Catenary System Detection, Localization and Classification ... - MDPI

remote sensing Article

Catenary System Detection, Localization and Classification Using Mobile Scanning Data El˙zbieta Pastucha Department of Geoinformation, Photogrammetry and Environmental Remote Sensing, AGH University of Science and Technology, Al. A.Mickiewicza 30, 30-059 Kraków, Poland; [email protected] Academic Editors: Gonzalo Pajares Martinsanz and Prasad S. Thenkabail Received: 18 July 2016; Accepted: 22 September 2016; Published: 27 September 2016

Abstract: This paper presents a new method for detecting, locating and classifying overhead contact systems (catenary systems) in point clouds collected by mobile mapping systems (MMS) on rail roads. Contrary to many other application types, railway embankments are highly regulated and standardized. Railway infrastructure geometric relations remain roughly unchanged within established regions and have similarities between them. The newly-developed method exploits both these characteristics, as well as the survey process. There are several steps in this approach. Firstly, it restricts the search for catenaries relative to the distance to registered MMS trajectory, then finds possible support structures according to the density of points above the track. Subsequently, the method verifies the structures’ presence and classifies the points with the use of the RANSAC algorithm. It establishes the presence of cantilevers, as well as poles or structural beams, depending on the type of detected support structure. The method also determines the coordinates of the identified object on the ground. Finally, a classification is clarified with the use of a modified DBSCAN algorithm. The design method has been verified with data collected in four surveys where the cumulative length of the route was almost 90 km. Over 97% of support structures were correctly detected, and out of these, over 95% were completely classified. Keywords: LiDAR; mobile mapping; point cloud classification; railway monitoring; object recognition

1. Introduction Mobile laser scanning (MLS) has become quite popular in recent years and has numerous applications. Technology is advancing, and current mobile mapping system (MMS) accuracies allow them to be used in almost any survey mission. Although there are a wide range of MMS systems providing large amounts of data (Figure 1), there are far fewer algorithms and methods able to automatically process the data. Various research has been done on the automatic processing of point clouds collected by airborne scanners [1,2]. There are also many scientific studies on the detection of primitives or specifically-shaped objects in point clouds [3,4]. Some of them can be implemented in processing MLS point clouds. However, as these data are different due to the specific collection process, view perspective and density variation [5,6], further research into the subject is needed. There are various types of works that can be conducted using MLS. The first MMS were stabilized on cars [7] and subsequently have had numerous applications already implemented in road maintenance. MLS can be used to take stock and measure the position of road infrastructure elements [8–10]. Data obtained by terrestrial MMS can also be used to create a spatial database [11], to carry out road safety inspections [12,13], to model the road area [14], to detect voids and cracks in the pavement [8] and to detect road signs [15,16]. LiDAR technology is also used in the evaluation of road infrastructure, such as tunnels, bridges or retaining walls [17–19]. MMS were later adapted to rail cars. Remote Sens. 2016, 8, 801; doi:10.3390/rs8100801

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There are 1,021,457 1,021,457 km km of of railway railway lines lines world-wide world-wide [20]. [20]. In Europe, where rail routes first emerged, there are 349,365 km of tracks [20], of which 19,617 tracks [20], of which 19,617 km km are are in in Poland Poland [21]. [21]. Rail Rail transport transport remains one of the most cost-effective and most ecological type of transportation compared to other types. The existence and also the competitiveness of railways in relation to other modes of transport requires surveys that that have have to to be becarried carriedout outregularly. regularly. requires constant monitoring. There are several types of surveys Surveys include assessing track parameters, such as chainage, cant, twist, gradients, gauge and also clearance gauge monitoring [22]. Current accuracies of point clouds collected by MMS on rails make it possible to use it in clearance clearance gauge monitoring [23] or for the purpose of 3D railroad corridor creation Traditionally, this creation [6]. Traditionally, thistype typeof of work work was was done done using using a trolley operated operated by an operator walking on foot [22,24–26]. MLS provides data far faster, but while the trolley operator decides what is [22,24–26]. MLS provides data far faster, important to measure, point clouds include multiple measurements to single objects, both those of the utmost importance and those that are redundant. With the existing technology, massive amounts of data are obtained after each survey mission, the processing of which still requires a lot of manual, tedious work. Therefore, Therefore, the the next step in the development of MMS for railways is to automate the data processing.

Figure 1. 1. Point Figure Point cloud cloud collected collected by by aa mobile mobile mapping mapping system system (MMS) (MMS) on on aa rail. rail. Points Points colored colored according according to intensity; MMS trajectory in blue. to intensity; MMS trajectory in blue.

Railway infrastructure monitoring requires methods that are efficient both at the stage of data Railway infrastructure monitoring requires methods that are efficient both at the stage of data collection, as well as at the stage of data processing. Therefore, the data processing algorithm must collection, as well as at the stage of data processing. Therefore, the data processing algorithm must be, in addition to reliable, highly efficient computationally. The amount of data necessitated the be, in addition to reliable, highly efficient computationally. The amount of data necessitated the development of an algorithm that is both simple and effective. It is true that the processing of large development of an algorithm that is both simple and effective. It is true that the processing of large datasets can be accelerated by the use of high-performance computing farms, but simplicity is always datasets can be accelerated by the use of high-performance computing farms, but simplicity is always an advantage. The demand for efficient monitoring of railway infrastructures will grow, as will the an advantage. The demand for efficient monitoring of railway infrastructures will grow, as will the requirement for MLS. The amount of MLS data is growing and will always be an obstacle on the road requirement for MLS. The amount of MLS data is growing and will always be an obstacle on the road to high performance. Simplicity and efficiency were very important criteria in the development of to high performance. Simplicity and efficiency were very important criteria in the development of the algorithm. the algorithm. This work’s goal is to automate the detection of the most common objects within the rail bed, This work’s goal is to automate the detection of the most common objects within the rail bed, the catenary system. This includes extracting a class of points collected on objects belonging to the the catenary system. This includes extracting a class of points collected on objects belonging to the catenary, contact cables, catenary wires and support structures and also determining the position of catenary, contact cables, catenary wires and support structures and also determining the position of the the detected support structures on the ground. For the method to be useful to railway operators, it detected support structures on the ground. For the method to be useful to railway operators, it has to has to be able to process data collected in various environments and from various MMS on the rail. be able to process data collected in various environments and from various MMS on the rail. It has to It has to be efficient, precise and easily tuned to certain object properties. Algorithms with all of these be efficient, precise and easily tuned to certain object properties. Algorithms with all of these features features could have many applications. It could help determine if the catenary does not jeopardize could have many applications. It could help determine if the catenary does not jeopardize railway railway safety, help with creating inventories, narrow down the data for processing during safety inspections and also prepare data for automatic railway corridor modelling. To achieve all of these

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safety, help with creating inventories, narrow down the data for processing during safety inspections and also prepare data for automatic railway corridor modelling. To achieve all of these objectives, a prototype method was created that uses simple calculations and relies only on the geometrical parameters of the sought after objects. The method is a sequential filtration process that is heuristic in its core. All parameters and thresholds in the algorithm can be easily tuned to specific data by the end user. The structure of the paper is as follows. Firstly, there is a brief summary of existing methods (Section 2). Secondly, the basic characteristics and properties of a catenary system are presented (Section 3.1). Section 3.2 contains the algorithm structure description in detail, data preparation (Section 3.2.1), density analysis (Section 3.2.2.), verification of the detected support structures and their location (Section 3.2.3) and classification clarification (Section 3.2.4). The algorithm test data are described in Section 4. Lastly, the results of experimental tests and a discussion are presented (Section 5). Conclusions are made in Section 6. 2. Related Work The ideas of how to automatically process MMS point clouds collected for road and railroad are quite similar; therefore, algorithms created for both environments have been included in this section. Most algorithms, created to help automate the processing of point clouds acquired by MSL, relate to the detection of road pavements and road curbs. These algorithms usually utilize characteristics both of the measuring sensors and the object of evaluation. Basic assumptions for most methods are: the road must be an almost flat surface with a locally small slope; curbs must be in its immediate vicinity and have a predetermined height difference [8,9]. Described methods usually fall into one of two groups, firstly, a local analysis approach and, secondly, a global approach. The first group includes all detection algorithms whose base concept is analysis in small point cloud subsets, sections perpendicular to the trajectory or subsequent profiles recorded by the scanner [11,12,27,28]. Then, the algorithms detect the road pavements and curbs using the sliding window method [27] or their position directly under the trajectory and slight changes in altitude or fitting a line [9,11,12,28]. Global approaches are a bit more diverse. Some use road geometry and position, flat and below the trajectory [13]; others use a depth image to filter out points with significant elevation change in the near vicinity [14]. In other research, the surface is found by using morphological operations (erosion) [29]. A very interesting approach was presented in [5], where the authors search for road pavements and facades using the geometric index calculated using the roughness value. The detection of slender vertical objects may include: power poles, lanterns, sign posts and trees. The determination of the position of these objects is used in the inventory of roads [8], surveying [13], as well as to improve the accuracy of automatic navigating vehicles [30]. Depending on the application and its data, algorithms are structured differently. There are more general methods, designed to detect all pole-shaped objects near to roads [5,30,31], or more specialized, for traction poles only [32]. Methods for detecting pole-like objects in point clouds differ vastly, though most use at least two-step procedures, where the first step consists of some type of segmentation or restriction of the search area. A couple of algorithms propose two-step procedures with segmentation in voxels first and then the actual search for pole-like objects [5,30]. Another method was proposed in [31], where point clouds are analyzed in single scanner profiles. Short circular sweeps that are removed from the rest of the data and presented directly above each other in subsequent profiles are classified as poles. An algorithm with a slightly wider application presented in [33] detects poles and other objects near roads using derived object features, both shape and context. Processing of point clouds collected for railroads include mostly rail detection [34–39], sometimes catenary wires [34,36,39] and catenary support structures [6,32,36,39]. Similar to methods described earlier, most algorithms limit the search area in point clouds, by segmentation, buffering or a basic classification process. For this purpose, some algorithms use the approximated position derived from orthophotomaps [35], embankments detected by moving window operators [38] or the trajectory


