PFG 2015 / 1, 0095–00104 ArticleStuttgart, February 2015

© 2015 E. Schweizerbart'sche Verlagsbuchhandlung, Stuttgart, Germany www.schweizerbart.deDOI: 10.1127/pfg/2015/0255 1432-8364/15/0255 $ 2.50

An Algorithm to Generate a Simplified Railway Networkthrough Generalization

PAUL CZIOSKA, FRANK THIEMANN, MONIKA SESTER, ROBIN GIESE & HERMANN VOGT,Hannover

Keywords: generalization, line merging, railway, skeletonisation

don Tube. Since this type of map lacks a lotof additional cartographic information, it hasbecome also common to show the geometry ofthe route as an overlay on a real map, so thatthe user is able to locate stations and the trav-elled route in between.A dynamic enhancement of this type of map

is the so called Live Map, where, in addition tothe tracks, the positions of the moving vehiclesare drawn in real-time. The position informa-tion can be gathered either directly from GPSor indirectly calculated through spatiotempo-ral interpolation on the given track, like it canbe seen for example at the German “DB Zug-radar”, www.bahn.de/zugradar (Fig. 1).A basic requirement for the routing of the

trains is a graph structure of the track network.

1 Introduction

The sector of public transportation is of out-standing importance for the infrastructureand thereby for the wealth of a country. Ac-cording to DESTATIS (2013), approximately 30million people per day use the public trans-portation system in Germany. It is obviousthat such a huge and complex network needsan efficient way to communicate traffic infor-mation to its users.Maps play a major role in this task. They

are able to illustrate connections between dif-ferent means of transport in a way that everyuser is able to understand quickly. In most cas-es, the connections are shown in a schematicmanner, like the popular route map of the Lon-

Summary:Maps play a major role in communicat-ing information in the context of public railwaytransportation, for instance as route maps. In addi-tion, the current position of the trains can be shownon such a map to enrich the information content(Live Map). For the positioning and routing of thetrains on the track, a graph structure of the trafficnetwork is necessary. Since railway tracks aremostly arranged in a parallel manner, it makessense to merge the track lines into representative(centre-)lines, which reduces significantly theamount of edges and helps to identify possible top-ological errors in the input data. This work presentsan algorithm which merges track data based ontopological properties, so that branches and cross-ings can be distinguished. The implementationuses generalization techniques like an area collapseoperator and methods from computational geome-try like polygon triangulation. An evaluation showsthat the output graph is capable for routing tasks.

Zusammenfassung: Ein Algorithmus zur Erstel-lung eines vereinfachten Bahnnetzes durch Gene-ralisierung. Karten spielen eine wichtige Rolle beider Informationskommunikation im Rahmen desöffentlichen Verkehrs, etwa als Liniennetzplan, aufdem zusätzlich die aktuelle Position des Verkehrs-mittels dargestellt wird (Live Map). Um solche Kar-ten zu erstellen, ist eine routingfähige Graphstruk-tur der Gleisdaten nötig. Da Gleise meist parallelverlaufen, ist es sinnvoll, die Gleise zu repräsenta-tiven Linien zu aggregieren, um die Redundanz zuverringern und mögliche Topologiefehler der Ein-gangsdaten zu beheben. In dieser Arbeit wird einAlgorithmus vorgestellt, der einen Gleisdatensatznach topologischen Eigenschaften zusammenfasst.Der Implementierungsansatz nutzt hierzu Techni-ken aus dem Bereich der Skelettierung von Polygo-nen durch Triangulation. Eine abschließende Eva-luation zeigt, dass das Ergebnis für Routinganwen-dungen geeignet ist.

