones appear to be ideal in relation to cost and time, as they utilize GIS roadway centerline shapefiles, already available in state DOTs’ data repository. there are only a few publicly available tools that can be utilized by researchers and analysts. The most notable GIS-based tools are Curve Calculator extension by ArcGIS software tool ( 20 ), CurveFinder ( 21 ), Curvature Extension, a toolbar in ArcGIS software developed by the FLDOT ( 22 ), and ROCA (Road Curvature Analyst) ( 23 ). Curve Calculator requires users to identify a curve manually by defining its limits. The tool then automatically calculates the radius and curve length. Similarly, Curvature Extension requires manual identification of each curve by specifying its limits. As stated in Xu and Wei, the accuracy of the extracted curvature information depends highly on users’ judgment and experience ( 24 ). Curve Finder, however, automatically detects curves on a network of roadways by calculating the heading angle between consecutive GIS data points. If the angle is greater than a threshold, then a curve begins, otherwise it is assumed a tangent section ( 21 ). However, Curve Finder is not publicly available. ROCA is an ESRI ArcGIS toolbox application. The tool can automatically process a network of roadway and extract horizontal curvature information. The identification of curves is based on the naïve Bayes classifier. ROCA is available on request ( 23 ). Currently its training dataset is based on 32 roadways and 43 mi of rural roadways in the Czech Republic. Analysts who intend to utilize this tool for another region are urged to preprocess a training dataset, which poses a shortcoming, as generating a training dataset demands time and it is often compiled via manual identification of curves.

Therefore, as mentioned in Bartin et al. ( 19 ), there is a need for a computer tool designed for researchers that embodies the following properties:

Utilizes GIS roadway centerline shapefiles,

Detects different types of curves and calculates curvature information quickly and accurately,

Performs network-wide analysis,

Produces output files that can easily be integrated to an existing roadway feature database,

Is accessible to other researchers and improves the efficiency of their safety-related work.

The study by Bartin et al. ( 19 ) was the first step toward such a tool with the above-listed properties, presenting a reliable and efficient method for identifying and measuring curvature data. They used clustering analysis of the approximated curvatures of discrete data points from GIS roadway centerline shapefiles. This paper is intended to be the next step toward this goal. Thus, the objective of this paper is to introduce CurvS, an online tool that encompasses the desired properties listed above, and validate its accuracy using ground truth data. CurvS is based on an improved version of the clustering approach presented by Bartin et al. ( 19 ). CurvS is conceived as a tool to allow researchers and analysts to extract, analyze, and visualize horizontal alignment information using readily available GIS roadway centerline data.

The next section presents the methodology used by CurvS to detect horizontal curvature. The functionalities of CurvS are then demonstrated. The validation of its estimation results is conducted by using two different roadway types, a rural two-lane two-way roadway in New Jersey (NJ) and a freeway segment in Nevada (NV). Conclusions are presented in the last section.

Methodology

CurvS’s horizontal alignment estimation is based on the clustering approach. The use of clustering approach for horizontal alignment estimation stems from the idea that distinct road sections, either curved or tangent, have similar explanatory variables. CurvS detects these sections by identifying the clusters of these variables.

Let us consider a roadway represented by discrete points (vertices) in a GIS shapefile. Suppose that the roadway is discretized by $i = 1 to n$ vertices. Using the forward finite-difference approximation, the heading angle, $θ$ , at any vertex can be written as:

θ_{i} \approx \arctan (\frac{Y_{i + 1} - Y_{i}}{X_{i + 1} - X_{i}})

(1)

where $X$ and $Y$ are the latitude and longitude readings of vertices. Note that the tangent of $θ$ is the approximation of the first-order derivative at vertex i. Similarly, the finite-difference approximation of the second-order derivative at vertex $i$ can be written as:

f^{”} (i) \approx \frac{\tan (θ_{i}) - \tan (θ_{i - 1})}{X_{i} - X_{i - 1}}

(2)

Using the approximated first and second-order derivatives, the curvature at vertex i can be calculated as:

κ_{i} \approx \frac{f^{”} (i)}{{[1 + \tan {(θ)}^{2}]}^{\frac{3}{2}}}

(3)

Although $κ_{i}$ are approximations, one can assert that vertices within a distinct roadway section, curved or tangent, will have similar values. This assertion is demonstrated in Bartin et al. using a hypothetical roadway, where $κ$ values of vertices within distinct sections had similar values ( 19 ). Determining sections that have similar values is the objective of the common clustering algorithm, which is based on minimum within-group distance criterion ( 25 ). With this notion, Bartin et al. ( 19 ) utilized a modified version of the global K-means algorithm of Likas et al. ( 26 ) to detect horizontal curves by using $κ$ values, as obtained by Equation 3. Once detected, radii $R$ of each horizontal curve are then calculated using the chord method ( 27 ).

This study extends the clustering algorithm used in Bartin et al. ( 19 ) by utilizing multiple explanatory variables to detect horizontal curved sections. The selected explanatory variables are:

Heading angle ( $θ$ )

Curvature ( $κ$ )

Change in heading angle ( $d θ$ )

Distance between consecutive vertices ( $dL$ )

Milepost (MP)

Radius calculated using the chord method (R)

Radius of a circumscribed circle (RCC)

Cumulative change in heading angles at three consecutive points $(Σ$ )

The difference in cumulative heading angles around each vertex $(λ$ ).