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of the MLS [32,36]. Actual rail detection is usually performed by the local analysis of elevation differences [5,34,35,37–39], but there are also methods that involve using the fitting of the rail model into the data [36] or search by the continuity and parallel position properties of rails [38]. Methods using Remote Sens. 801 4 of 22 the analysis of 2016, local8,height jumps have their drawbacks: they often incorrectly classify points belonging to the railway sleepers or various railway line control devices [37]. For this reason, some methods Methods using the analysis of local height jumps have their drawbacks: they often incorrectly classify include an additional verification step. points belonging to the railway sleepers or various railway line control devices [37]. For this reason, Catenary detection classification are done some methods includeand an additional verification step.usually by limiting the distance vertically and horizontally from the previously-detected rails system trajectory [32,34,36]. Verification of and detected Catenary detection and classification areor done usually by limiting the distance vertically overhead wires isfrom performed using a simplified to fit into detected rails and catenaryofin the horizontally the previously-detected railsmodel or system trajectory [32,34,36]. Verification detected overhead is performed using a simplifiedalgorithm model to fit into detected and catenary planar horizontal viewwires [34] or by usage of the RANSAC combined withrails intensity values [36]. in the planar horizontal view [34] or by usage of the RANSAC algorithm combined with intensity Catenary cables are also detected by a point neighborhood check together with other derived geometric values Catenary cables areto also detected a point check together with other features [39].[36]. Other methods used find objectsby similar to neighborhood catenary wires include powerline searches. derived geometric features [39]. Other methods used to find objects similar to catenary wires include In [40,41], powerlines, typical properties, neighborhood, continuity and detachment are used to locate powerline searches. In [40,41], powerlines, typical properties, neighborhood, continuity and them. To verify found objects, polynomial functions are used to fit the model. detachment are used to locate them. To verify found objects, polynomial functions are used to fit Support structures are detected by several algorithms [6,32,39]. Each method approaches the the model. problem differently. Pastucha localize supportalgorithms structures[6,32,39]. along the corridor a density Support structures are[32] detected by several Each methodwith approaches thecheck over the rail track, but do not perform classification. Arastounia [39] calculates points neighborhoods problem differently. Pastucha [32] localize support structures along the corridor with a density check and recognizes by their propertiesArastounia and topological relationships. Zhu [6] implement over the railobjects track, but do notgeometrical perform classification. [39] calculates points neighborhoods and recognizes their geometrical and digital topological relationships. rasterization of pointobjects cloudsby into a digital image,properties and then use image processing. Zhu [6] implement rasterization of point clouds into a digital image, and then use digital image processing.

3. Methodology 3. Methodology

3.1. Geometrical Properties and Spatial Relations 3.1. Geometrical Properties and Spatial Relations

The objective of this work is to automatically detect and classify points belonging to the catenary The objective of this work is to automatically detect and classify belonging to theon catenary system within the registered track. This includes classifying thepoints points registered any object system within the registered track. This includes classifying the points registered on any object belonging to the rail catenary system and locating its support structure. The overhead contact system belonging to the rail catenary system and locating its support structure. The overhead contact system provides the railway cars with the necessary electric power. The whole system consists of a series of provides the railway cars with the necessary electric power. The whole system consists of a series of objects. Those taken into consideration gaugeclearance clearance monitoring be divided objects. Those taken into considerationin inrailway railway gauge monitoring cancan be divided into into two basic groups, cables and support structures. The cables include catenary wires, contact wires two basic groups, cables and support structures. The cables include catenary wires, contact wires and and return wireswires (Figure 2). 2). return (Figure

Figure2. 2. Catenary Catenary cables. Figure cables.

There are many different types of support structures, with various construction, material and

There aresolutions. many different types of support structures,towith various construction, material technical Due to the number of tracks connected said structure, they can be divided into and technical solutions.the Due to the number tracks connected to said structure, they can be divided into two categories, single solution andofthe multi-track solution (Figure 3). two categories, the single solution and the multi-track solution (Figure 3).

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Remote Sens. 2016, 8, 801 are 8,many RemoteThere Sens. 2016, 801

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different types of support structures, with various construction, technical solutions. Due to the number of tracks connected to said structure, they can be divided into two categories, the single solution and the multi-track solution (Figure 3).

(a)

(b)

(a) (b) Figure 3. 3. Catenary Figure Catenary system system support support structures. structures. Single Single solution solution (a) (a) and and multi-track multi-track solution, solution, portal (b). Figurestructure 3. Catenary portal structure (b). system support structures. Single solution (a) and multi-track solution, portal structure (b).

Analysis of the rail catenary system provides several clear geometrical observations. Analysis of the rail catenary system provides several clear geometrical observations. Analysis of the rail catenary system provides several clear geometrical observations. 1. The relative position of the catenary wires and the rails remains roughly the same throughout 1. The relative position of the catenary wires and the rails remains roughly the same throughout the the whole route. 1. The relative position of the catenary wires and the rails remains roughly the same throughout whole route. 2. Traction masts the whole route.or portal structures are placed in fairly regular intervals. 2. Traction masts orbetween portal structures structures are placed in regular intervals. 3. connections the catenary and the support system are achieved by cantilevers, 2. The Traction masts or portal arewires placed in fairly fairly regular intervals. The connections between the catenary wires and the support system achieved by cantilevers, 3. which protrude over the rail track. The main axis of each cantilever is roughly perpendicular to 3. The connections between the catenary wires and the support are system are achieved by which protrude over the rail track. The main axis of each cantilever is roughly perpendicular to the track direction. cantilevers, which protrude over the rail track. The main axis of each cantilever is roughly the track direction. 4. The support structures, both single mast and portal structures, are constructed from beam-like perpendicular to the track direction. which are either vertical horizontal. The support structures, both singleormast mast and portal structures, are constructed from beam-like 4. elements, The support structures, both single elements, which which are are either vertical or horizontal. elements, The designed method tries to incorporate these geometric characteristics into the process in orderThe to make it quicker and more efficient. As thegeometric relative position of the into catenary wires and the The designed method tries incorporate these geometric characteristics intoprocess the process in designed method tries toto incorporate these characteristics the in order system trajectory remains roughly the same throughout the whole route, the search for overhead order to make it quicker and more efficient. As the relative position of the catenary wires and the to make it quicker and more efficient. As the relative position of the catenary wires and the system cables be limited to a narrow corridor of data 4). asthe the cantilevers intrude systemcan trajectory remains roughly the same throughout theAdditionally, whole route,for search for overhead trajectory remains roughly the same throughout the(Figure whole route, the search overhead cables can be into this spatial range, they cause a local increase of point density. In this way, a set of possible cables can be limited to a narrow corridor of data (Figure 4). Additionally, as the cantilevers intrude limited to a narrow corridor of data (Figure 4). Additionally, as the cantilevers intrude into this spatial support structures bethey detected. Then, todensity. verify detection, several criteria canway, besupport established, based into this spatial causeof a point local increase of this point density. Inpossible this a set of possible range, they causerange, acan local increase In way, a set of structures on the support structure characteristics. support structures can to beverify detected. Then, several to verify detection, criteria can on be the established, can be detected. Then, detection, criteria can beseveral established, based support based on characteristics. the support structure characteristics. structure

Figure 4. 4. Narrow Narrowcorridor corridorcontaining containing catenary wires against selected points the MMS point Figure catenary wires against selected points fromfrom the MMS point cloud. cloud. Catenary blue;red; rails, red; trajectory, Catenary system,system, blue; rails, trajectory, green. green.


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Sens. 2016, 8, 801 3.2.Remote Algorithm Structure

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whole has been divided into into four consecutive steps. The first twofirst stepstwo are steps relatively wholealgorithm algorithm has been divided four consecutive steps. The are 3.2.The Algorithm Structure easy and rely on the typical properties the railway environment. The first setsThe upfirst parameters relatively easysolely and rely solely on the typical of properties of the railway environment. sets up The whole algorithm has been divided into four consecutive steps. The first two steps are and organizes the data in order to simplify order theand calculations. second step the parameters and organizes the data in orderand to simplify order the The calculations. Theconducts second step relatively easy and rely solely on the typical properties of the railway environment. The first sets up calculations tocalculations extract the to possible support structures from the whole point cloud. The lastcloud. two steps conducts the extract the possible support structures from the whole point The parameters and organizes the data in order to simplify and order the calculations. The second step conduct thethe calculations in order to verify the to objects detected, thepoint points and lastconducts two steps conduct thelocally calculations locally in order verify the objects detected, classify the clarify points calculations to extract the possible support structures fromclassify the whole cloud. The their classification. The simplified algorithm structure is shown in Figure 5. and clarify their classification. The simplified algorithm structure is shown in Figure 5. last two steps conduct the calculations locally in order to verify the objects detected, classify the points and clarify their classification. The simplified algorithm structure is shown in Figure 5.

Figure Figure 5. 5. The The simplified simplified algorithm algorithm structure. structure. Figure 5. The simplified algorithm structure.

