ISPRS Journal of Photogrammetry and Remote Sensing 74 (2012) 90–100

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ISPRS Journal of Photogrammetry and Remote Sensing

journal homepage: www.elsevier .com/ locate/ isprs jprs

Automated planimetric quality control in high accuracy airborne laserscanning surveys

George VosselmanUniversity of Twente, Faculty ITC, The Netherlands

a r t i c l e i n f o a b s t r a c t

Article history:Received 21 May 2012Received in revised form 11 September2012Accepted 13 September 2012Available online 17 October 2012

Keywords:Laser scanningMappingQuality analysisPoint cloudFeature extraction

0924-2716/$ - see front matter � 2012 Internationalhttp://dx.doi.org/10.1016/j.isprsjprs.2012.09.002

E-mail address: vosselman@itc.nl

With the increasing point densities of airborne laser scanning surveys, the applications of the generatedpoint clouds have evolved from the production of digital terrain models to 3D modelling of a wide varietyof objects. Likewise in quality control procedures criteria for height accuracy are extended with measuresto describe the planimetric accuracy. This paper introduces a measure for the potential accuracy of out-lining objects in a point cloud. It describes how this accuracy can be verified with the use of ridge lines ofgable roofs in strip overlaps. Because of the high accuracy of modern laser scanning surveys, the influenceof roof tiles onto the estimation of ridge lines is explicitly modelled. New selection criteria are introducedthat allow an automated, reliable and accurate extraction of ridge lines from point clouds. The applica-bility of the procedure is demonstrated in a pilot project in an area covering 100,000 ha with around20 billion points.� 2012 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS) Published by Elsevier

B.V. All rights reserved.

1. Introduction

In the last two decades airborne laser scanning has beenadopted as the preferred technology for the acquisition of digitalterrain models (Briese, 2010). Driven by application demands inthe field of water or forestry management larger regional or evennational laser scanning surveys have been conducted. As the heightof the terrain or vegetation was seen as the most important infor-mation to be gathered, quality control procedures of these surveystypically had a strong, if not exclusive, focus on the evaluation ofheight accuracy (Crombaghs et al., 2000, 2002; Ahokas et al., 2003).

In the meantime the pulse frequencies of laser scanners contin-ued to increase and nowadays reach up to 500 kHz. With this tech-nology point clouds with 10–20 points/m2 can be easily acquiredfrom low speed aircrafts. The acquisition of such high density pointclouds over large areas has therefore become feasible. The highpoint densities enable the use of point clouds for a much widerrange of applications including building detection, outlining and3D modelling (Verma et al., 2006; Sampath and Shan, 2007; Haalaand Kada, 2010; Oude Elberink and Vosselman, 2011), 3D model-ling of road networks (Hatger and Brenner, 2003; Clode et al.,2007; Oude Elberink and Vosselman, 2009a; Zhou and Vosselman,2012), power line mapping (Jwa and Sohn, 2010) and monitoring ofindividual trees (Reitberger et al., 2009; Yu et al., 2011).

Society for Photogrammetry and R

In the Netherlands the regional water authorities (Wikipedia,2012) have been using this kind of high density laser scanning incorridor surveys for the management of water barriers and water-ways next to lower density nationwide surveys for the determina-tion of optimal ground water levels. Recognising the potential ofmapping in high point density point clouds, in 2007 the regionalwater authorities, together with the (then) Ministry of Transport,Public Works and Water Management, decided to start a nation-wide laser scanning survey with a point density of 8–10 points/m2. The final flights have been conducted spring 2012. The com-plete dataset will consist of some 400–500 billion points.

For this project an extensive quality control procedure has beendefined. As the point cloud should be suitable for 3D mapping theplanimetric accuracy has to be considered, next to the height accu-racy. A methodology has therefore been developed to assess thepotential planimetric accuracy of mapping objects in a point cloud.This paper reports on the developed methodology for planimetricquality control and demonstrates the applicability to a largedataset.

In the next section the related literature is discussed. The largerpart of this literature is about strip adjustment, where offsets be-tween corresponding features in overlapping strips are used toestimate strip deformations or sensor calibration errors. Section 3defines the requirement a point cloud should fulfil in order to en-able mapping with a given maximum planimetric error. Calibrationprocedures typically make use of (locally) planar surfaces. Whilecorresponding planar surfaces can be used to estimate 3D offsets

emote Sensing, Inc. (ISPRS) Published by Elsevier B.V. All rights reserved.

G. Vosselman / ISPRS Journal of Photogrammetry and Remote Sensing 74 (2012) 90–100 91

between strips, it cannot be distinguished to what extent theremaining errors are caused by errors in height or errors in planim-etry. Hence, one cannot estimate the noise in the planimetry. Todefine the planimetric mapping accuracy requirement we there-fore make use of corresponding horizontal roof ridge lines in over-lapping strips. The use of ridge lines for the estimation of stripoffsets and sensor positioning noise is making use of earlier workreported in (Vosselman, 2002; 2008). This is extended in this paperto take into account the influence of roof tiles onto the accuracy ofridge line estimations. Without doing so offsets between ridgelines would incorrectly completely be attributed to sensor posi-tioning noise, and thus to the planimetric point cloud accuracy.In case of roof faces with a limited number of points or with a smallslope, the influence of the roof tile structure onto the ridge line off-sets estimation may become very significant, in particular for highaccuracy surveys. In Section 4 we describe the procedure to extractthe ridge lines from the point cloud. Because of the project size,this procedure has to be largely automated. At the same time esti-mated ridge lines should be precise and reliable such that errorswill not lead to overestimated standard deviations. In quality con-trol procedures such overestimations would cause incorrect rejec-tions of delivered point clouds. Therefore several new criteria aredefined to ensure that selected ridge line pairs have been accu-rately extracted. Errors in the extraction process should be keptclearly smaller than the expected sensor positioning noise. In Sec-tion 5 the developed methodology is applied to a 20 billion pointdataset that was acquired in 2007 in a pilot project to study thefeasibility of the now acquired high point density nationwide pointcloud. Results are analysed w.r.t. different strategies for ridge lineselection and planimetric and height accuracy.