Figure 1 illustrates the key explanatory variables. These can be described as follows. The heading angle $θ_{i}$ , and curvature $κ_{i}$ are as shown in Equations 1 and 3, respectively. MP of each vertex is obtained via linear interpolation of the start and end MP of each section. Change in heading angle at vertex i, $d θ_{i} = θ_{i} - θ_{i - 1}$ . Distance between consecutive vertices, $d L_{i} = M P_{i} - M P_{i - 1}$ . $R_{i}$ , is calculated by the chord method as follows:

R_{i} = \frac{M^{2} + (L C^{2} / 4)}{2 M}

(4)

where $LC$ is the length of the chord between the point of curvature (PC) and the point of tangent (PT), and $M$ is the middle ordinate. Here $R_{i}$ of vertex i is calculated using three vertices, namely vertex $i - 1$ , $i$ and $i + 1$ . Radius of a circumscribed circle, $RC C_{i}$ is calculated as ( 23 ):

RC C_{i} = (d L_{i + 1} + d L_{i}) / (2 \sin (π - d θ_{i}))

(5)

Cumulative change in heading angle at three consecutive points, $Σ_{i}$ is calculated as:

Σ_{i} = d θ_{i - 1} + d θ_{i} + d θ_{i + 1}

(6)

The difference in cumulative heading angles around each vertex, $λ_{i}$ is calculated as:

λ_{i} = \sum_{q = 1}^{m} θ_{i + q} - \sum_{q = 1}^{m} θ_{i - q}

(7)

These explanatory variables are selected to represent quantitatively how each vertex is positioned with respect to its neighboring vertices. Many of these explanatory variables are also used in the literature. Change in heading angle, $d θ$ is commonly used to detect curves ( 21 , 23 , 24 ). Variables $Σ$ , $RCC$ and $dL$ are used in Andrasik and Bil ( 28 ) and Bíl et al. ( 23 ). Variable $λ$ is similar to the one used by Xu and Wei ( 24 ), where they assumed m = 4 in Equation 7. In this study m is taken as 3; in other words, $λ$ signifies the difference in the cumulative heading angles of three vertices ahead and before vertex i.

Figure 1.

Illustration of the key explanatory variables.

Each vertex, therefore, has a vector of explanatory variables, denoted by $x_{i}$ where $x_{i} = (κ_{i}, θ_{i}, d θ_{i}, d L_{i}, M P_{i}, R_{i}, RC C_{i}, Σ_{i}, λ_{i})$ . Because some of these variables are measured on a much larger scale than others, vectors $x_{i}$ are standardized into $z_{i}$ by subtracting their mean, and dividing by their standard deviation. K-means clustering algorithm can then be used to detect the distinct roadway sections. The objective of a general K-means algorithm is to minimize the function value $SS E_{K}$ , which is the total within-cluster sum of squared errors (SSE) of $K$ clusters:

\min SS E_{K} = \sum_{k = 1}^{K} \sum_{j = 1}^{N_{k}} {(z_{j}^{(k)} - {\bar{z}}_{k})}^{2}

(8)

where $K$ is the desired number of clusters, $z_{j}^{(k)}$ is the standardized vector of explanatory variables at vertex $j$ within cluster $k$ , ${\bar{z}}_{k}$ is the average $z$ vector of cluster $k$ and $N_{k}$ is the number of data points within cluster $k$ , where $\sum_{k = 1}^{K} N_{k} = n$ vertices. Note that when $K = 1$ , $N_{k}$ becomes $n$ , the total number of discrete vertices, and $SS E_{1}$ is equal to the $SSE$ of the whole dataset. In the current context, a cluster $k$ connotes to a distinct road section, a curve or a tangent section; $N_{k}$ is the number of data points within that section and $K$ is the total number of distinct sections on a road ( 19 ).

Because the common K-means algorithm often fails to find the optimum cluster, the modified global K-means algorithm by Bartin et al. ( 19 ) is utilized. Readers are referred to this study for further details of this algorithm and how its results are used in detecting distinct roadway section on a roadway.

CurvS Tool

In this section, the functionalities of the CurvS tool are demonstrated. Its estimation results are also validated by using horizontal alignment data of one rural roadway in NJ and one freeway in NV.

Functionalities of CurvS

CurvS is a web-based tool that adopts a typical client-server model. The server component of the tool is written in PHP programming language and provides data analysis and processing service to one or many clients, which initiate requests for the service. The client-side interface is developed using JavaScript (JS), HTML, CSS, and Google Maps™ Application Programming Interface. The interface accepts the inputs for the analysis and uploads the data to the server via an AJAX (Asynchronous JavaScript and XML) request without interfering with the display of the interface. On receiving the input parameters and the data, the server executes the C code developed by Bartin et al. ( 19 ) using these inputs. The progress of the execution is continuously monitored by the server, and after the completion the output is automatically converted to a JSON (JavaScript Object Notation) object which is a convenient data format used in AJAX queries. Then, the output is sent to the client to be processed by the built-in JS functions to create curves from the output in a format that can be mapped on Google Maps of the interface.

