5.4 Optimizing Parameters for Light Distributions on Real Roads
5.4.3 Road Categorization
Since the driver’s gaze behaviour is not only of relevance in general, but for specific situations as well, the whole test drive needs to be categorized. This can be done for both, soft and hard parameters. Hard parameters are, for this thesis, defined as parameters that will stay, within a margin of error, the same for each driver. This includes road geometry, speed limits, lane numbers, traffic sign locations, motorways, country roads and rural roads. Soft parameters on the other hand are parameters that will change for each test run and of course for each test driver. Soft parameters include the illuminance measured at the driver’s eye, driven speed, acceleration, individual driving manoeuvres like overtaking or lane changes, traffic volume, weather traffic lights and many more. In the next couple of section, the both parameters sets will be identified, specified and as far as possible grouped into several bins. Soft parameters that cannot be grouped into feasible bins will be listed and their influence on the test results will be discussed.
hard parameters
Since hard parameters are constant for each run and every test person, all hard parameters can be grouped together successfully and therefore be used for analysis of the gaze distribu-tions and behaviour. The hard parameters that were identified for this particular road are:
• Road Location
• Road Curvature
• Speed Limits
• Traffic Lanes
• Traffic Signs
• Day/Night Drives
To match each recorded GPS location to one of the mentioned hard parameters, the OSM database is chosen [182]. The OSM database is an open source and license free database, where users can submit road data to any given road. This approach leads both advantages as well as disadvantages. Compared to commercial solutions, everyone, who is interested, can submit data to road segments they have information on. This has the benefit of a large
infor-168 analysis and optimization of light distributions
mation pool and a large number of people working on the database. Additionally, there is no preference for densely inhabited areas as such. The main drawback on the other hand, is that the information passed on online, is not reviewed by anyone else than the users themselves.
However, since no other database is availabe, that provides the same amount of information, this approach is decided to be feasible. The OSM data is available for download online via theOSM overpass Application Programming Interface (API). After selecting the area, all data available is downloaded using theJava-OpenStreetMap-Editor[183]. This dataset is shown as a graphical visualization in figure5.68a. It can be seen, that data is now available for the com-plete region. To avoid mismatching between the recorded GPS data and the OSM data, this data is now matched once by finding the closest coordinates between both datasets. Since the result still contains some data points that are outside of the specified route, the result-ing data is checked manually and mismatched data is deleted from the OSM data set. The reduced dataset is visualized in figure5.68b
(a) (b)
Figure5.68– Visualization of the OSM data used to match the hard data to the recorded GPS data. In(a), the data for the complete area is shown,(b)shows the reduced data for the recorded course.
The data itself now consists of so called Nodes and Ways, while a way is the connection between two nodes. The GPS information is stored in the nodes, while the road information is stored in theways. To match the data from theOSM data set to the recordedGPS data, the information stored in thenodesis combined with the information of thewaysusing the tool OSM Converter[184]. The resulting data now contains all required information - both GPS lo-cation and the hard parameters. These parameters are listed in appendixE.1in the listingE.2.
5.4 optimizing parameters for light distributions on real roads 169 This data is now being matched with the recorded GPS data by finding the closest possible
distance between the recorded data and the position data of theOSMdata.
road location
To categorize the different road locations, Damasky, Kuhland Schwabused the general clas-sification of Motorways, Country Roadsand Rural Roads, Schulz and Hristov each only focused on one of the mentioned road locations [131, 134, 140,159,160]. This paper follows this suggestion to a given extend and the each data point is merged into one of these three categories.
Since the OSM database is created and filled by volunteers, not all ways are filled with all information. Therefore, it is necessary to identify the key parameters that are viable to group the GPS data into one of the three categories. To identify which parameters are suited for the categorization, a pre-selection is done. Parameters that are obviously not suited for the categorization are:OSM-ID, since no correlation between the ID and any other metric can be found,OSM-Latitude and -Longitude, since this would involve manual selection of the cate-gories for each test subject,OSM-Speed Limit, since the Speed Limit can vary for each road segment depending on the current infrastructure, however this can be used as secondary pa-rameter,OSM-Lanes, since again there is no correlation between the number of lanes and the road type andOSM-Surface, -Smoothness, -Construction, -Bridge and -Cycleway since these parameters are mostly arbitrary for road types.OSM-City can only distinguish between rural and non-rural roads and can therefore only be used to further improve the binning of the recorded data set but not as a key parameter.