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the algorithm, while the single tracks are ofno importance for a macroscopic routing ap-plication. In addition, users could be irritatedwhen the Live Map shows a train pulling intoa station on a specific platform, but in realitythis platform was only chosen because it rep-resents the shortest way in the graph and notthe platform defined in the timetable. Hence, atransformation into a representative geometryis desirable in many cases.In order to handle those issues, the task is

therefore to generalize the redundant trackswhile preserving the topologic relationship. Inthe context of generalization, this procedurecan be classified as merging (SHEA & MCMAS-TER 1989). As a by-product, the use of such anoperator has the possibility to identify and re-pair incorrect input data. In detail, the follow-ing requirements are necessary:● Bundle parallel tracks that belong to thesame transport route and create a graphwith real world coordinates that representsthe approximate centre of the route (Fig. 2)

● Preserve the topology of the input data. Inother words: insert a node at track switches(Fig. 3), but do not insert a node at cross-ings, e.g. bridges or tunnels (Fig. 4)

● Repair topological errors in the input data,so that the network is routable (Fig. 5).

In this paper we present an algorithm thatfulfils these requirements and generates a sim-plified rail network graph. It combines differ-ent existing computational geometry meth-ods such as buffering and skeletonisation anduses in addition a new technique called TrackTracing.The outline of this paper is as follows. Sec-

tion 2 gives a brief overview over other top-ics that are related to the current problem. In

The nodes of this graph thus have real worldcoordinates, so that the correct geometry ofthe tracks can be shown. Such a graph struc-ture is necessary for different tasks: the edgescan be used to interpolate an approximationof the current position of the train when posi-tion signals are available only at discrete sur-vey stations along the track, and a routing onthe graph can be used to determine the com-plete route of a train. In some Live Map ap-plications, this route can be highlighted whendesired by the user (like the red line in the ex-ample of Fig. 1 shows).A trivial solution to obtain a track graph is

to use raw track data without any modifica-tion, that is, the line data of the tracks sim-ply converted into a graph structure withoutany further processing. In fact, many LiveMap applications at present use such an un-processed data basis.Track datasets for this purpose can be ob-

tained either from official sources (like railoperators or transport associations) or derivedfrom volunteered geographical information(VGI), accessible through portals like Open-StreetMap (OSM). Unfortunately, dependingon the quality of the input data, one cannot besure that the obtained track data is topolog-ically correct, i.e. that line endings are con-nected properly. If this basic condition is notfulfilled, a routing will lead to unexpected er-rors, such as confusing detours or no possibleconnection at all. Especially when VGI is usedas input data the quality cannot be ensured, sothat an additional check is recommended.Furthermore, it is apparent that railway

tracks are mostly arranged in a parallel man-ner. If the whole track network is used for arouting application, a significant redundancyof track information is present that slows down

Fig. 1: Screenshot of the Live Map “DB Zugradar”. Source: www.bahn.de/zugradar (24.6.2014)

Paul Czioska et al., An Algorithm to Generate a Simplified Railway Network 97

old (we used an empirical value of 0.75 m), anode pair is marked as erroneous. The resultof this systematic analysis showed that the rawrailway track data in the region of Germanyseems very suitable for the purpose of rout-ing: in 175,000 nodes only 44 errors have beendetected, corresponding to an error probabil-ity of ~ 0.03%. Certainly, for more accurateresults a more sophisticated analysis is neces-sary since not every error type is covered inthis test.In terms of line network generalization,

most previous work focuses also on road net-works. A common approach is the principleof good continuation proposed by THOMSON &RICHARDSON (1999). In this work, a road net-work is grouped into linear elements calledstrokes, which represents a chain of road sec-tions which have a good continuation. Basedon this technique, THOM (2005) presents amethod to collapse dual carriageways into asingle centre line. Unfortunately, since rail-way vehicles have a huge turning radius, near-ly all rail tracks have a relatively good con-tinuation which makes this principle not ap-plicable.A topic that also deals with line merging is

the map inference from movement trajecto-ries. One of the main research topics in thisfield is the construction of a road map by pro-cessing vehicle tracking data. Due to the un-certainty of GPS measurements, trajectories

section 3, the algorithm is presented. Further-more, in section 4 results of the process areshown. Section 5 discusses the evaluation ofthe results with a test routing. Finally, section6 provides the conclusion and directions forfuture work.