CurvS utilizes the methodology explained in the previous section. The tool’s main interface provides users with four main modules: (1) Input Module, (2) Scope of Analysis, (3) Analysis Preferences, and (4) Visualization & Reporting. Below are the descriptions of each module.

Input Module

The main input files to the tool are the geometric information for the roadway(s) of interest. CurvS requires users to upload this information in two separate files in *.csv format: nodes and links, as shown in Figure 2. The required fields in the links file are highway name, link id number, and coordinates of the start and end nodes of each link. The required fields in the nodes file are highway name, link id number of the node, node index, and node coordinates. These fields can be easily extracted from roadway centerline shape files using any available GIS software. The required coordinate referencing system for CurvS is World Geodetic System (WGS) 84.

Figure 2.

Demonstration of CurvS modules.

It should be noted that users can either upload the geometric information on a single roadway, multiple roadways, or the entire roadway network.

Scope of Analysis Module

Once the input files are read, users are asked to define the scope of analysis. If users have a list of roadways for analyses it can be uploaded as an input file, as shown in Figure 2. The required fields in this input file are roadway name, start and end mileposts. If users prefer not to upload a list of roadways, the tool generates a table of roadway names from the links file. Users can select the ones to be included in the analyses by simply clicking on the check boxes, as shown in Figure 2.

Analysis Preferences Module

This module provides the users with the ability to modify the default options and parameter values used in the analysis. These are (1) minimum cluster size, (2) radius threshold, (3) curve sensitivity, (4) radius sensitivity, (5) Monte Carlo simulation toggle on/off, and (6) number of Monte Carlo simulation runs.

A brief explanation is warranted here in relation to how CurvS applies the results of the clustering algorithm for identifying curves. $K$ , the desired number of clusters, that is, distinct roadway section in this context, used in Equation 8 is unknown before the clustering analysis. There are available methods for determining the optimal number of clusters, such as the elbow-method, the silhouette method, gap statistics, and Bayesian Information Criterion ( 29 ), yet none of these apply in the context of accurately identifying distinct road sections because they are based on the marginal reduction of $SSE$ . Any method based on the marginal gain in reducing $SSE$ fails to detect slight curves, that is, large radius and short section length, as dividing a noticeably curved section will reduce $SSE$ more than dividing a nearly tangent section and detecting the slight curvature ( 19 ). CurvS method applies the “patch-up routine” introduced by Bartin et al. ( 19 ). CurvS runs the clustering algorithm by setting a large value for $K$ , and terminates when $SSE$ does not change by increasing $K$ . A minimum cluster size restriction is imposed within the clustering method because at least three data points are required to calculate $κ$ in Equation 3. This is the default value for the minimum cluster size parameter in CurvS, and can be modified by the user.

Once the clustering results are obtained, CurvS calculates the radius of each section using the chord method and determines whether the section is curved or tangent based on the radius threshold. The default value of the radius threshold parameter is 12,000 ft; any value above is identified as a tangent section. If there are contiguous curved sections as depicted in Figure 3, CurvS applies the “patch-up routine” and calculates the distance between the centers of contiguous curves, if $d (C_{k}, C_{k + 1})$ . If $d (C_{k}, C_{k + 1}) \leq min (R_{k}, R_{k + 1}) . \propto$ , then it is assumed that both clusters are parts of the same curve. Here, ∝ is the curve sensitivity parameter within the range of [0, 1]. The default value of ∝ is 1.0 in CurvS. The smaller the ∝ value the harder it will be to combine contiguous curves into a single one, and therefore the higher the number of distinct curved segments will be.

Figure 3.

Example of two contiguous clusters.

During the digitization of orthophotos, tangent sections are usually represented by few vertices. Depending on the accuracy of digitization, wider gaps between vertices are bound to inaccurate estimation of PC and PT locations. Note that in Figure 3, the start and end vertices of clusters are labeled as PC and PT, yet between clusters there are sections, highlighted in gray, as a result of discretization of roadway centerlines. For example, if another vertex was inserted within this area, it would be selected as a more suitable choice for the PC or PT of these identified curves, which would yield different curve radius and length. Thus, CurvS further discretizes these gray sections by small intervals of size $dS$ and runs the chord method for each combination of possible PC and PT, finds the average, standard deviation, and coefficient of variation (CV) of estimated radii for each curve. The value of $dS$ is set to 5 ft. An analogous approach is also adopted by Wood and Zhang ( 13 ). One would expect that a curve that is well represented by discrete vertices would have a low standard deviation and CV.

The default clustering runs are conducted by assigning equal weights to each explanatory variable listed in the Methodology section. One could suggest that curvature $κ$ is intrinsically more important than other variables and should have more weight in clustering analysis. Users are allowed to switch the weight of each explanatory variable. Another option is the random assignment of weights. Therefore, using sliding bar users can enter the desired number of Monte Carlo runs, shown in Figure 2. At each run a random weight, $w_{i}$ is assigned to each explanatory variable, where $\sum_{\forall i} w_{i} = 1.0$ . Clusters found at each run are stored and the most frequently detected clusters are applied in estimating curvature information. Users are advised to conduct Monte Carlo simulation runs only when a limited number of roadways are being analyzed because of the computation time required for these runs.