The pre-selected parameters then only include OSM-Reference, -Motorway Type and -City.
After matching the OSM data to the recordedGPS data, each of the parameters was checked for availability for the route. Table5.13shows the total availability for the datasets as well as the average availability in percent for the whole route.
Table5.13– Total and average coverage for the selected parameters,OSM-Reference,OSM-Motorway-Type andOSM-City
complete data covered motorway type
Total Number of Data Points 83 856 357
Number of Data Types 13
Total Data Covered 83 856 357 66 922 154
Total Data Not Covered 0 16 934 203
Average Data Covered 100 % 79.8 %
Average Data Not Covered 0.0 % 10.2 %
Due to the low coverage of OSM-Reference with 79.8 %, the Motorway Type is the key parameter to group the data into one of the three bins. The keyOSM-Motorway Type is now split into the 13 different categories with their definitions from the OSM-Database [185] as seen in the appendixE.1in the listingE.2.
170 analysis and optimization of light distributions
The next step is, to calculate average distance and time spent in each of those categories.
Since the distance in each category should be roughly the same for each participant, with slight deviations caused byGPSissues, or blocked roads, the time spent in each section may vary largely depending on the actual speed the participants drive. Furthermore, the distance does not give a reproduction of the amount of data collected per category since the data rate is fixed to the time. The results for the time in each category are shown in appendixE.2 in table E.2. The data for the distance per category can be found in appendixE.2 for all 54 test runs as well in tableE.3. This data is later used to normalize the acquired data for each category.
rural roads
AGPSdatapoint is marked as a rural road, as soon as one of the following rules applies.
• TheOSM-Motorway Typeis eitherFootpath,Path,Residentialor Service.
• The OSM-Motorway Type is eitherPrimary,Primary Link, Secondary, Tertiary,Unclassified and theOSM-Speed Limitis equal to, or lower than 50 km h−1.
• The OSM-Motorway Typeis Trunkor Trunk Link and the OSM-Speed Limit is equal to, or below 50 km h−1 and theOSM-Cityis either Frankfurt or Darmstadt.
country roads
AGPSdatapoint is marked as a country road, as soon as one of the following rule applies:
• TheOSM-Motorway Typeis eitherPrimary,Primary Link,Secondary,TertiaryorUnclassified while theOSM-Speed Limitis higher than 50 km h−1andOSM-Lanesis equal to two with
OSM-Oneway yielding false.
• item TheOSM-Motorway Typeis either Primary, Primary Link, Secondary, Tertiary or Un-classifiedwhile theOSM-Speed Limitis higher than 50 km h−1and below100km h−1OSM -Lanesis equal to one withOSM-Onewayyielding true.
motorways and multi-lane country roads
AGPSdatapoint is marked as a motorway, as soon as one of the following rules applies.
• TheOSM-Motorway Typeis eitherMotorwayorMotorway Linkand theOSM-Speed Limitis above 50 km h−1.
• theOSM-Motorway Type is either Trunk, Trunk Link, Primary, Primary Link or Secondary and theOSM-Oneway yields true, withOSM-Lanesbeing larger than one.
The matching rules are then checked for double entries in each category and then checked for entries marked in more than one category. While this is not the case, single GPS values cannot be assigned to any of the three categories. These points have theirOSM-Motorway Types marked as Primary or Secondary but no other parameters were filled in. Since this leads to an average of 552 uncategorised data points (<0.1 %), these points are left out of the follow-ing data analysis. Table 5.14 shows the portion of the driven time for the three major road categories.
5.4 optimizing parameters for light distributions on real roads 171
Table5.14– Average time driven and standard deviation between all 108 test runs in the three road cate-gories.
rel. time spent
abs. time
spent std. time rel. std.