3.2.1. Data Preparation 3.2.1. Data Preparation 3.2.1. Data Preparation Data preparation preparationconsists consistsofof the following three procedures, ground filtering, reducing point Data the following three procedures, ground filtering, reducing point cloud Data preparation consists of the following three procedures, ground filtering, reducing point cloud size and setting the calculation order.ground Firstly, ground has filtering has to be performed. This size and setting calculation order. Firstly, to behas performed. This procedure cloud size andthe setting the calculation order. Firstly, filtering ground filtering to be performed. This procedure is necessary for calculating the coordinates of the detected support structure on the is procedure necessary isfornecessary calculating the coordinates of the detected support support structure on theon ground. for calculating the coordinates of the detected structure the ground. The classification might be executed by a number of algorithms, but as it was not the main The classification might bemight executed by a number of algorithms, but notthe themain main ground. The classification be executed by a number of algorithms, butasasitit was was not goal of this work, it was decided to use ground classification algorithms found in the TerraScan goal of of this work, algorithmsfound foundininthethe TerraScan goal this work,it itwas wasdecided decidedto to use use ground ground classification classification algorithms TerraScan software. The results show typical holes in terrain that arise duetotothat theocclusions occlusions (Figure software (version 016.003). results show typical holes inarise the terrain arise due to the occlusions software. The results showThe typical holes in the the terrain that due the (Figure 6).6). AsAs thethe classification objective elevation coordinates forthe thepositions positions ofthethe support classification objectiveisisto toprovide provideisthe the elevation for support (Figure 6). As the classification objective to provide thecoordinates elevation coordinates for theofpositions of the structures situated directly next to the rail track, the results are sufficient. structures situated directlydirectly next to the thetrack, results sufficient. support structures situated nextrail to track, the rail theare results are sufficient.

Figure Pointsbelonging belongingto to the the ground ground class. class. Example in in Figure 6. 6.Points Examplefrom fromthe theMLS MLSpoint pointcloud cloudclassified classified Figure 6. Points belonging to the ground class. Example from the MLS point cloud classified in TerraScan software. TerraScan software (version 016.003). TerraScan software.

The second procedure limits the calculations of the later algorithm to points positioned up to a The second second procedure procedure limits limits the calculations calculationsof ofthe thelater lateralgorithm algorithmtotopoints pointspositioned positionedupuptoto setThe distance horizontally from thethe registered trajectory: bd (Figure 7). It is necessary to set the limit a asetsetdistance distancehorizontally horizontallyfrom fromthe theregistered registeredtrajectory: trajectory:bd bd(Figure (Figure7). 7).ItItisis necessary necessary to to set set the the limit limit according to regulations in force in the area where the survey took place. The limit should incorporate according to regulations in force in the area where the survey took place. The limit should incorporate according to regulations force in the area where the survey took The limitdistance should incorporate both railway clearance in monitoring maximum distance, as well asplace. the maximum from the both railway monitoring maximum distance, distance, as as well well as as the from the both railway clearance monitoring the maximum maximum distance distance from the track to oneclearance line support structure. maximum track to one line support structure. track toTo one lineorder support structure. keep in point cloud processing and to be able to directly relate to specific parts of the data, indexing system been introduced. cloud is divided intoparts sections To an keep order in pointhas cloud processing andThe to processed be able to point directly relate to specific of the

data, an indexing system has been introduced. The processed point cloud is divided into sections


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To keep order in point cloud processing and to be able to directly relate to specific parts of the data, Remote an indexing Sens. 2016,system 8, 801 has been introduced. The processed point cloud is divided into sections 7 of 22along the route. Remote Subsequent Sens. 2016, 8, 801sections are given one, unchangeable index i {1, 2, 3...}. Each section is 7 ofdefined 22 the route. Subsequent are given index i {1, 2, 3...}. Each section is key by itsalong trajectory key point (KPi ),sections directional pointone, (DPunchangeable ) and section depth (sd). Sets of consecutive i defined byroute. its trajectory keysections point i), directional point i) index and section depth (sd). Sets of Subsequent are given one, from unchangeable i {1,established, 2, 3...}. Each section is pointsalong (KPithe ) and directional points (DPi(KP ) are derived the(DP trajectory in even intervals, consecutive key points (KP i ) and directional points (DP i ) are derived from the trajectory in defined by its trajectory key point (KP i), directional point (DPi) and section depth (sd). Sets of section steps (sst) (Figure 7). Key points belong directly to the trajectory. Each KPi together with its established, even section (sst) (Figure 7). Key belong directly to the trajectory. consecutive key intervals, points (KP i) andsteps directional points (DPi)points are derived from the trajectory in corresponding DPi forms a horizontal lineDP perpendicular to the trajectory in said KPtrajectory i . The DPi is Each KP i together with its corresponding i forms a horizontal line perpendicular to the established, even intervals, section steps (sst) (Figure 7). Key points belong directly to the trajectory. positioned to the right of the trajectory, butright its distance is of no importance and, as no such, has been set in said i. The DP i is positioned to the of theatrajectory, distance is of importance Each KPKP i together with its corresponding DPi forms horizontalbut lineits perpendicular to the trajectory to 1 m. Section i (S ) is then a set of points lying within half a section depth from the vertical i and, as KP such, hasDP been to 1 m. Section (Si) isofthen set of points within is half section depthplane in said i. The i isset positioned to the iright the atrajectory, but lying its distance of ano importance containing appropriate KP and DP . from as thesuch, vertical containing i and DPof i. points lying within half a section depth i to 1 m. Section i appropriate and, has plane been set i (Si) isKP then a set from the vertical plane containing appropriate KPi and DPi.

Figure 7. Sample point cloud. redtrajectory trajectory key key points directional points, in blue Figure 7. Sample point cloud. InInred points(KP), (KP),ininyellow yellow directional points, in blue border of calculation area. Figure 7. Sample point cloud. In red trajectory key points (KP), in yellow directional points, in blue border of calculation area. border of calculation area.

Two coordinate systems also need to be defined. The first coordinate system, the projected ENH

Two coordinate systems also defined. Theprovided. firstcoordinate coordinate system, the projected (easting, northing, elevation) in need which MLS data are The other is the coordinate Two coordinate systems also needtothe tobe be defined. The first system, thelocal projected ENHENH (easting, northing, elevation) in which the MLS data are provided. The other is the local coordinate system X i Y i Z i , which is different for each section S(i) (Figure 8). Its origin lies in the KP i ; the X i axis is (easting, northing, elevation) in which the MLS data are provided. The other is the local coordinate directed towards the DP i (off-track direction); the Y i axis is perpendicular anti-clock-wise to the X i system X Y Z , which is different for each section S(i) (Figure 8). Its origin lies in the KP ; the X axis is system i i XiYiZi, which is different for each section S(i) (Figure 8). Its origin lies in the KPi; the i Xi axisi is axis (along the track direction); and the Z i axis is parallel to the H axis of the projected ENH coordinate directed towards the DP (off-track direction); thethe Yi Yaxis is is perpendicular to the the X Xii axis directed towards thei DP i (off-track direction); i axis perpendicularanti-clock-wise anti-clock-wise to system. Units between the coordinate systems remain the same. axis (along the track direction); andZthe Z i axis is parallel to the H axis of the projected ENH coordinate (along the track direction); and the axis is parallel to the H axis of the projected ENH coordinate i system. Units between coordinatesystems systemsremain remain the system. Units between thethe coordinate thesame. same.

Figure 8. Sample point cloud section. Easting, northing, elevation (ENH) coordinate system in teal, section local coordinate system in white, sectionnorthing, key pointelevation in red, section directional point in yellow. Figure 8. Sample point cloud section. Easting, northing, (ENH) coordinate system in teal, Figure 8. Sample point cloud section. Easting, elevation (ENH) coordinate system in teal, section coordinate system white,section section key key point directional point in yellow. section locallocal coordinate system inin white, pointin inred, red,section section directional point in yellow.


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3.2.2. Initial Density Analysis As previously explained, the design method uses geometric relationships in the MLS data. Point density is used to limit the search for support structures. A matrix is created with one column and rows corresponding to the index i. The value of the i-th cell is a number of points within an i-th section at a set distance from the trajectory both horizontally and vertically: oi,1 = #T (i)

(1)

T (i) : = {p (X, Y, Z) ∈ S (i) : Z ∈ [hl , hh ] ∧ X ∈ [−d, d]}

(2)

where where, S(i), set of points belonging to section i; hl , hh , elevation distance limits; d, horizontal distance limits along the X axis. Additionally, for each section, a region boundary is saved. Border vertices are calculated using the maximum values of the coordinates of the set of section points in the local 2D coordinate system, anchored in the trajectory key point and set in the section plane. Points lying within the calculated boundaries are assigned to the class catenary system. The lower left vertex (LL) is calculated: LL : = (XLL , 0, ZLL )

(3)

where

• •

XLL , lowest X coordinate value within points in the subset T, ZLL , lowest Z coordinate value within points in the subset T. Accordingly, the upper right vertex (UR): UR : = (XUR , 0, ZUR )

(4)

where

• •

XUR , highest X coordinate value within points in the subset T, ZUR , highest Z coordinate value within points in the subset T.

The statistical parameters of the density matrix have been calculated to provide the information necessary to establish the correct binarization threshold. Firstly, the average number of points per section and, then, the population standard deviation are calculated. o = s σ = ±

∑ni=1 oi,1 n ∑ni=1 (oi,1 − o) n

(5) 2

(6)

where

•

n, number of sections in a point cloud.

The matrix is then binarized with a threshold equal to the average number of points together with m times the population standard deviation [32]: ( obi,1 =

1,

oi,1 ≥ (o + mσ)

0,

in other cases

(7)

The value of the m parameter was determined during threshold sensitivity analysis in Section 5.1.