Visualization and Reporting Module

Once the analysis is complete, the results are tabulated in an interactive output table as shown in Figure 4. Each line in the result table include the following information: (1) highway name, (2) start and end milepost of section, (3) section length, (4) curve flag (1: curve, 0: tangent), (5) average radius, (6) lower and upper bound for radius, (7) CV of radius estimation, (8) section start and end coordinates, (9) center coordinates (if curved).

Figure 4.

Reporting module of CurvS.

As shown in Figure 4, users can click on each line in the output table and display the section on the map along with its relevant information. The tool provides users the option to save the output table in a variety of formats such as *.csv and *.xlsx.

Validation of CurvS

The validation of CurvS’s results is performed by using two different roadways: (1) Route 83, a two-lane two-way rural roadway, in Cape May County, NJ, and (2) a freeway segment on I-80, between mileposts 15 and 25.7, in Eureka County, NV in the eastbound direction. The horizontal alignment information for Route 83 is extracted from as-built plan sheets provided by the NJDOT, the information for I-80 is presented thoroughly in the analysis results of Xu and Wei ( 24 ).The GIS roadway centerline shape file for Route 83 and I-80 are available at NJDOT ( 30 ) and NDOT ( 31 ) websites, respectively.

Let us first define the notation used in the formulation of the metrics for the comparison of the actual horizontal alignment data, denoted by a , with the estimated ones by CurvS, denoted by e . Suppose that the actual data indicate that there are $K^{a}$ distinct sections on the roadway of interest with $C^{a}$ curved and $T^{a}$ tangent sections, where $C^{a} + T^{a}$ = $K^{a}$ . The curve flag for each section is denoted by F, where $F_{i}^{a}$ is 1 for curved sections and 0 for tangent sections for $i = 1 \dots K^{a}$ . Similarly, the length and radius of each section are denoted by $L_{i}^{a}$ and $R_{i}^{a}$ , and the start and end mileposts are denoted by $X_{i}^{a}$ and $Y_{i}^{a}$ , respectively. Similar notations are used for CurvS’s estimations with respective scripts, for example, $C^{e}, T^{e},$ $K^{e}$ .

Five different comparison metrics are employed:

Metric 1 ( $M_{1}$ ): Curve identification rate

Metric 2 ( $M_{2})$ : Tangent identification rate

Metric 3 ( $M_{3}$ ): Overlap ratio of curves

Metric 4 ( $M_{4}$ ): Overlap ratio of tangents

Metric 5 ( $M_{5}$ ): Percent fit of curve radii.

$M_{1}$ is defined as follows:

M_{1} = \sum_{i = 1}^{K^{a}} I_{i} / C^{a}

(9)

M_{2} = \sum_{i = 1}^{K^{a}} I_{i} / T^{a}

(10)

where $I_{i}$ is an indicator function defined as:

I_{i} = {\begin{matrix} 1, \\ 0, \end{matrix} \begin{matrix} if [X_{i}^{a}, Y_{i}^{a}] \cap^{} [X_{j}^{e}, Y_{j}^{e}] \neq ϕ and \\ F_{i}^{a} = F_{j}^{e} = γ for j = 1 \dots K^{e} \\ otherwise \end{matrix}

(10)

where $γ$ is equal to 1 for $M_{1}$ and 0 for $M_{2}$ . In essence, for each curved section in the actual dataset, it checks whether there are any overlapping curved sections in the estimation results, and calculates the ratio of correctly overlapped curved sections to the actual number of curve sections. $M_{2}$ is the equivalent metric for tangent sections.

$M_{1}$ is a frequently used metric in the literature, demonstrating the performance of curve detection algorithms ( 8 , 9 , 21 , 24 ). However, neither $M_{1}$ nor $M_{2}$ can be used as a decisive comparison metric to demonstrate the accuracy of a curve detection algorithm because, as shown in the condition for Equations 9 and 10, they measure the existence of, not how much, the overlap between the estimated and actual sections. Consequently, $M_{3}$ or $M_{4}$ are used to measure the ratio of overlap in length between curve and tangent sections, respectively, between the actual and estimated alignment information, as:

M_{3} = \sum_{i = 1}^{K^{a}} I_{i} . ‖ [X_{i}^{a}, Y_{i}^{a}] \cap [X_{j}^{e}, Y_{j}^{e}] ‖ / \sum_{i = 1}^{K^{a}} L_{i}^{a} . F_{i}^{a}

(11)

M_{4} = \sum_{i = 1}^{K^{a}} I_{i} . ‖ [X_{i}^{a}, Y_{i}^{a}] \cap [X_{j}^{e}, Y_{j}^{e}] ‖ / \sum_{i = 1}^{K^{a}} L_{i}^{a} . (1 - F_{i}^{a})

(12)

where $‖ [X_{i}^{a}, Y_{i}^{a}] \cap [X_{j}^{e}, Y_{j}^{e}] ‖$ is the length of section i of the actual section overlapped with estimated section length, and $I_{i}$ is as defined above, where $γ$ is equal to 1 for $M_{3}$ and 0 for $M_{4}$ .