2 Related Work

The generation of a routable graph networkfrom line data without further simplificationis a fairly simple task since it is sufficient totreat all vertices as nodes and add the cor-responding line connections as edges to thegraph. Problems may only arise when the in-put data is somehow flawed. NEIS et al. (2011)discovered that the amount of topological er-rors at street connections in OpenStreetMaphas declined rapidly in the past several years.Nevertheless, the street topology is not

flawless, so that an additional data preparationis still necessary.However, most articles focus on street or

pedestrian routing, whereas a routing on rail-way tracks or the quality of its geometry is notexamined. Due to the lack of such measure-ments, we checked the topological integrityof railway track data from OpenStreetMap bya simple check of the distance between everynode and its nearest neighbour. If the distanceis greater than zero and above a certain thresh-

Fig. 2: Task: Bundle parallel tracks.

Fig. 3: Task: Insert a node at track routebranches.

Fig. 4: Task: No node insertion at crossings.

Fig. 5: Task: Handle topologic errors in theinput dataset.

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In detail, the algorithm consists of the fol-lowing four steps, which are explained morein detail in the course of this section:1) buffering of the tracks and amalgamation ofall buffer polygons,

2) removal of holes,3) triangulation of the buffer polygon,4) creating the skeleton in consideration of theunderlying tracks.Optionally, point information, e.g. stations,

can be added in a fifth step by a map matchingoperation to enable station-to-station routing.Due to the limited space, this step is not cov-ered in this article.

3.1 Buffering of the Tracks

In the first step, a buffer operation is per-formed on every track segment of the inputdata. The buffer width has to be defined man-ually by the user – the smaller the distancevalue is chosen, the more single tracks willbe created in the output dataset. A big valuecorresponds thereby to a more generalised re-sult. In the experiments, a typical buffer dis-tance of 12 m was selected in order to span allneighbouring tracks, which corresponds tothe tripled value of the normal track distanceof 4 m. Subsequently, all buffer polygons areamalgamated into one large polygon, respec-tively multipolygon in the case of an incoher-ent track network, with holes.

3.2 Removal of Holes

In areas with a high track density and manyparallel tracks, e.g. at marshalling yards orbig stations, some holes may occur in the to-tal polygon when the gap between two tracksis slightly higher than the chosen buffer dis-tance in step one. Those holes lead to disrup-tive splits in the resulting graph, because anoutput line will be created on both sides of thehole. This effect can be avoided by a removalof holes which have a size smaller than a de-fined threshold. The threshold size has to bechosen carefully – too big values may destroyuseful information while small values lead tomany forks in the graph. In practice, valuesbetween 4000 m2 and 10000 m2 have lead to

are mostly scattered around the true move-ment path. A reasonable way to infer a roadnetwork is therefore the creation of a centre-line of all trajectories belonging to a commonstreet segment, which is also a form of a merg-ing operation.One approach to achieve this goal using k-

means clustering is presented by EDELKAMP& SCHRÖDL (2003). In the work of LEE et al.(2007), similar trajectories are detected andgrouped in order to derive a representativetrajectory for common parts, which is close tothe problem investigated in this paper. Anoth-er inspiring idea comes from CAO & KRUMM(2009), who simulate physical attraction be-tween the trajectories. ZHANG et al. (2010)describe a method to extract a centreline outof GPS traces with perpendicular lines usingfuzzy c-means clustering in order to separateclose roads. BIAGIONI & ERIKSSON (2012) pre-sent a map inference pipeline similar to theworkflow described in this paper. First, a ker-nel density estimation (KDE) is applied on theraw GPS traces, which produces a density ras-ter. Subsequently, a gray-scale skeletonisationis used to derive the road centrelines.However, car trajectories differ in some

characteristics from railway track data. Tra-jectories have measurement errors, while atrack derived from a map is assumed to havethe correct coordinates. Also, single lines areoften treated as outliers in a car trajectory anal-ysis and are thus neglected, but a single railwaytrack has to be preserved. These differencesreveal the requirement of a new algorithm.