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Then, the process, similar to morphological image processing, dilatation, is conducted to gather areas of interest lying in the near vicinity. A circle with a radius equal to 1 matrix unit has been used as a structuring element. Next, all existing area centers are found, and their index numbers (row numbers) are derived, to form a set of places of interest (W). 3.2.3. Support Structure Verification and Classification The verification process has a couple of consecutive steps. The simplified algorithm structure is presented in Figure 9. PEER REVIEW Remote Sens. 2016, 8, x FOR 9 of 23

Figure process. Figure 9. 9. Simplified Simplified structure structure of of the the verification verification process.

(i) Cantilever Criteria (i) Cantilever Criteria A higher point density above the track can indicate not only the presence of cantilevers A higher point density above the track can indicate not only the presence of cantilevers (Figure 10a), but also the joining of an additional track on turnouts/crossings (Figure 10b), double (Figure 10a), but also the joining of an additional track on turnouts/crossings (Figure 10b), catenary wires at the ends of tensioning sections or vegetation growing too close to the catenary double catenary wires at the ends of tensioning sections or vegetation growing too close to the catenary wires. Depending on the object causing the increase of point density, the points registered above the wires. Depending on the object causing the increase of point density, the points registered above track projected on a horizontal plane will form a different pattern. As cantilevers are positioned the track projected on a horizontal plane will form a different pattern. As cantilevers are positioned almost perpendicular to the track, the pattern will resemble a cross. In other cases, there might be almost perpendicular to the track, the pattern will resemble a cross. In other cases, there might be two lines meeting at an acute angle, turnouts, section tensioning ending, or the shapeless formation two lines meeting at an acute angle, turnouts, section tensioning ending, or the shapeless formation of of points, vegetation. points, vegetation. To rule out false positives, each place of interest must be considered separately. Firstly, a set of To rule out false positives, each place of interest must be considered separately. Firstly, a set of points that should contain a catenary, together with the object causing the density increase, is points that should contain a catenary, together with the object causing the density increase, is selected selected based on the distance to the considered location. If a cantilever is present in a selected set of points, far more points should be registered on it than on catenary wires. All points are then projected onto a horizontal plane; the elevation coordinate is taken out of the equation; and then, a line is fitted to this set of points to determine the presence of cantilevers. The RANSAC algorithm [42] has been used, as it performs well in very noisy environments. Through the years, this algorithm has been implemented in many point cloud-processing


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based on the distance to the considered location. If a cantilever is present in a selected set of points, far more points should be registered on it than on catenary wires. All points are then projected onto a horizontal plane; the elevation coordinate is taken out of the equation; and then, a line is fitted to this set of points to determine the presence of cantilevers. The RANSAC algorithm [42] has been used, as it performs well in very noisy environments. Through the years, this algorithm has been implemented in many point cloud-processing algorithms, including primitive shape detection [3] and roof detection [43]. RANSAC considers that the given data can be categorized into two sets, noise and model data. It then proceeds to fit the model to randomly-selected minimal sample data. The model that incorporates maximum data entities is chosen as the proper one. In the case of these calculations, cantilevers are the model (model distance r1 ), Remote Sens.points 2016, 8, 801 10 of 22 and all other are treated as noise. If a determined line is almost perpendicular to the trajectory, a support structure can be verified; If a determined line is almost perpendicular to the trajectory, a support structure can be verified; if not,if the location is treated as a false positive. In the case of positive authentication, all model points not, the location is treated as a false positive. In the case of positive authentication, all model points are classified as the catenary system. are classified as the catenary system.

(a)

(b)

Figure 10. Sample point clouds in the place of interest and near vicinity. Increase of density caused

Figure 10. Sample point clouds in the place of interest and near vicinity. Increase of density caused by by cantilever (a) and additional track (b). Search area limited by pink circle, catenary system in blue, cantilever (a) and additional track (b). Search area limited by pink circle, catenary system in blue, rails, rails, red, remaining points in white. red, remaining points in white.

All verified places of interest are passed on for further categorization and support structure positioning. All verified places of interest are passed on for further categorization and support

structure (ii) positioning. Vertical Mast and Horizontal Beam Criteria (ii) Vertical Mast and Horizontal Beam Criteria Detected support structures are divided into two categories, traction poles and portal structures. Detected supportincludes structures are divided where into two categories, traction poles portal structures. The first category all construction masts are located directly next and to the applicable The first category includes all construction where masts are located directly next to the applicable track, both single and multi-track solutions. The second includes all remaining portal structures. track, both single andismulti-track solutions. The second includes remaining portal structures. The division performed based on localizing a mast in close all proximity to the measured track. The division performed basedlimited on localizing a mast closethe proximity the±s measured Firstly, a set ofispoints is selected, horizontally to sin h along trajectorytoand z from thetrack. trajectory pointisvertically. area horizontally to the right and the leftthe sidetrajectory of the track Firstly, a set ofkey points selected,The limited to stoh along andis±checked sz from the separately. There are four possible outcomes of said procedure. trajectory key point vertically. The area to the right and to the left side of the track is checked separately. There1.areNumber four possible outcomes of said procedure. of points to the right exceeds set threshold and to the left does not. 1. 2. 3. 4.

2. Number of points to the left exceeds set threshold and to the right does not. Number of points to to the right setleft threshold and to the left does not. 3. Number of points the rightexceeds and to the exceed set threshold. Number of points to to the left exceeds to the right does not. 4. Number of points the right and toset thethreshold left do not and exceed set threshold.

Number of points to the right and to the left settothreshold. The two first cases suggest the possibility of aexceed mast next the rail track. The third shows objects Number of points the right andfourth to theimplies left doanot exceed set threshold. on both sides of the to track, and the portal structure. As there are a great deal of different objects that might identify the existence of a significant number of points in the aforementioned subset, each case needs to be verified. Case 1 and 2: A RANSAC algorithm is used to fit a line into a point selected by set horizontal and vertical limitations (model distance r2). If the fitted line is almost vertical, the intersection of it and the terrain is calculated as the position of the traction pole. If the fitted line is not vertical, the place of interest is moved and is to be verified by the process for Case Scenario 4. Case 3: To find a pole in this case, its separation from other objects is taken into consideration.


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The two first cases suggest the possibility of a mast next to the rail track. The third shows objects on both sides of the track, and the fourth implies a portal structure. As there are a great deal of different objects that might identify the existence of a significant number of points in the aforementioned subset, each case needs to be verified. Case 1 and 2: A RANSAC algorithm is used to fit a line into a point selected by set horizontal and vertical limitations (model distance r2 ). If the fitted line is almost vertical, the intersection of it and the terrain is calculated as the position of the traction pole. If the fitted line is not vertical, the place of interest is moved and is to be verified by the process for Case Scenario 4. Case 3: To find a pole in this case, its separation from other objects is taken into consideration. Thus, on both sides, the RANSAC algorithm is used twice: once with a threshold distance r2 and also with a threshold distance of 2r2 . Firstly, the vertical requirement is checked, and then, the number of model points between the 1st and 2nd set is compared. The pole is detected in the place where the difference between the number of set points in between iterations is smaller. The pole coordinates are calculated as in Cases 1 and 2. If none of the objects are established as vertical, the place of interest is moved and is then verified by the process for Case Scenario 4. Case 4: There are no vertical pole-like objects next to the track. Therefore, either the support structure was verified incorrectly or this is a multi-track solution (portal structure) where the cantilever is secured to the structural beam above it. Again, RANSAC (threshold distance r3 ) is used to fit the line to points above the catenary. If the line is perpendicular to the track and contains more points than the set threshold portal structure, it is verified, and its position trajectory key point is confirmed. In other cases, the point of interest is deleted from the checked set. In all of the above cases, upon support structure verification, all RANSAC model points are classified as a catenary system. The minimal point count thresholds are set manually, according to point density. 3.2.4. Data Classification Clarification As the process of classification has been simplified, not all points registered on the sought after infrastructure were found, and therefore, not all classified points were assigned correctly. The process of classification has been divided into two separate operations. The first considers detected support structures (i), the second catenary wires (ii). (i) Support Structures To refine the classification of support structures, a modification of the DBSCAN clustering algorithm was used. The DBSCAN algorithm, as published in [44], is used to perform data clustering of unorganized sets of data points. It can be applied to various sets of data, including point clouds [45]. It groups together points according to their neighborhood and distance. The algorithm proposes an iterative clustering method, which considers three types of points, core points, border points and outliers. Both core points and border points belong to the group. To assign unclassified points to the group, the point has to be within a set distance to one of the core points. It becomes a core point if there are more than a set number of group points in its neighborhood; otherwise, it becomes a border point. DBSCAN’s simple principles make it easy to adapt it to this study. The algorithm has been modified to not detect a group of points, but being provided a set of points, among which some have been assigned to a certain group, to detect points among unassigned, which belong to said group. It has then been applied to each detected support structure in two separate calculations. The first considers all points from the middle (dm) vertically-wise and up and the second from the middle vertically-wise and down to stop the classification process from spreading along low vegetation and ground points. Figure 11 presents detected support structures before and after the modified DBSCAN processing. Both distance and neighborhood thresholds have to be set according to the available data. DBSCAN parameters maximal distance (dd) and neighborhood count (nc) have to be set manually according to point density.