$M_{5}$ , adopted from Rasdorf et al. ( 32 ), indicates the percentages of estimated curves with radii within 10, 25, and 50% of the actual radii, formulated as follows:

M_{5}^{P} = \sum_{i = 1}^{K^{a}} I_{i} . H_{i}^{P} / C^{a}

(13)

where $H_{i}^{P}$ is another indicator and $H_{i}^{P} = 1$ , if $| R_{i}^{a} - R_{j}^{e} | / R_{i}^{a} \leq P$ ; 0, otherwise, where P has three values, 0.1, 0.25, and 0.5. $I_{i}$ is as defined above, where $γ$ is equal to 1.

To elucidate the calculations of these metrics, let us consider the hypothetical sets of actual and estimated horizontal alignment data of a 1-mi roadway shown in Figure 5. There are three curved and two tangent sections in the actual alignment data, that is, $C^{a} = 3$ , $T^{a} = 2$ , and they are all identified in the estimated dataset ( $C^{e} = 4$ , $T^{e} = 2$ ). In other words, their milepost ranges, indicated by lower and upper bound ranges in feet in Figure 5, are overlapped by the estimated milepost ranges of the respective curved and tangent sections. Therefore, $M_{1} = 1.0$ and $M_{2} = 1.0$ , as per Equations 9 and 10. It is clear that although the curve and tangent identification rates are impeccable, they alone do not reflect the accuracy of estimations, as evidenced from this hypothetical example. Therefore the use of $M_{3}$ and $M_{4}$ is warranted. The total length of curved and tangent sections, used in the denominator of Equations 11 and 12, respectively, are 1,330 ft and 3,950 ft. The length of actual sections overlapped with estimated curved and tangent sections, used in the numerator of Equations 11 and 12 are 1,180 ft (= 300 ft + 300 ft + 580 ft) and 3,150 ft (= 670 ft + 2,480 ft), respectively. $M_{3}$ and $M_{4}$ are calculated as 0.887 and 0.797, respectively. The actual and estimated curve radii are also shown in Figure 5. Using these values, the relative error of estimated curve radii for sections 1, 3, and 5 can be calculated as 0.03, 0.29, and 0.19. As $C^{a}$ = 3 the fifth metric can be calculated as, $M_{5}^{0.15} = 0 .$ 333, $M_{5}^{0.25} = 0.667, M_{5}^{0.5} = 1.0$ .

Figure 5.

Hypothetical sets of actual and estimated horizontal alignment data.

Table 1 shows the actual horizontal alignment and the ones estimated by CurvS for Route 83 in NJ and I-80 in NV, along with the comparison metrics results. The table rows are arranged to align the actual sections with the estimated ones for presentation purposes.

Table 1.