3 Merging Operator

The basic concept of the proposed simplifica-tion operator is the merging of tracks whichare located close to each other while preserv-ing the underlying topological informationof the traffic routes. In order to carry out thistask, a kind of morphological operation is per-formed: At first, the tracks are buffered (Di-lation), and subsequently the buffered area istransformed back to a line (Erosion), whichcorresponds to the Closing operation. The ma-jor challenge – which is also different fromconventional skeleton approaches – is thepreservation of the topological relations.

Paul Czioska et al., An Algorithm to Generate a Simplified Railway Network 99

2) repairing topology errors,3) analysis of the track connectivity,4) inserting connection lines,5) at interior triangles: track tracing.

Track search

In order to detect the underlying topology ofthe tracks, the first step is the retrieval of theaffected track data in the area of the currentlyprocessed triangle. To avoid a wrong connec-tivity analysis, it is necessary to cut the tracksat the triangle edges.

Repairing topology errors

Depending on the quality of the input data,topological errors like not correctly connect-ed track segments may occur in the input dataand can lead to gross errors in the output data.They can be detected by measuring the dis-tance and angle difference between track lineendings and/or vertices – if the distance isvery small and the track segments have an ap-proximately similar direction, an error may bepresent. It can be repaired by connecting theseparated nodes.

Analysis of the connectivity

The topologically clean tracks are then inves-tigated with regard to the connectivity. Fig. 6shows exemplarily three possible track con-stellations in a triangle:a) two tracks simply pass the triangle,b) a track merges (Branch),c) a trac splits (Branch).The connectivity analysis contains mainly

the partition of the tracks into distinct tracksets. Distinct means that a track set has noconnection to another track set.

good results, depending on the desired levelof detail. For the results shown in this work athreshold of 7500 m2 was used.

3.3 Triangulation of the Polygon

In order to obtain a line dataset based on thecreated polygon, an area collapse mechanismis needed which returns the skeleton of thepolygon. Several different approaches for askeletonisation exist in the literature. A goodoverview is given for example by HAUNERT &SESTER (2008).For the algorithm presented in this paper it

is required to use the method of skeletonisa-tion by polygon triangulation, as proposed byCHITHAMBARAM et al. (1991). A brief descrip-tion of the procedure is given in section 3.4.The triangulation itself is based on a con-

strained Delaunay triangulation of the poly-gon, where triangles outside the polygon areremoved. The more homogeneous the trian-gles are shaped, the smoother the skeletongets. Therefore, the algorithm uses a Con-forming Delaunay Triangulation, where addi-tional Steiner Points are inserted into the poly-gon edges. For further details we refer to BERN& EPPSTEIN (1992).

3.4 Creation of the Skeleton

A conventional skeleton based on a triangu-lated polygon is created by an analysis of thetriangles and distinguishes two types of tri-angles: Normal triangles (1) have at least onecommon edge with the polygon boundary,while interior triangles (2) have no edge co-incident with the polygon and occur on junc-tions. The skeleton edge is then created forevery triangle by linking the midpoints of theinterior triangle edges. When triangles of type(2) are processed, a centre point of the triangleis inserted and linked with all three midpointsof the triangle edges.In contrast to a conventional skeleton op-

eration, the proposed algorithm uses also thetopologic relations from the original tracks.All triangles are processed iteratively and thefollowing steps are executed:1) track search,

Fig. 6: Examples of different trackconstellations in a triangle, green: input edge,red: output edge.

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essary until the decision between branch andcrossing can be made. Fig. 7 shows the case ofa branch where the tracks meet a few trianglesfurther (labelled with 3). In contrast, Fig. 8 il-lustrates a crossing where the four tracks ofthe route from top left to the bottom right donot have a common node with the two tracksof the other route until they diverge again inthe triangle labelled with 3.The proceeding of the track tracing is as

follows. At first, all three edges of the start-ing triangle are classified as input or outputedge. Usually, a starting triangle has two in-put edges and one output edge where all tracksfrom both input edges converge, as shown inFig. 6b. In rare cases it can happen that thisassumption is not fulfilled, e.g. when there aredirect connections between all three edges. Inthis case, a tracing is not possible and the al-gorithm only inserts output edges between thecorresponding intersection points.In all other cases, the following loop is ex-

ecuted:1) Label distinct track sets All distinct tracksets that intersect the same input edge aregrouped into a route track set (RTS). Thisholds also if new tracks accrue during theloop.