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(ii) Catenary Wires The goal of this step is to find points that do not belong to the catenary, but, due to simplified classification procedures, were included in this class. This includes greenery growing too close to the track, isolated noise points or other objects that might come into contact with the catenary. That also might include incorrectly excluded support structures. Boundaries determined during the initial density check procedure are considered (Section 3.2.2). In ideal circumstances, these boundaries would include only points registered on the catenary and, between the support structures, only the catenary cables. As the cables are being stretched, boundaries should linearly change between the consecutive sections. Remote Sens. 2016, 8, 801 12 of 22

(a)

(b)

Figure 11. Detected support structure before (a) and after (b) submission to modified DBSCAN

Figure 11. Detected support structure before (a) and after (b) submission to modified DBSCAN processing. Red, rails, catenary class, blue, unclassified points, white. processing. Red, rails, catenary class, blue, unclassified points, white. To detect places of interest, the following procedure is implemented. Firstly, the whole analyzed railway is divided into segments by all ofprocedure the detected structures. Then, the To detect line places of interest, the following issupport implemented. Firstly, theboundary whole analyzed diagonal is calculated for every section belonging to a considered segment. If, in between the railway line is divided into segments by all of the detected support structures. Then, the boundary consecutive sections, a discrepancy of the diagonal exceeds set threshold, c, then the region is diagonal is calculated for are every section belonging to can a considered segment. If, in between the evaluated again. There two case scenarios where this happen:

consecutive sections, a discrepancy of the diagonal exceeds set threshold, c, then the region is evaluated • an unidentified object too close to the catenary system, again. There are two case scenarios where this can happen: • catenary cables heading towards tension poles or other tracks.

• •

Determining each too caseclose is relatively easy. The cables heading towards tension poles or other an unidentified object to the catenary system, tracks cause only one significant discrepancy between consecutive sections. In other case scenarios, catenary cables heading towards tension poles or other tracks.

there have to be at least two significant discrepancies nearby. In the event of the first case scenario, cables departing from the main thread, said cables are located by the RANSAC algorithm (model Determining each case is relatively easy. The cables heading towards tension poles or other distance r4). As it might be a set of cables instead of one thread, the search is conducted in sets of tracks cause one onto significant discrepancy between consecutive other case scenarios, points only projected a horizontal plane. The RANSAC model pointssections. are againInclassified as the there have to be at least two significant discrepancies nearby. In the event of the first case catenary system. The second case scenario, for all of the sections where a significant discrepancyscenario, occurs, a new boundary is calculated. vertices are determined by the intersection of (model cables departing from the main thread,New saidboundary cables are located by the RANSAC algorithm lines to might nearby be boundary said section Allthe points excluded from the in sets distance r4 ).fitted As it a set ofvertices cablesand instead of oneplane. thread, search is conducted boundary in the newly-evaluated section are moved to an unassigned class. Additionally, the set of of points projected onto a horizontal plane. The RANSAC model points are again classified as the all corrected sections for the whole analyzed rail line is written to a separate file as objects that might catenary system. The second case scenario, for all of the sections where a significant discrepancy jeopardize rail safety.

occurs, a new boundary is calculated. New boundary vertices are determined by the intersection of 4. Datasets’ Description lines fitted to nearby boundary vertices and said section plane. All points excluded from the boundary in the newly-evaluated are moved to an unassigned Additionally, the project set of all corrected Data used in section this research have been obtained in the class. framework of a research (No. sections5.72.130.151) for the whole analyzed rail line is written to a separate file as objects that might jeopardize conducted by the AGH University for PKP Polskie Linie Kolejowe S.A. in Warsaw, Poland. Data were collected in 2011 and 2012 using RIEGL MMS VMX-250 and VMX-450 on a rail rail safety.

route between Cracow and Warsaw in Poland near the towns of Słomniki and Miechów. Both point clouds and trajectory coordinates were provided in the Polish National Coordinate System Poland 4. Datasets’ Description CS2000 zone 7, which is a grid reference system using ENH coordinates. Collected data were divided Data in thisaccording research have been obtained theof survey framework a research into used four datasets, to the MMS system used, thein date and theofdirection of the project survey (southbound/northbound) (Table University 1). Each set was into aLinie number of point clouds. (No. 5.72.130.151) conducted by the AGH for then PKPsplit Polskie Kolejowe S.A. in Warsaw,


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Poland. Data were collected in 2011 and 2012 using RIEGL MMS VMX-250 and VMX-450 on a rail route between Cracow and Warsaw in Poland near the towns of Słomniki and Miechów. Both point clouds and trajectory coordinates were provided in the Polish National Coordinate System Poland CS2000 zone 7, which is a grid reference system using ENH coordinates. Collected data were divided into four datasets, according to the MMS system used, the date of survey and the direction of the survey (southbound/northbound) (Table 1). Each set was then split into a number of point clouds. Remote Sens. 2016, 8, 801Table

Set I II III IV

MLS System

1. Datasets used in the algorithm verification process.

Table 1. Datasets used in the algorithm verification process.

Date of Measurement

Set System Date of Measurement RIEGLMLS VMX-250 September 2011 RIEGL VMX-250 December 2012 I RIEGL VMX-250 September 2011 RIEGL VMX-450 November 2012 II RIEGL VMX-250 December 2012 RIEGL VMX-450 November 2012 III RIEGL VMX-450 November 2012 IV RIEGL VMX-450 November 2012

No. of Points

Route Length (m)

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Direction

No. of Points Route Length31,711 (m) Directionnorthbound 780,468,277 609,748,916 northbound 780,468,277 31,711 20,065northbound 677,251,514 southbound 609,748,916 20,065 18,938northbound 666,585,270 18,739 northbound 677,251,514 18,938 southbound 666,585,270 18,739 northbound

The survey was conducted mostly on the same part of the rail route, though there are some survey conducted mostly of on every the same part ofmission. the rail route, though there are exceptions. The Figure 12 was presents the extent survey During surveys, thesome MMS were exceptions. Figure 12 presents the extent of every survey mission. During surveys, the MMS were stabilized on the rail platforms differently (Figure 13), and so, all set distances had to be established stabilized on the rail platforms differently (Figure 13), and so, all set distances had to be established individually. The test route length enabledthethe algorithm be verified in various individually. The test route lengthand andlocation location enabled algorithm to betoverified in various environments, the railway stations and areas between them, bends and straight sections. Within the environments, the railway stations and areas between them, bends and straight sections. Within the test route, numerous types of support structures were found. They vary in terms of the type of test route, numerous types of support structures were found. They vary in terms of the type of construction, material level degradation. construction, material and and the the level of of degradation.

Figure 12.12.Ranges test routes. Figure Ranges of of individual individual test routes.


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Figure 13. Models of mounting MMS on open rail cars used during surveys. Left RIEGL VMX-250 Figure 13. Models of mounting MMS on open rail cars used during surveys. Left RIEGL VMX-250 survey in 2011, center RIEGL VMX-250 survey in 2012, right VMX-450 survey in 2012. survey in 2011, center RIEGL VMX-250 survey in 2012, right VMX-450 survey in 2012.

5. Results and Discussion 5. Results and Discussion The assessment of the algorithm was conducted in three steps. Firstly, a threshold analysis was The assessment of the algorithm as was three steps.levels. Firstly, a threshold analysis was conducted to provide information toconducted how to setinup correct Then, a detection check conducted to provide information as to how to set up correct levels. Then, a detection check (verification (verification of the support structure positioning process) was carried out and, secondly, a of the support structure classification check. positioning process) was carried out and, secondly, a classification check.

5.1.5.1. Threshold Analysis Threshold Analysis The proposed Allofofthem themcan canbebedivided divided into The proposedmethod methodrelies relieson onaaset set of of adopted adopted thresholds. thresholds. All into three categories: three categories: calculation parameters(Section (Section5.1.1), 5.1.1), • • calculation parameters • thresholds dependent on the geometry of the sought after objects (Section 5.1.2), • thresholds dependent on the geometry of the sought after objects (Section 5.1.2), • thresholds dependent on the properties of MMS (Section 5.1.3). • thresholds dependent on the properties of MMS (Section 5.1.3). Out of the four datasets, four point clouds form Set II, with a cumulative length of the route of Out of the four point clouds form SettoII,setwith a cumulative of distances. the route of approximately 2700datasets, m, were four chosen as the training data all thresholds and length model all approximately m, were chosen the training set alltrack, thresholds and modeland all distances. Selected point2700 clouds include both as railway stationdata and to regular straight sections bends. There are 59 clouds supportinclude structures, singlestation solution and portaltrack, structures, registered the Selected point bothboth railway and regular straight sectionswithin and bends. chosen track. Therestructures, is also a tensioning section and and a turnout. There are 59 support both single solution portal structures, registered within the chosen track. There is also a tensioning section and a turnout. 5.1.1. Calculation Parameters 5.1.1. Calculation Parameters Calculation parameters include basic thresholds and parameters, that is section step (sst), section depth (sd) and parameter (Equation (11)).thresholds Section stepand andparameters, section depththat have have the same Calculation parametersm include basic is tosection step (sst), valuedepth to perform the calculation loss of(11)). data.Section step and section depth have to have the section (sd) and parameter without m (Equation To estimate thresholds’ optimalwithout values, loss a sensitivity same value to perform the calculation of data. analysis was conducted. A two-stage approach was implemented for this purpose [46]. Firstly, thresholds set intuitivelyA(Table 2). To estimate thresholds’ optimal values, a sensitivity analysis were was conducted. two-stage Then, calculations were conducted with one threshold set and the other changing. As both thresholds approach was implemented for this purpose [46]. Firstly, thresholds were set intuitively (Table 2). are used within the initial density analysis (Section 3.2.2), precision, recall and F1 score [47] were Then, calculations were conducted with one threshold set and the other changing. As both thresholds calculated for the case of the correct place of interest detection. The results for the analysis for the sst are used within the initial density analysis (Section 3.2.2), precision, recall and F1 score [47] were parameter are presented in Table 3 and Figure 14; the results for the analysis for the m parameter are calculated for the case of the correct place of interest detection. The results for the analysis for the sst presented in Table 4 and Figure 15. parameter are presented in Table 3 and Figure 14; the results for the analysis for the m parameter are Tables 3 and 4 and Figures 14 and 15 present the results of the calculations with the tested presented in Table 4 and Figure 15. parameter values. Tables and thresholds 4 and Figures 14 and resultsBecause of the of calculations with thecases’ tested Both 3tested concern place15ofpresent interest the detection. that, false positive parameter values. impact is far less important than false negatives. Later calculations, among other things, are designed Both tested thresholds concern place of interest detection. Because of that, false positive cases’ impact is far less important than false negatives. Later calculations, among other things, are designed