Comparison Results

Actual alignment data						Estimated alignment data by CurvS
Route 83 in Cape May County, NJ
i	$X_{i}^{a}$	$Y_{i}^{a}$	$L_{i}^{a}$	$F_{i}^{a}$	$R_{i}^{a}$	j	$X_{j}^{e}$	$Y_{j}^{e}$	$L_{j}^{e}$	$F_{j}^{e}$	$R_{j}^{e}$	$R_{j}^{e}$ Range	CV
1	0.00	0.03	150.0 ft	0	na
2	0.03	0.04	85.6	1	385 ft	1	0.00	0.04	193.9	1	430	[424–435]	0.03
3*	0.04	0.47	2,246.9	0	na	2	0.04	0.29	1,336.5	0	na	na	na
						3	0.29	0.35	327.4	1	5,320	[5,119–5,521]	0.08
						4	0.35	0.41	321.8	0	na	na	na
4*	0.47	0.49	131.0	1	2,523	5	0.41	0.67	1,338.3	1	5,590	[5,534–5,647]	0.02
5*	0.49	0.51	81.7	0	na
6*	0.51	0.75	1,277.6	1	5,671	6	0.67	0.74	384.3	1	3,496	[2,940–4,051]	0.32
7	0.75	0.87	644.0	0	-	7	0.74	0.88	752.0	0	na	na	na
8^†	0.87	0.96	440.3	1	2,201	8	0.88	1.07	990.3	1	1,554	[1,544–1,565]	0.01
9^†	0.96	1.07	609.9	1	1,444
10	1.07	1.25	908.9	0	na	9	1.07	1.23	867.9	0	na	na	na
11	1.25	1.29	243.8	1	1,669	10	1.23	1.28	226.4	1	1,936	[1,607–2,265]	0.34
12	1.29	1.55	1,379.7	0	na	11	1.28	1.55	1,429.1	0	na	na	na
13	1.55	1.61	292.8	1	2,284	12	1.55	1.58	162.9	1	2,068	[1,737–2,399]	0.32
14	1.61	1.72	577.0	0	na	13	1.58	1.74	870.2	0	na	na	na
15	1.72	1.78	304.2	1	1,839	14	1.74	1.78	221.1	1	5,532	[4,562–6,502]	0.35
16	1.78	2.12	1,809.0	0	na	15	1.78	2.13	1,832.2	0	na	na	na
17	2.12	2.19	366.1	1	6,910	16	2.13	2.18	240.3	1	7,159	[4,844–9,475]	0.65
18	2.19	2.44	1,311.9	0	-	17	2.18	2.41	1,239.8	0	na	na	na
19	2.44	2.63	1,029.5	1	5,384	18	2.41	2.56	796.3	1	6,090	[5,975–6,204]	0.04
20	2.63	3.22	3,090.0	0	na	19	2.56	3.21	3,440.3	0	na	na	na
21	3.22	3.31	517.7	1	1,379	20	3.21	3.28	355.4	1	1,368	[1,338–1,398]	0.04
22	3.31	3.79	2,534.7	0	na	21	3.28	3.76	2,517.6	0	na	na	na
						22*	3.76	3.79	188.2	1	568	[373–762]	0.69
$M_{1}$ = 1.0, $M_{2}$ =0.88, $M_{3} = 0.71, M_{4} = 0.96$ , $M_{5}^{0.1} = 0 .$ 38, $M_{5}^{0.25} = 0.88, M_{5}^{0.5} = 0.88$ ^†
I-80 in Eureka County, NV
i	$X_{i}^{a}$	$Y_{i}^{a}$	$L_{i}^{a}$	$F_{i}^{a}$	$R_{i}^{a}$	j	$X_{j}^{e}$	$Y_{j}^{e}$	$L_{j}^{e}$	$F_{j}^{e}$	$R_{j}^{e}$	$R_{j}^{e}$ Range	CV
1	15.00	15.48	2,534.4	0	na	1	15.00	15.49	2,599	0	na	na	na
2	15.48	15.91	2,270.4	1	5,500	2	15.49	15.91	2,218	1	5,351	[5,330–5,371]	0.004
3	15.91	15.99	422.4	0	na	3	15.91	16.05	743	0	na	na	na
4	15.99	16.38	2,059.2	1	5,000	4	16.05	16.41	1,865	1	4,979	[4,948–5,009]	0.006
5	16.38	16.66	1,478.4	0	na	5	16.41	16.71	1,628	0	na	na	na
6	16.66	16.95	1,531.2	1	3,000	6	16.71	17.01	1,581	1	3,082	[3,063–3,101]	0.006
7	16.95	17.05	528.0	0	na
8	17.05	17.24	1,003.2	1	3,078	7	17.01	17.26	1,308	1	3,457	[3,373–3,542]	0.024
9	17.24	18.75	7,972.8	0	na	8	17.26	18.78	8,001	0	na	na	na
10	18.75	19.19	2,323.2	1	6,000	9	18.78	19.24	2,462	1	5,953	[5,944–5,962]	0.002
11	19.19	19.31	633.6	0	na
12	19.31	19.57	1,372.8	1	3,584	10	19.24	19.55	1,639	1	4,058	[3,842–4,273]	0.053
13	19.57	20.12	2,904.0	0	na	11	19.55	20.14	3,111	0	na	na	na
14	20.12	20.47	1,848.0	1	6,000	12	20.14	20.46	1,692	1	6,011	[5,974–6,047]	0.006
15	20.47	22.46	10,507.2	0	na	13	20.46	22.47	10,569	0	na	na	na
16	22.46	22.72	1,372.8	1	5,000	14	22.47	22.75	1,485	1	5,583	[5,388–5,777]	0.035
17	22.72	23.35	3,326.4	0	na	15	22.75	23.29	2,860	0	na	na	na
18	23.35	24.17	4,329.6	1	5,108	16	23.29	24.09	4,203	1	5,115	[5,004–5,226]	0.022
19	24.17	24.54	1,953.6	0	na	17	24.09	24.48	2,072	0	na	na	na
20	24.54	25.13	3,115.2	1	5,909	18	24.48	25.02	2,839	1	5,736	[5,721–5,750]	0.002
21	25.13	25.70	3,009.6	0	na	19	25.02	25.70	3,690	0	na	na	na
$M_{1}$ = 1.0, $M_{2}$ =0.82, $M_{3} = 0.90, M_{4} = 0.94$ , $M_{5}^{0.1} = 0.7$ , $M_{5}^{0.25} = 1.0$ , $M_{5}^{0.5} = 1.0$

These sections are not considered in the calculations of comparison metrics for Route 83, as explained in remark (2) of analyses results.

†

When calculating the $M_{5}^{P}$ metric for Route 83 compound curve (i = 8, 9) radius is converted to a single curve radius by [(440).(2201) + (610).(1444)]/(440 + 610).Note: na = not applicable.

Route 83, being a rural roadway, is a more challenging one for horizontal alignment detection than I-80 because there are more curves per route length, and the curves are shorter in length and larger in radius than those of I-80. For example, the central angles, Δ, of the curves on Route 83 vary from 3.0° to 24.2° with an average of 11.4°, whereas the ones on I-80 vary from 15.7° to 48.6° with an average of 25.1°.