Urban Roads 49.1 % 1 h 4 min 45 s ± 21 min 45 s ± 33.6 %
Country Roads 29.0 % 38 min 13 s ± 8 min 19 s ± 21.8 %
Motorways 21.9 % 28 min 53 s ± 5 min 34 s ± 19.3 %
This data shows a high deviation in all three categories. This is due to different traffic situations and different driven velocities for all drivers. Since all data points, that do not align with the planned route are not taken into account for the evaluation, this leads to the unexpected high variance in valid data points. Similar to the procedure above, the distance driven in each category is listed in the appendixE.2in tableE.4.
curvature of roads
To enable the possibility to investigate the above mentioned metrics for driving through bends, a method was developed to derive the curvature as well as the direction of the cur-vature from the GPS-Coordinates. This has been done before by Pratt and Ai [186, 187].
Implementing and testing those methods however, did not lead to satisfying results for the presented data.
The first step of the proposed algorithm is the proper identification of a curve and its ori-entation. To calculate the orientation-angle Θ in degrees for each recorded GPS point, the tangent for the current path is being calculated. To do so, the latitude and longitude values have to be transformed into Universal Transverse Mercator (UTM) coordinates. In this coordi-nate system, distances in X and Y direction are equidistant and the distance is directly given in m. By taking the 5 prior and the 5 following GPS points of the current position, and sub-tracting the current position from these points, the data points are now accumulated around the axis origin. Using a least square mean fit, the a straight line, with axis intercept at (0/0) is then fitted onto those11points. Using the fitted value for the slopem, the angle can now be calculated by arctan(m). Since this angle does not distinguish between the quadrants I and III or II and IV, the actual direction is then calculated by the using the equations5.24to5.27.
for XUTM(i+1) > XUTM(i) and YUTM(i+1) > YUTM(i)
Θ = 90−arctan(m) (5.24)
for XUTM(i+1) > XUTM(i) and YUTM(i+1) < YUTM(i)
Θ = 90+arctan(m) (5.25)
for XUTM(i+1) < XUTM(i) and YUTM(i+1) > YUTM(i)
Θ = 270+arctan(m) (5.26)
for XUTM(i+1) < XUTM(i) and YUTM(i+1) < YUTM(i)
Θ = 270−arctan(m) (5.27)
172 analysis and optimization of light distributions
with the calculated orientation for eachGPS point, the orientation change between succes-sive data points can be calculated. A negative orientation change now indicates a left bend and a positive change in orientation, will indicate a right corner. Since the data was recorded in real traffic situations, orientation changes will occur between all successive data points, since this will still be the case for straight roads, in the next step, a threshold is defined for identifying corners. Since the possible orientation change differs for different velocities, this threshold was defined dependent on the current velocity. Equations5.28ato 5.28cdefine, if a orientation change is regarded as a straight road or a left or right-hand side corner and the corner-markerCM is defined.
if −0.02·v2 < ∆Θ <0.02·v2
CM =0 (5.28a)
if ∆Θ > 0.02·v2
CM =1 (5.28b)
if ∆Θ < −0.02·v2
CM =−1 (5.28c)
A∆Θof 0 describes a straight road,−1 describes a left corner and+1 marks a right-hand side corner. The threshold of 0.02·v2 was defined by manually trying out several thresholds, ve-locity independent, dependent depending onv2as shown5.28a. In the next step, the amount of consecutive corner - markers need to be defined, before a stretch of road is actually defined as a corner. For this thesis, the threshold was set to5consecutiveGPSpoints, or 1 s of driving with a change in direction over the set threshold. If during a set of5or more points a single data point is calculated to belong to another corner type, this single point is then overwritten to ensure that small fluctuations within theGPScoordinates do not influence the definition of corners. The datasets with the same corner-marker are used to calculate the corresponding radius for each corner. Therefore, for each identified corner, the point with the largest change in orientation∆Θmax is extracted. Then the minimal distance between∆Θmax and either end of the corner is calculated. This distance is then used to calculate the number of data points, in both directions, that are used to calculate the actual corner radius. If the larger distance from∆Θmax to the other end of the corner, is larger than 1.5 times the distance to the closer end and contains more than5GPS points, a new curve is defined here. This is done to avoid miscalculation of corner radii for situations in which a corner with a small radius directly leads into a corner of the same orientation, but with much larger corner radius, or the other way around. The defined points for a single curve x1, ...x11 andy1, ...y11 are then used to fit a circle onto the given data points by minimizing the sum of squared radial deviations. The general equation for a circle is given by the function5.29a with the centre point of the circle (−g,−f)and the radius Rgiven by equation5.29b.