Remote Sens. 2016, 8, 801 Remote Sens. 2016, 8, x FOR PEER REVIEW

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designed to exclude incorrectly chosenofplaces of Bearing interest. that Bearing that less in mind, less falsecases positive to exclude incorrectly chosen places interest. in mind, false positive means cases less calculations andand lesscomputing time and computing power. lessmeans calculations and less time power. According to to thethe results of sensitivity analysis, the the section stepstep was was set to According results of sensitivity analysis, section set0.5 tom, 0.5and m, the andmthe parameter was set to two. m parameter was set to two. Table 2. Adopted parameter sstsst and mm values. Table 2. Adopted parameter and values.

Parameter Intuitive Value Parameter

sst

sst

m m

Intuitive Value

0.5 2

0.5 2

Tested Values

Tested Values

0.25, 0.50, 0.75, 1.00

0.25, 0.50, 0.75, 1.00

0.25, 0.5, 0.75, 1.75, 2.00, 2.25,2.50, 2.50,2.75, 2.75, 3.00 3.00 0.25, 0.5, 0.75, 1.00,1.00, 1.25,1.25, 1.50,1.50, 1.75, 2.00, 2.25,

Table 3. Detection of the places of interest results according to to various section step (sst) values. Table 3. Detection of the places of interest results according various section step (sst) values.

sst Parameter Detected Places TrueTrue False False sst Parameter Detected Places False False (m) (m) of Interest of Interest Positive Positive Negative Negative Positive Positive 0.25 0.25 60 60 59 59 00 11 0.50 0.50 59 59 59 59 00 0 0.75 0.75 49 49 49 49 1010 00 1.00 30 30 19 1.00 30 30 19 00

Precision Recall Recall F Precision F11 Score Score 0.98 0.98 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.83 0.83 0.61

0.99 0.99 1.00 1.00 0.91 0.91 0.76 0.76

0.61

Figure 14. Precision, recall and F1 score values according to different section step (sst) values. Figure 14. Precision, recall and F1 score values according to different section step (sst) values. Table 4. Detection of the places of interest results according to various m parameter values. Table 4. Detection of the places of interest results according to various m parameter values.

Detected Places True False False Precision Detected Places Positive True Negative False False of Interest Positive m Parameter Precision of Interest Positive Negative Positive 0.25 98 51 7 47 0.52 0.25 98 51 7 47 0.52 0.50 74 57 2 17 0.77 0.50 74 57 2 17 0.77 0.750.75 6565 5757 22 88 0.88 0.88 1.001.00 6464 5757 22 77 0.89 0.89 0.97 1.251.25 6161 5959 00 22 0.97 1.50 61 59 0 2 0.97 1.50 61 59 0 2 0.97 1.75 60 59 0 1 0.98 1.752.00 6059 5959 00 10 0.98 1.00 1.00 2.002.25 5959 5959 00 00 1.00 2.50 58 58 1 0 1.00 2.25 59 59 0 0 1.00 2.75 58 58 1 0 1.00 2.503.00 5857 5857 12 00 1.00 1.00 2.75 58 58 1 0 1.00 3.00 57 57 2 0 1.00

m Parameter

Recall

Recall

0.88

0.88 0.97 0.97 0.97 0.97 0.97 0.97 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.98 1.00 0.98 0.98 0.97

0.98 0.97

F1 Score

F1 Score

0.65

0.65 0.86 0.86 0.92 0.92 0.93 0.93 0.98 0.98 0.98 0.98 0.99 0.99 1.00 1.00 1.00 0.99 1.00 0.99 0.99 0.98

0.99 0.98


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Figure 15. 15. Precision, recall and and FF1 score values according to different m parameter values. Figure Precision, recall 1 score values according to different m parameter values.

5.1.2. Thresholds Dependent on the Geometry of the Sought after Objects 5.1.2. Thresholds Dependent on the Geometry of the Sought after Objects This category includes all of the set values and thresholds based on the properties of the This category includes all of the set values and thresholds based on the properties of the catenary catenary system. These thresholds are: system. These thresholds are:  bd, horizontal distance limiting the calculations of the algorithm, • bd, horizontaldistance distancelimits limiting theXcalculations of density the algorithm, d, horizontal along axis in initial analysis, • d, horizontal distance limits along X axis in initial density analysis, r1, RANSAC model distance in the cantilever detection process, • r12, RANSAC model distance in the cantilever detection process, vertical pole detection process, • r23 , RANSAC model distance in the vertical pole detection process, horizontal beam detection process, catenary wire classification clarification process, • r34, RANSAC model distance in the horizontal beam detection process, • sr4h, RANSAC sz, distances used to determine the case in vertical and horizontal beam search, model distance in the catenary wire classification clarification process, elevation level dividing the support structure into two cases for DBSCAN processing, • sdm, , s , distances used to determine the case in vertical and horizontal beam search, h z • c, threshold for diagonal discrepancy in between consecutive sections’ catenary wire dm, elevation level dividing the support structure into two cases for DBSCAN processing, boundaries. • c, threshold for diagonal discrepancy in between consecutive sections’ catenary wire boundaries. Railway embankments are highly regulated and standardized. Depending on the country or Railway embankments highly regulated andtrack standardized. Depending on the or region, the parameters of theare objects within the rail and their relative position arecountry arbitrarily region, thetoparameters of the objects within rail track and relative positionwill are never arbitrarily set. set. Due the constant monitoring, thosetheparameters andtheir relative positions change Due to the constant monitoring, those parameters and relative positions will never change significantly. significantly. The parameters listed above were set in the algorithm according to Polish railway The parameters listed above were setthe in the algorithm according to Polishvalues railwayare: guidelines or cases guidelines or cases observed within dataset. The adopted thresholds observed within the dataset. The adopted thresholds values are:  bd, 5 m, the railway clearance monitoring does not go beyond this limit, and one-line support • bd, 5 m, the railway clearance does notfrom go beyond this limit, and one-line support structure masts are situated notmonitoring further than 4.5 m the track center, structure are situated not further than 4.5 m from track center,  d, 1.5 m, masts set according to cantilever properties and thethe minimal distance from the rail axis to support • d, 1.5 m,structures, set according to cantilever properties and the minimal distance from the rail axis to  r1, 0.1 m,structures, the width of the cantilever does not exceed a couple of cm, support r12, 0.2 of the thickestdoes support structures does not exceed 0.4 m, • 0.1 m, the diagonal width of the cantilever not exceed a couple of cm, beam structures in portal structures does not 0.6 m, • rr23,, 0.4 0.2 m, m, the the diagonal diagonal of of the the horizontal thickest support does not exceed 0.4exceed m, • rr 4,, the model distance was set to 0.1 m to include cases of more and less tensioned wires, 3 0.4 m, the diagonal of the horizontal beam in portal structures does not exceed 0.6 m, 1.5 model m (3 sst), the value to possible the cantilever and section • rp4h,, the distance wasadopted set to 0.1according m to include cases ofdeflection more and of less tensioned wires, step value, • ph , 1.5 m (3 sst), the value adopted according to possible deflection of the cantilever and section  pz, 0.25 m from the trajectory, elevation below the catenary wires, but off the ground enough as step value, not to include low vegetation, • pz , 0.25 m from the trajectory, elevation below the catenary wires, but off the ground enough as  dm, hl-0.5 m, elevation below the catenary wires, clearly dividing detected support structure not to include low vegetation, into two point sets, • dm, hl -0.5 m, elevation below the catenary wires, clearly dividing detected support structure into  c, 0.4 sst m, value adopted according to the section step and the angle of possible outgoing two point sets, cables. • c, 0.4 sst m, value adopted according to the section step and the angle of possible outgoing cables. 5.1.3. Thresholds Dependent on the Properties of MMS There are two groups of thresholds dependent on the properties of MMS. The first group includes thresholds hl, hh, the trajectory to the catenary wires’ distances. To set the distance between


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5.1.3. Thresholds Dependent on the Properties of MMS There are two groups of thresholds dependent on the properties of MMS. The first group includes thresholds hl , hh , the trajectory to the catenary wires’ distances. To set the distance between MMS trajectory and catenary wires, two sample point cloud sections were chosen, one on a bend and one on a straight route, in all datasets. Adopted height differences according to the set are presented in Table 5. Table 5. Adopted height difference between the trajectory and catenary wires’ lower boundary (hl ) and upper boundary (hh ). Set

hl

hh

I II III IV

1.85 m 1.90 m 1.60 m 1.60 m

4.85 m 4.90 m 4.60 m 4.60 m

The second group includes DBSCAN set distance and neighborhood count (dd, nc). In this algorithm, for all sets, threshold dd was set to 0.1 m and nc to 20. The values were derived from the observation of a couple of randomly-chosen support structures. This value is the worst case scenario, but incorporates cases of both lattice and solid poles. The determination of these thresholds could be automated using the measurement of point density on the ground. 5.2. Support Structures Detection Check All existing support structures were divided into three categories with regards to their detection: true positive, false positive and false negative. To qualify a support structure as detected, its location on the ground and type (single solution or multi-track solution) had to be written to the appropriate set. All entries in said sets were compared to manually-collected ground truth sets. Table 6 lists all results according to the dataset. Table 7 presents performance measures, precision, recall and F1 score [47], which were calculated separately for each dataset. Table 6. Detection and positioning of support structure results. Support structures single solution, SS; multi-track solution, MTS. Existing Set I II III IV