Route 83 is 3.79 mi long with 11 curves, whereas the I-80 segment is 10.7 mi long with 10 curves. As shown in Table 1, CurvS detected all curves, and thus $M_{1}$ is 1.0 for both roadways.

Several remarks are in order as to the other comparison metrics:

The start and end points of curves do not match precisely. Therefore, the overlap ratio of estimated curves with the actual ones, $M_{3}$ , is 0.71 and 0.9 for Route 83 and I-80, respectively. The average undetected curve length is 125.7 ft and 210.0 ft for Route 83 and I-80, respectively. The overlap ratio for tangent sections, $M_{4}$ , is 0.96 and 0.94 for Route 83 and I-80, respectively. The average undetected tangent length is 53.5 ft and 196.8 ft for Route 83 and I-80, respectively. Such discrepancy is expected as the CurvS detection is based on discrete points in space. The vertex resolutions of Route 83 and I-80 are 120 ft (0.022 mi) and 183 ft (0.03 mi) between two vertices on average, respectively. However, this issue is not specific to GIS-based methods, as there are also discrepancies between different methods of field measurements, as reported in Findley et al. ( 8 ).

These discrepancies, however, are more conspicuous between mileposts 0.29 and 0.75 on Route 83. Whereas two curves are observed in the plan sheets (i = 4, 6), CurvS detected three curves within the same milepost range (j = 3, 5, and 6) with significantly different curve lengths and radii. This difference stems from the apparently incomplete information provided in the plan sheets. Namely, there are three additional curves detected in the as-built plan sheets, not indexed as a curve but only marked by their point of intersection (PI) and its station numbers, without further details. A quick examination of satellite images shows that these points in fact coincide with horizontal curves. Their PI station numbers correspond to mileposts 0.25, 0.34, and 0.42 on Route 83. Therefore, sections between mileposts 0.29 and 0.75 are not included in the calculation of metrics reported in Table 1. In addition, there is a short curve at the end of Route 83, which is also not shown in the plan sheets. Therefore, this section too is not included in the calculation of comparison metrics.

The compound curve on Route 83 (i = 8, 9) is estimated as a single curve by CurvS (j = 8). The estimation results are based on the default value of ∝ = 1.0. When the sensitivity is increased that is, lower ∝ value, this specific compound curve can be detected by CurvS. However, in general unless the digitization of orthophotos is conducted meticulously it is often difficult to discern compound or spiral curves using discrete data points.

Two tangent section on Route 83, i = 1,5, and two tangent sections on I-80, i = 7, 11, are not identified by CurvS. This is because few vertices are used to represent these sections in the GIS shapefile, and because of the minimum cluster size parameter, these are not considered as a separate section (i.e., cluster) by CurvS. Therefore $M_{2}$ is 0.82 for both roadways.

Estimation of curve radius is highly dependent on the correct detection of PC and PT points, vertex resolution, and how close the vertices follow the roadway centerline. The results show that $M_{5}^{0.1} = 0 .$ 38, $M_{5}^{0.25} = 0.88, M_{5}^{0.5} = 0.88$ for Route 83; in other words 38% of the estimated curve radii are within 10% of actual curve radii, and 88% are within 25 and 50% of the actual radii. Only the estimated radius for curve i = 15 is significantly different from the actual radius. Further investigation revealed that some vertices are placed significantly out of alignment with the centerline during the digitization process of orthophotos. The similar metrics for I-80 are $M_{5}^{0.1} = 0.7$ , $M_{5}^{0.25} = 1.0$ , $M_{5}^{0.5} = 1.0$ .

Route 83 is one of the roadways used in the analysis conducted by Bartin et al. ( 19 ). Because the curved sections were of interest only the curvature information of Route 83 is reported as obtained via the MAV method and manual extraction method. These results also attest to the remark (2) listed above, where both methods indicate a different horizontal alignment between mileposts 0.29 and 0.75. Also, in relation to the remark (3) above, both methods labeled the compound curve (i = 8, 9) as a single curve. Comparing these results with the actual curvature information shown in Table 1, the metrics for the MAV method are calculated as $M_{1}$ = 0.82, $M_{3} = 0.57, M_{5}^{0.1} = 0.50$ , $M_{5}^{0.25} = 0.83, M_{5}^{0.5} = 1.0$ . The average undetected curve length by the MAV method is 286.1 ft, compared with 109.3 ft by CurvS. Similarly, the metrics for the manual extraction method is calculated as $M_{1}$ = 0.91, $M_{3} = 0.73, M_{5}^{0.1} = 0.71$ , $M_{5}^{0.25} = 0.86, M_{5}^{0.5} = 1.0$ . The average undetected curve length is calculated as 180.5 ft.

Comparing with the other available methods, it can be asserted that CurvS can provide valid horizontal roadway alignment information.