2) Go to the neighbouring triangle(s) at theoutput edge(s) and group the underlyingtracks to the RTS.

3) Check for connections All RTS are checkedamong each other if a connection exists.If so, a branch is present and the RTS areunited. If desired by the user, RTS can alsobe united due to a certain similarity, e.g.if the angle difference and/or distance be-tween the RTS are below a certain thresh-old.

4) Insert output edges between the intersec-tion centres of the RTS at the triangle edg-es. Old output edges in the current triangleare removed and overwritten unless a Col-lision exit is present, see below.

5) Check the stop criteria○ Branch exit: Only one RTS remains dueto a branch

○ Crossing exit: Two RTS leave the trian-gle through two different output edges

○ Collision exit: The current triangle is theend of a tracing from the opposite direc-tion.

Inserting connection lines

This information is now used to determinethe necessary connection lines in the outputgraph. In most cases like in Fig. 6a, this is atrivial task where just the centres of track in-tersections at two triangle edges are connect-ed. The only exception occurs at interior tri-angles, which marks the initial situation for atrack tracing.

Track tracing

Since it is not possible to distinguish branch-es from crossings in just one single triangle, itis necessary to trace the tracks further until aproof is found that the tracks that are comingfrom different triangle edges merge (Branch)or divide without any common node in be-tween (Crossing). For such a tracing, the tri-angle structure provides a good frame condi-tion since the calculations can thus be locallylimited.An interior triangle of type (2) always

marks the start of a tracing function if all threeedges are crossed by tracks. An example canbe seen in Figs. 7 and 8: The green interiortriangle labelled with 1 has different trackscrossing each triangle edge, thus a track trac-ing over the triangles labelled with 2 is nec-

Fig. 7: Branch of two rail routes.

Fig. 8: Crossing of two rail routes.

Paul Czioska et al., An Algorithm to Generate a Simplified Railway Network 101

5 Evaluation

Besides the examination of the visual appear-ance, the results were evaluated concerningthe topological correctness and routing abil-ity. The topological correctness of a processedGerman-wide track network obtained fromOSMwas estimated by an automatic check fornode connections (see Related Work for moreinformation about the test configuration). Ityielded only two errors out of 28.528 testednode pairs, which is a rather good result thatindicates a highly reliable quality of the topol-ogy. On the contrary, it shows also that the al-gorithm does not work faultlessly since errors

Otherwise, if two or more RTS leavethrough an output edge, continue withstep 1.

The track tracing is in principle able to han-dle an arbitrary number of traced RTS simul-taneously. Note that care is necessary whena new tracing overwrites an old tracing butstops at an earlier triangle compared to the oldtracing – in this case, the output edges may notmatch at the triangle edge.Since the output edges only span the based

triangle and are thus relatively short, it is use-ful to connect those fragments in a final stepto create longer polylines.

4 Results

The following examples show the result ofprocessing a German-wide railway datasetobtained from OpenStreetMap. For the cal-culation, only standard tracks have been usedexcluding tracks in marshalling and mainte-nance yards. In Fig. 12 the result network isvisualized as a red line on top of an Open-StreetMap background in the area of the mainstation in Hamburg. It can be seen that theparallel running railway tracks in OSM havebeen replaced by one single line which followsapproximately the medial axis of the tracks.Fig. 9 shows exemplarily the output of pro-

cessing a branch with several tracks. Here,the original railway tracks are drawn in or-ange and the output line is overlaid in blue.Fig. 10 shows a more complex track junctionnear Kreiensen, Germany, where the originaltopology is also preserved correctly. In thisspecial case, the stop criterion was a Collisionexitwhere the central part was processed fromthe left side as well as from the right side.In general, however, it is not always pos-

sible to generate a visually attractive appear-ance in addition to topological correctness.Such visual drawbacks mostly occur at bigmarshalling yards or junctions with more thanthree track routes converging, as the complexexample of Saarbrücken (Fig. 11) shows. Al-though the topology of the blue output graphis correct, the visual appearance is not satisfy-ing due to many successive track tracings withoverwriting the existing output.