True Positive Detection

False Negative Detection

False Positive Detection

SS

MTS

SS

MTS

SS

MTS

SS

MTS

575 357 356 348

24 11 7 8

546 352 351 346

24 11 7 8

29 5 5 2

0 0 0 0

1 0 0 0

2 0 0 0

Table 7. Precision, recall and F1 score according to dataset. Set

Precision

Recall

F1 Score

I II III IV

0.9948 1.0000 1.0000 1.0000

0.9516 0.9864 0.9862 0.9944

0.9727 0.9932 0.9931 0.9972

All of the calculated performance measures are very high. The algorithm has proven to be both efficient and precise. It was able to detect over 97% of existing support structures, and false positives make up less than 0.2% of all detected objects. There are a few factors contributing to the false negative detection cases. Mostly, the blame can be attributed to random sampling in the RANSAC algorithm. No matter how low the probability, it is


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still possible that during the sampling process, no points registered at a cantilever were taken into consideration. The probability of this further increases in places with double cables, as in tensioning sections. This can be eliminated if instead of random samples, all possible combinations are used in the sample stage of RANSAC, but the computational time required and the rather small amount of omitted support structures deem it, in the author’s opinion, as excessive. The other reason for false negative detection was also the extreme degradation of some support structures. For example, there was one case where another support structure was already placed next to a damaged pole (within 0.5 m); but both were registered, and as a consequence, neither was detected. All in all, every single undetected support structure was registered in a subset of objects lying too close to the track and, in the end, could be classified manually. False positive detection was caused either by greenery growing too close to the track and, thus, causing false verification and detection or by the existence of additional cables. Only three cases of false positive detection were recorded. 5.3. Classification Check The second step of the algorithm assessment included classification evaluation. Each detected support structure was checked for the completeness of classification and for the possible false classification of objects nearby. One thousand five hundred eight one out of 1645 detected poles and portal structures (96.11%) were classified correctly and completely (Figure 16a). The confusion matrix for the classification process (object level) is shown in Table 8. Table 8. Confusion matrix for the complete classification of detected support structures.

Catenary Class Other Class

Catenary Class

Other Class

1581 8

56 no data

Incorrect classification cases can be divided into one of three categories. Category I includes support structures with additional wire-stretchers at the end of the overhead contact line tensioning section (Figure 16b), 34 cases. Due to atypical support structure construction, DBSCAN processing might be done on an incomplete dataset. This consequently caused partial classification of masts. Category II incorporates all support structures whose cantilevers were constructed with thin steel cables, and due to their size, not many points were registered on its surface, 22 cases. Poor sampling resulted in the incorrect omission of said points by modified DBSCAN (Figure 16c). Category III considers all support structures that were classified together with adjoining greenery, eight cases (Figure 16d). Trees or shrubs growing too close to detected poles caused modified DBSCAN to falsely assign their points to the catenary class. All cases according to the datasets are presented in Table 9. Table 9. Incompletely- or incorrectly-classified support structures according to type of error.

Set

Correct

Incorrect

I II III IV sum

552 350 336 343 1581

18 13 22 11 64

Classification Category I (%) Category II (%) 16.67 23.08 100.00 54.55 53.12

55.56 61.54 0.00 36.36 34.38

Category III (%) 27.78 15.38 0.00 9.09 12.50

Remote Sens. 2016, 8, 801 Remote Sens. 2016, Remote Sens. 2016,8,8,801 801

(a) (a)

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1922of 22 19 of

(b) (b)

(c)

(c)

(d)

(d)

Figure 16.Detected Detectedand andclassified classified support support structures: (a), support structure with Figure 16. structures:correct correctclassification classification (a); support structure with Figure 16. Detected and classified support correct with classification (a),constructed support structure with additional wire stretchers (b) (Category I),structures: support structure cantilevers with thin additional wire stretchers (b) (Category I); support structure with cantilevers constructed with thin additional wire stretchers (b) (Category I), support structure with cantilevers constructed with steel cables (c) (Category II), support structure with incorrectly-classified greenery (d) (Category III).thin steel cables (c) (Category II); support structure with incorrectly-classified greenery (d) (Category III). steel cables (c) (Category structure with incorrectly-classified greenery (d) (Category III). Blue, catenary class, red, II), railsupport class, orange, ground class, white, remaining points. Blue, catenary class, red, rail class, orange, ground class, white, remaining points.

Blue, catenary class, red, rail class, orange, ground class, white, remaining points.

All of the immediate contact wires were classified correctly; any problems that arose were due All of the correctly; any problems that arose were due to the immediate immediate contactwires wires were classified correctly; any problems that arose were to additional wiring on contact turnouts or bywere the classified ends of the tensioning sections. Figure 17 presents adue additional wiring on turnouts or byor the ends the tensioning sections.sections. Figure 17Figure presents classifieda toclassified additional wiring on turnouts the ofends of the tensioning 17 apresents point cloud in the vicinity ofby turnouts. point cloud in the vicinity ofvicinity turnouts. classified point cloud in the of turnouts.

Figure 17. Part of the route including turnouts. Detected overhead contact system points in blue, rails in red, remaining points in white.

Figure 17. turnouts. Detected overhead contact system points in blue, rails Figure 17. Part Partofofthe theroute routeincluding including turnouts. Detected overhead contact system points in blue, In conclusion, the algorithm performed really well on all provided datasets. It did not fail to in red, points in white. rails in remaining red, remaining points in white.

detect and correctly classify catenary systems regardless of the environment, complexity and degradation. Simple and obvious assumptions, that led to the of thedatasets. algorithm,It are same In conclusion, the algorithm performed really well on creation all provided didthe not fail to conclusion, the algorithm performed really on Contrary all provided datasets. It did not fail to detect forIn almost overhead contact catenary systems around thewell world. to previously-published research detect and all correctly classify systems regardless of the environment, complexity and and correctly classify catenary systems on regardless of the environment, complexity and degradation. on the topic, all of the points registered the catenary system were classified into one class. It is not degradation. Simple and obvious assumptions, that led to the creation of the algorithm, are the same Simple and obvious assumptions, that to thebut creation of the algorithm, are the same for almost all automatic creation of 3Dled models, it is more than enough for the purpose of railway forenough almostfor allthe overhead contact systems around the world. Contrary to previously-published research overhead contact systems around the world. Contrary to previously-published research on the topic, gauge clearance monitoring. Furthermore, including this algorithm as a preparation step in on the topic, all of the points registered on the catenary system were classified into one class.more It is not allcomplex of the points registered on the catenary system were classified into one class. It is not enough for could creation significantly reduce their calculations. enough forsolutions the automatic of 3D models, but it is more than enough for the purpose of railway the automatic creation of 3D models, but it is more than enough for the purpose of railway gauge gauge clearance monitoring. Furthermore, including this algorithm as a preparation step in more clearance monitoring. Furthermore, including this algorithm as a preparation step in more complex complex solutions could significantly reduce their calculations. solutions could significantly reduce their calculations.


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6. Conclusions The test route included railway bridges, railway stations, turnouts, crossings, straight sections and bends. The created method utilized specific object properties and simple geometrical observations. Its simplicity and limited use to obvious and common properties made it possible to detect support structures regardless of the type of construction or degradation. Out of the total 1686 existing support structures, only 41 were not detected, which gives a success rate of over 97%. Additionally, only three non-existent support structures (false positives) were detected. In conclusion, the algorithm proved to be both reliable and efficient. The simplicity of the algorithm might enable it to work with any available MMS point cloud, but this hypothesis requires verification. There are a couple of drawbacks to this method that will be improved in future research. There are a few thresholds set manually, some of which relate to point cloud local density. They could easily be replaced with statistically-computed values according to local ground point density. Those that cannot be replaced are the geometrical distances and properties of specific objects. These need to be specified by the end user. Another problem is massive data management. The extremely large amounts of data provided by MMS need to be stored in such a way as to facilitate quick navigation and processing. This could be achieved with the available GIS tools. These tools are required in order to modify the algorithm into software. With further research, the authors are also planning to extend the algorithm to include neighboring tracks. It would require implementing rail detection, then railroad centerline determination and, finally, the incorporation of the rail axis instead of the trajectory in calculations. Acknowledgments: This research was conducted using funds from Research Grant No. 15.11.150.404. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5.

6. 7. 8. 9. 10. 11.

12.