In addition, to explore the impact of vertex resolution on the estimation accuracy, the centerline shapefile of Route 83 is regenerated using high-resolution satellite images downloaded from US Geological Survey website ( 33 ) as overlays. The vertex resolution of Route 83 is increased by reducing the average distance between two vertices to 68 ft (0.013 mi) from its original value of 120 ft (0.022 mi). Using CurvS results, the validation metrics are computed as $M_{1}$ = 1.0, $M_{2}$ = 1.0, $M_{3} = 0.94, M_{4} = 0.94$ , $M_{5}^{0.1} = 0 .$ 56, $M_{5}^{0.25} = 0.89, M_{5}^{0.5} = 0.89$ . The average undetected curve length is reduced to 24.5 ft from its previously reported value of 125.7 ft; whereas the undetected tangent length increased slightly to 68.3 ft from 53.5 ft. With this enhanced vertex dataset, CurvS is able to detect the compound curve (i = 8, 9) even with a low sensitivity parameter value, α = 1.0.

Finally, to demonstrate the degree of accuracy of CurvS’s results in reference to another available tool, the same roadways are processed in ROCA. As mentioned earlier, ROCA is the only other publicly available tool used to process horizontal curvature at a network-wide scale. ROCA requires jurisdiction-specific training data for its naïve Bayes classifier, and thus a training dataset specific to the U.S. roadways is created, consisting of nearly 4,000 data points. Although a dataset comprised of two roadways with a total of 21 curves cannot be deemed sufficient for a comparative analysis, it can be used to demonstrate the level of accuracy provided by CurvS in comparison to ROCA. The similar validation metrics are computed using the ROCA outputs for Route 83 and I-80. For Route 83 the metrics are calculated as $M_{1}$ = 1.0, $M_{2} = 1.0, M_{3} = 0.77, M_{4} = 0.97$ , $M_{5}^{0.1} = 0.25$ , $M_{5}^{0.25} = 0.625, M_{5}^{0.5} = 0.75$ . It can be seen that although ROCA outperforms CurvS in $M_{3}$ and $M_{4}$ metrics specifically, its curve radii estimations, that is, $M_{5}$ underperform. Similarly for I-80, the validation metrics are computed as $M_{1}$ = 1.0, $M_{2} = 1.0, M_{3} = 0.81, M_{4} = 0.97$ , $M_{5}^{0.1} = 0.6$ , $M_{5}^{0.25} = 1.0, M_{5}^{0.5} = 1.0$ . These results show that both tools yield very similar horizontal alignment estimations.

Summary and Conclusions

This paper demonstrates CurvS, a web-based tool that allows researchers and analysts to automatically extract, visualize, and analyze roadway horizontal alignment information using readily available GIS roadway centerline data. The functionalities of CurvS are presented along with a brief background on its methodology, which is an improved version of the clustering approach presented in Bartin et al. ( 19 ). In addition, a thorough validation of its estimation results is presented using the actual horizontal alignment data from two different roadway types, a two-lane two-way rural roadway in NJ, and a freeway segment in NV.

The validation results in Table 1 indicate that CurvS provides satisfactory horizontal roadway alignment estimations. As discussed, even though there are some inherent estimation errors, these are inevitable because of the (1) space discretization of continuous lines and (2) errors during the digitization process of orthophotos. The review of the literature indicates that such errors also exist in other available methods for collecting horizontal alignment data ( 8 , 34 ). CurvS is able to identify all the curves on these two roadways, and the estimated section lengths are significantly close to the actual alignment data, especially for the I-80 freeway segment, where 90% of curved length and 94% of tangent section length are correctly matched. Even when curves have small central angles, such as the ones in Route 83, CurvS’s estimations covers 71% of curved length and 96% of tangent section length. In addition, using the data generated by the MAV method and manual extraction on Route 83 reported in Bartin et al. ( 19 ), it is found that the MAV method correctly identified 82% of the curves, covering 57% of curved length, and the manual extraction process correctly identified 91% of the curves, covering 77% of the curved length. Based on these metrics, CurvS outperforms these two time-consuming and costly methods.

In addition, it is shown that when the vertex resolution of Route 83 GIS shape file is enhanced, all curved and tangent sections are identified by CurvS, and 94% of both curved and tangent lengths are correctly matched.

It should be underlined that these results are obtained in a matter of seconds in CurvS and can be easily utilized in various safety analyses, such as computing CMF values for roadway curvature, required by the HSM’s crash prediction models.

Currently the only disadvantage of CurvS is that it requires users to preprocess the nodes and link input files in *.csv format. Although this process can be performed easily in any GIS software, future work will include modifying CurvS so that it can directly import shape files (*.shp) and conduct the preprocessing internally.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: Study conception and design: Bekir Bartin, Sami Demiroluk, Kaan Ozbay; data collection: Bekir Bartin, Mojibulrahman Jami, Sami Demiroluk; analysis and interpretation of results: Bekir Bartin, Kaan Ozbay, Mojibulrahman Jami; draft manuscript preparation: Bekir Bartin, Kaan Ozbay, Sami Demiroluk, Mojibulrahman Jami. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The study is supported by the NJDOT (FHWA-NJ-2017-001) and partially by C2SMART, a Tier 1 UTC at New York University funded by the U.S. DOT.

ORCID iDs

Bekir Bartin

Sami Demiroluk

Kaan Ozbay

The contents of this paper only reflect the views of the authors who are responsible for the facts and do not represent any official views of any sponsoring organizations or agencies.

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