Fig. 9: Example of a simple branch.

Fig. 10: Example of a more complex branch inKreiensen, Germany.

Fig. 11: Example of a very complex track fieldnear Saarbrücken, Germany.

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The result: both the visual inspection of theroute and the speed check yielded no problems– all trains could take the assumed route withan appropriate speed.When processing large datasets, time and

memory complexity is an important aspect asit describes how much the time- and memoryusage grows with increasing input size. Thetheoretical complexity mainly determined bythe buffering and union steps is O (n log n).The memory and time usage was determinedexperimentally. Thereby a near-linear behav-iour of both time and memory usage was ob-served. In our case, the calculation of smalldatasets (~ 14.000 line segments) took approx-imately 3 minutes, whereas the whole Germanrailway network (~ 130.000 line segments) re-quired approximately 40 minutes (CPU: XeonE5 processor with 2,4 GHz).A drawback in terms of calculation time is

the dependence of the processing direction ofthe tracks; that is, different input datasets re-sult in a different geometry of the output data,even in regions where the original data is con-gruent. Thus, a tile based partition of the inputdata in order to parallelize the computation isnot directly possible.

6 Conclusion

In this work we presented a new algorithm toderive a routable rail network from detailedrailway track data in consideration of the to-

may still appear in rare cases. In various otherexperiments with different parameter settings,such errors occurred particularly at helicaltunnels or huge marshalling yards.In order to verify the result with respect to

the routing ability, it is not sufficient to checkonly node connections, because other topo-logical errors can as well significantly influ-ence the routing and may result in large de-tours of the routed trains. Hence, a test routingwas carried out. The basis for the test routingwas:● Railway track data from OSM● Station coordinates from OSM● Timetable information, accessed atwww.bahn.dewww.der-metronom.de

The routing itself was executed by the rout-ing algorithm of the HAFAS journey plannerfrom HaCon. A total of 4 relations in north-ern Germany have been tested and analyzed(Fig. 13). The evaluation was carried out intwo ways: on the one hand manually by vis-ual inspection of the route between the startand end nodes, and on the other hand by cal-culating the needed train speed between thestations. If the calculated speed of a train risesto unrealistic values, e.g. above 200 km/h forlocal trains, it can be assumed that this errorcomes from a topological issue in the routingdataset. The train has to take a detour and thusa longer distance, but the travel time keeps thesame, which results in a higher speed.

Fig. 12: Output railway network in the area of Hamburg, Germany (background: OpenStreetMap).

Paul Czioska et al., An Algorithm to Generate a Simplified Railway Network 103

thus to preserve the topology of the originaltrack network.Different evaluation approaches like a test

routing indicate a very good quality in termsof topological correctness and routing abilityof the output graph. The visual appearanceof the resulting representative lines is rathergood in most cases, although some complex

pology of the input tracks. The algorithm usesdifferent methods of geometry type change(buffer operation and dimensional collapse)in order to create a representative line of thetrack routes. The core of the operator is a tracktracing mechanism based on triangles in orderto distinguish branches from crossings and

Fig. 13: Routed relations in northern Germany, based on a processed OSM dataset.

104 Photogrammetrie • Fernerkundung • Geoinformation 1/2015

NEIS, P., ZIELSTRA, D. & ZIPF, A., 2011: The Streetnetwork evolution of crowdsourced maps: Open-StreetMap in Germany 2007–2011. – Future In-ternet 4 (1): 1–21.