Mongus, D.; Žalik, B. Parameter-free ground filtering of LiDAR data for automatic DTM generation. ISPRS J. Photogramm. Remote Sens. 2012, 67, 1–12. [CrossRef] Meng, X.; Wang, L.; Silván-Cárdenas, J.L.; Currit, N. A multi-directional ground filtering algorithm for airborne LiDAR. ISPRS J. Photogramm. Remote Sens. 2009, 64, 117–124. [CrossRef] Schnabel, R.; Wahl, R.; Klein, R. Efficient RANSAC for point-cloud shape detection. Comput. Graph. Forum 2007, 26, 214–226. [CrossRef] Borrmann, D.; Elseberg, J.; Lingemann, K.; Nüchter, A. The 3D Hough Transform for plane detection in point clouds: A review and a new accumulator design. 3D Res. 2011, 2, 1330–1334. [CrossRef] Rodríguez-Cuenca, B.; García-Cortés, S.; Ordóñez, C.; Alonso, M.C. Automatic detection and classification of pole-like objects in urban point cloud data using an anomaly detection algorithm. Remote Sens. 2015, 7, 12680–12703. [CrossRef] Zhu, L.; Hyyppa, J. The use of airborne and mobile laser scanning for modeling railway environments in 3D. Remote Sens. 2014, 6, 3075–3100. [CrossRef] Novak, K. Integration of a GPS-receiver and a stereo-vision system in a vehicle. Close-Range Photogramm. Meet. Mach. Vis. 1990, 1395, 16–23. Guan, H.; Li, J.; Yu, Y.; Chapman, M.; Wang, H.; Wang, C.; Zhai, R. Iterative tensor voting for pavement crack extraction using mobile laser scanning data. IEEE Trans. Geosci. Remote Sens. 2015, 53, 1527–1537. [CrossRef] Zhou, L.; Vosselman, G. Mapping curbstones in airborne and mobile laser scanning data. Int. J. Appl. Earth Obs. Geoinf. 2012, 18, 293–304. [CrossRef] Golparvar-Fard, M.; Balali, V.; de la Garza, J.M. Segmentation and recognition of highway assets using image-based 3D point clouds and semantic Texton forests. J. Comput. Civ. Eng. 2012, 29. [CrossRef] Manandahar, D.; Shibasaki, R. Auto-extraction of urban features from vehicle-borne laser data. In Proceedings of the Commission IV Symposium, Geospatial Theory, Processing and Applications, Ottawa, ON, Canada, 9–12 July 2002. McElhinney, C.P.; Kumar, P.; Cahalane, C.; McCarthy, T. Initial results from European Road Safety Inspection (EURSI) mobile mapping project. In Proceedings of the ISPRS Commission V Technical Symposium, Newcastle, UK, 21–24 June 2010.


13. 14. 15.

16. 17. 18. 19. 20.

21. 22. 23. 24. 25. 26. 27. 28. 29.

30. 31. 32. 33.

34. 35.

21 of 22

Pu, S.; Rutzinger, M.; Vosselman, G.; Elberink, S.O. Recognizing basic structures from mobile laser scanning data for road inventory studies. ISPRS J. Photogramm. Remote Sens. 2011, 66, S28–S39. [CrossRef] Jaakkola, A.; Hyyppä, J.; Hyyppä, H.; Kukko, A. Retrieval Algorithms for road surface modelling using laser-based mobile mapping. Sensors 2008, 8, 5238–5249. [CrossRef] Balali, V.; Golparvar-Fard, M. Recognition and localization of traffic signs via 3D image-based point cloud models. In Proceedings of the ASCE International Workshop on Computing in Civil Engineering, Austin, TX, USA, 21–23 June 2015. Timofte, R.; Zimmermann, K.; Van Gool, L. Multi-view traffic sign detection, recognition, and 3D localisation. Mach. Vis. Appl. 2014, 25, 633–647. [CrossRef] Gikas, V. Three-dimensional laser scanning for geometry documentation and construction management of highway tunnels during excavation. Sensors 2012, 12, 11249–11270. [CrossRef] [PubMed] Oskouie, P.; Becerik-Gerber, B.; Soibelman, L. Automated measurement of highway retaining wall displacements using terrestrial laser scanners. Autom. Constr. 2016, 65, 86–101. [CrossRef] Villarino, A.; Riveiro, B.; Martínez-Sánchez, J.; Gonzalez-Aguilera, D. Successful applications of geotechnologies for the evaluation of road infrastructures. Remote Sens. 2014, 6, 7800–7818. [CrossRef] Markovic-Chenais, S. Trends in Rail Transport. In Proceedings of the Economic Commission for Europe, Inland Transport Committee, Working Party on Transport Trends and Economics, Geneva, Switzerland, 10–12 September 2013. European Commission on Mobility and Transport. EU Transport in Figures—Statistical Pocketbook 2014; Publications Office of the European Union: Luxembourg City, Luxembourg, 2014. Glaus, R. The Swiss Trolley—A Modular System for Track Surveying. Ph.D. Thesis, ETH Zurich – Swiss Federal Institue of Technology, Zürich, Switzerland, 2006. Mikrut, S.; Kohut, P.; Pyka, K.; Tokarczyk, R.; Barszcz, T.; Uhl, T. Mobile laser scanning systems for measuring the clearance gauge of railways: State of play, testing and outlook. Sensors 2016, 16. [CrossRef] [PubMed] Gikas, V.; Daskalakis, S. Determining rail track axis geometry using satellite and terrestrial geodetic data. Surv. Rev. 2008, 40, 392–405. [CrossRef] Gikas, V. Geodetic survey and track recording vehicle data combined for the accurate setting out of rails on slab track. J. Spat. Sci. 2005, 5, 13–23. [CrossRef] Wei, H.; Zhu, H.; Wang, Z.; Wu, W. Center line coordinates survey for existing railway by 3-D constraints method. Telkomnika 2013, 11, 2816–2821. [CrossRef] Yang, B.; Fang, L.; Li, J. Semi-automated extraction and delineation of 3D roads of street scene from mobile laser scanning point clouds. ISPRS J. Photogramm. Remote Sens. 2013, 79, 80–93. [CrossRef] Yu, C.; Zhang, D. Road curbs detection based on laser radar. In Proceedings of the IEEE 8th International Conference on Signal Processing, Beijing, China, 16–20 November 2006. Hernandez, J.; Marcotegui, B. Filtering of artifacts and pavement segmentation from mobile lidar data. In The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences; ISPRS: Vienna, Austria, 2009; Volume XXXVIII, Part 3/W8, pp. 329–333. Brenner, C. Extraction of features from mobile laser scanning data for future driver assistance systems. In Proceedings of the 12th Agile Conference, Hannover, Germany, 2–5 June 2009. Lehtomäki, M.; Jaakkola, A.; Hyyppä, J.; Kukko, A.; Kaartinen, H. Detection of vertical pole-like objects in a road environment using vehicle-based laser scanning data. Remote Sens. 2010, 2, 641–664. [CrossRef] Pastucha, E.; Słota, M. Automatic extraction of traction poles using mobile laser scanning data. Arch. Photogramm. Cartogr. Remote Sens. 2012, 24, 267–278. Golovinskiy, A.; Kim, V.G.; Funkhouser, T. Shape-based recognition of 3D point clouds in urban environments. In Proceedings of the 12th International Conference on Computer Vision (ICCV09), Kyoto, Japan, 27 September–4 October 2009. Arastounia, M. Automatic Classification of LiDAR Point Clouds in a Railway Environment. Master’s Thesis, University of Twente, Enschede, The Netherlands, 2012. Beger, R.; Gedrange, C.; Hecht, R.; Neubert, M. Data fusion of extremely high resolution aerial imagery and LiDAR data for automated railroad centre line reconstruction. ISPRS J. Photogramm. Remote Sens. 2011, 66, S40–S51. [CrossRef]


36.

37. 38. 39. 40. 41. 42. 43.

44. 45. 46. 47.

22 of 22

Neubert, M.; Hecht, R.; Gedrange, C.; Trommler, M.; Herold, H.; Krüger, T. Extraction of railroad objects from very high resolution helicopterborne LiDAR and ortho-image data. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 2008, 38, 25–30. Yang, B.; Fang, L. Automated extraction of 3-D railway tracks from mobile laser scanning point clouds. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2014, 7, 4750–4761. [CrossRef] Elberink, S.O.; Khoshelham, K. Automatic extraction of railroad centerlines from mobile laser scanning data. Remote Sens. 2015, 7, 5565–5583. [CrossRef] Arastounia, M. Automated recognition of railroad infrastructure in rural areas from LiDAR Data. Remote Sens. 2015, 7, 14916–14938. [CrossRef] Jwa, Y.; Sohn, G.; Kim, H.B. Automatic 3D power line reconstruction using airborne LiDAR data. Int. Arch. Photogramm. Remote Sens. 2009, 38, 105–110. Jwa, Y.; Sohn, G. A multi-level span analysis for improving 3D power-line reconstruction performance using airborne laser scanning data. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 2010, 38, 97–102. Fischler, M.A.; Bolles, R.C. Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 1981, 24, 381–395. [CrossRef] Tarsha-Kurdi, F.; Landes, T.; Grussenmeyer, P. Hough-transform and extended ransac algorithms for automatic detection of 3D building roof planes from LiDAR data. In Proceedings of the ISPRS Workshop on Laser Scanning 2007 and SilviLaser 2007, Espoo, Finland, 12–14 September 2007. Ester, M.; Kriegel, H.P.; Xu, X. A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise; AAAI Press: Menlo Park, CA, USA, 1996. Gong, J.; Caldas, C.H. Data processing for real-time construction site spatial modeling. Autom. Constr. 2008, 17, 526–535. [CrossRef] Mongus, D.; Zalik, B. An efficient approach to 3D single tree-crown delineation in LiDAR data. ISPRS J. Photogramm. Remote Sens. 2015, 108, 219–233. [CrossRef] Powers, D.M.W. Evaluation: From precision, recall and F-measure to ROC, informedness, markedness and correlation. J. Mach. Learn. Technol. 2011, 2, 37–63. © 2016 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).