0 = x2 + y2 + 2gx + f y + c (5.29a)
R = √g2 + f2 − c (5.29b)
The equation system for the least square minimization is shown in equation5.30 withx and
5.4 optimizing parameters for light distributions on real roads 173 ybeing the givenUTM coordinates.⃗a is the coefficient-vector for the circle equation, and the
indicesa1,a2,a3 representing the circle function according to the equation5.31.
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
xi−5 yi−5 1 xi−4 yi−4 1 ... ... ...
xi yi 1 ... ... ...
xi+5 yi+5 1
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
∗⃗a =
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
x2i−5 + y2i−5 x2i−4 + y2i−4
...
x2i + y2i ...
x2i+5 + y2i+5
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
(5.30)
g = −0.5·a1
f = −0.5·a2
R =
√a21 + a22 4 −a3
(5.31)
The results for this curve detection and radius fit can be seen in figure 5.69. Curves with a radius over 1000 m are treated as straight roads and radii below 50 m are declared as intersections and will therefore not be reviewed.
4.69 4.7 4.71 4.72
·105 5.55
5.55 5.55 5.55 5.55 5.55 5.55 5.55 ·106
X-UTM Coordinates
X-UTMCoordinates
Straight Roads Left Corners Right Corners
Figure5.69– Visualization of the curve-fitting algorithm with a zoomed in example with successive left and right bends. Blue marks straight roads, yellow marks left bends and red marks right bends.
This curve fitting algorithm is used for each test run separately since each driver might use a different driving line for each bend. The resulting bend distribution over all test drives is shown in figure 5.70. Negative curve radii describe left-hand bends and positive radii describe right-hand bends. The distribution for the different road sections,Motorway,Country Roads and Rural Roads are marked in the usual colours. This shows, that the smaller curve radii are much more likely for urban roads, then intermediately frequent for country roads and the least frequent for motorways. Very large curve radii on the other hand do not appear in cities at all, but are only present on motorways and country roads.
174 analysis and optimization of light distributions
−01,000−800−600−400−200 0 200 400 600 800 1,000 20
40 60 80 100 120 140
Curve Radius im m
AbsoluteFrequency
Urban Roads Country Roads Motorways
Figure5.70– The results of the curve fitting divided by the three road categories. Blue marksRural Roads, yellow marks Country Roads and red marksMotorways. Negative radii describe left-hand bends, positive radii describe right-hand bends.
Furthermore, this data shows, that the curve distribution does not follow the distribution found by Kuhl with a much more pronounced height in the small radii and a much more pronounced antisymmetry. One of the reasons here might be the more or less elliptical shape of the route, that clearly favours right-hand side curves. Furthermore, the fact that despite the large distance recorded, only the same route is repeated over and over again thus limiting the amount of different road geometries. A much broader test setup with different, or much larger, routes for each participant might therefore lead to different curvature distributions but would, on the other hand lead to other restrictions regarding repeatability or the possible number of test subjects.
On average, 30.7 curves are recorded in cities, 32.2 curves are recorded on country roads and 16.8 curves are measured on motorways. While fractions of a curve should not exist in this context, the reason for these values is, that due toGPSglitches, not all test drives are recorded completely and thereby for some participants, a lower number of curves is recorded and by averaging over all participants, fractions of curves can occur.
speed limits
The road geometry is not the only limiting factor, that stays, with a few exceptions due to construction work, equal for all test drives. The speed limit for all driven segments stays similarly equal. For this reason, both, distance travelled and time spent within the limits of the different speed limits are evaluated. Speed limits available on the course are 30 km h−1, 50 km h−1, 60 km h−1, 70 km h−1, 80 km h−1, 100 km h−1, 120 km h−1 and 130 km h−1 and on motorways no speed limit. The average time spent and distance travelled within these speed limits for the recorded 108 test runs are shown in the appendixE.1in tableE.5.
This data however, is only the speed limit enforced by German government. This data needs to be compared and evaluated with the actual driven speed. Since the driven speed depends on many different parameters, the actual speed is set into the category of soft pa-rameters and will be discussed in the following sections.
5.4 optimizing parameters for light distributions on real roads 175