SHEA, K.S. & MCMASTER, R.B., 1989: Cartographicgeneralization in a digital environment: Whenand how to generalize. – AutoCarto 1989: 56–67.

THIEMANN, F., WERDER, S., GLOBIG, T. & SESTER, M.,2013: Investigations into partitioning of gener-alization processes in a distributed processingframework. – 26. International CartographicConference, Dresden, http://www.icc2013.org/_contxt/_medien/_upload/_proceeding/395_proceeding.pdf (15.9.2014).

THOM, S., 2005: A Strategy for collapsing OS Inte-grated Transport Network (ITN) dual carriage-ways. – 9th ICA Workshop on Generalisationand Multiple Representation, http://generalisation.icaci.org/images/files/workshop/workshop2005/Thom.pdf (15.9.2014).

THOMSON, R.C., & RICHARDSON, D.E., 1999: The‘good continuation’ principle of perceptual or-ganization applied to the generalization of roadnetworks. – ICA 19th International CartographicConference.

ZHANG, L., THIEMANN, F. & SESTER, M., 2010: Inte-gration of GPS Traces with Road Map. – Work-shop on Computational Transportation Sciencein conjunction with ACM SIGSPATIAL, SanJose, CA, USA.

Address of the Authors:

M.Sc. PAUL CZIOSKA, Dipl.-Ing. FRANK THIEMANN,Prof. Dr.-Ing. MONIKA SESTER, Leibniz UniversitätHannover, Institut für Kartographie und Geoinfor-matik (IKG), Appelstr. 9A, D-30167 Hannover,Tel.: +49-511-762-5422, Fax: +49-511-762-2780, e-mail: {czioska} {thiemann} {sester} @ikg.uni-hannover.de

ROBIN GIESE, Dr.HERMANN VOGT, HaCon Ingenieur-gesellschaft mbH, Lister Str. 15, D-30163 Han-nover, Tel.: +49-511-33699-0, Fax: +49-511-33699-99, e-mail: {robin.giese} {hermann.vogt} @hacon.de

Manuskript eingereicht: Juni 2014Angenommen: Oktober 2014

junctions may result in a confusing outputline constellation. At this point, the visual ap-pearance could benefit from an additional postprocessing which preserves the topology.A drawback of the presented method is

though the dependence of the processing di-rection, which complicates a parallelization ofthe computation. For this purpose, approach-es have to be used that deal with overlappingparts (see e.g. THIEMANN et al. 2013).

References

BERN, M. & EPPSTEIN, D., 1992: Mesh generationand optimal triangulation. – Computing in Eu-clidean geometry 1: 23–90.

BIAGIONI, J. & ERIKSSON, J., 2012: Map inference inthe face of noise and disparity. – 20th Interna-tional Conference on Advances in GeographicInformation Systems ACM: 79–88.

CAO, L. & KRUMM, J., 2009: From GPS traces to aroutable road map. – 17th ACM SIGSPATIAL2009: 3–12.

CHITHAMBARAM, R., BEARD, K. & BARRERA, R.,1991: Skeletonizing polygons for map generali-zation. – Technical Papers ACSM-ASPRS Con-vention, Cartography and GIS/LIS 2: 44–54.

DESTATIS (DEUTSCHES STATISTISCHES BUNDESAMT),2013: Busse und Bahnen mit neuem Fahrgast-rekord. https://www.destatis.de/DE/PresseService/Presse/Pressemitteilungen/2014/04/PD14_127_461.pdf(15.9.2014).

EDELKAMP, S. & SCHRÖDL, S., 2003: Route planningand map inference with global positioning trac-es. – Computer Science in Perspective, Springer:128–151.

HAUNERT, J.H. & SESTER, M., 2008: Area collapseand road centerlines based on straight skeletons.– Geoinformatica 12 (2): 169–191.

LEE, J., HAN, J. &WHANG, K., 2007: Trajectory clus-tering: a partition-and-group framework. –ACMSIGMOD International Conference on Manage-ment of Data.