2. Related literature

In the ideal case one would like to have many ground controlpoints that can be accurately identified in the point cloud. Csanyiand Toth (2007) designed lidar specific ground targets. The circularplates were slightly elevated above the ground to allow straightfor-ward identification. With a Hough transform-like approach theplate centre is estimated from the points on the plate. The platecentres could be identified with an accuracy of 10% of the pointspacing if the plate contains 16 points. Instead of selecting pointsbased on elevation, Anderson et al. (2010) investigated the use oflidar-activated phosphors and infrared retro-reflectors such thatpoints on the target can be selected based on their reflectancestrength. Experiments at different altitudes demonstrated thatthe targets could be very clearly distinguished from their back-ground. To remove the need for lidar specific targets, Toth et al.(2008) introduced the use of road pavement markings for groundcontrol. By estimating curves through points on markings thatwere selected based on reflectance strength, the markings couldbe measured with an accuracy of a few cm.

Ground control points are required for checking the absoluteaccuracy. Like in photogrammetric aerial triangulation the amountof ground control points has to be minimised to reduce costs. Inmost laser scanning surveys the discrepancies between corre-sponding locations in overlapping strips play an important rolein the quality control, similar to the use of tie points in photogram-metry. Among others Latypov (2002) uses the height differences instrip overlaps to assess the relative height accuracy. He notes thatthe need for absolute accuracy checks will be strongly reduced if agood relative accuracy between strips can be confirmed. This holdslikewise for height and planimetric accuracy control.

In literature planimetric errors in airborne laser scanning datahave been primarily discussed in the context of strip adjustmentprocedures. Strip adjustment aims to estimate and remove system-atic differences between overlapping strips of laser data. Initially

strip adjustment has been defined as a method to estimate trans-formations between strip coordinate systems that minimise thediscrepancies (Burman, 2000; Crombaghs et al., 2000; Kager,2004). Later, Friess (2006) as well as Skaloud and Lichti (2006) de-fined strip adjustment as a sensor calibration problem that mini-mises discrepancies by estimating corrections to calibrationparameters such as bore-sight angles and range offsets. In bothcases planar features have been used as the basis for the formula-tion of the observation equations (Kager, 2004; Friess, 2006; Ska-loud and Lichti, 2006; van der Sande et al., 2010). Whereas Kager(2004) and Friess (2006) first estimate plane parameters that arethen kept fixed in the strip adjustment, Skaloud and Lichti (2006)simultaneously estimate plane and calibration parameters.

The extraction of corresponding planar surfaces for the purposeof strip adjustment is further discussed in (Pfeifer et al., 2005).They use a clustering in a space of feature vectors including the lo-cally estimated normal surface vector. A region growing method isused to determine the extent of planar segments. This is requiredbecause co-planar segments will be mapped to the same locationin the feature space. To select corresponding segments in overlap-ping strips the points of the point in a segment of one strip shouldbe surrounding by points in the corresponding segment from theother strip. Furthermore the height difference between the twosegments should be within a pre-set range. For the height adjust-ment in (Pfeifer et al., 2005) only near vertical segments with alimited number of points were used. In his selection of correspond-ing surfaces Kager (2004), aiming at a 3D strip adjustment,demanded a minimum slope of the selected segments and set fur-ther fixed thresholds on the deviations of points from the plane,the number of outliers (caused by chimneys and dormers), andthe number of points in a segment.

In addition to planar features, Habib et al. (2008, 2010) and Ker-sting et al. (2008) also use linear features (ridge lines) in their stripadjustment. Corresponding linear features are selected based ondistance between the lines, direction difference and overlap. Theuser of the strip adjustment method has to interactively confirmthe correctness of the selected feature pairs.

3. Requirements to planimetric mapping accuracy

Technical specifications used in tendering and quality controlprocedures of laser scanning surveys often explicitly specify theminimum point density and point accuracy to be obtained. Pointaccuracy is usually split into a systematic error and a standarddeviation of the points that may remain after the processing, e.g.a strip adjustment, by the data provider. The potential accuracyof outlining objects in a point cloud is determined by the pointdensity and point accuracy together. Instead of specifying accep-tance conditions for the various components of the planimetricmapping accuracy, the tender document for the Dutch national la-ser scanning survey only specified a requirement on the maximumerror that may occur when outlining objects (with edges of at least2 m in size) in a point cloud. In this project this maximum errorwas set to 0.50 m. It was left up to the surveying companies howto balance between point density and point accuracy. With a high-er accuracy of the sensor positioning a company could lower thepoint density and still meet the planimetric mapping accuracyrequirement. A lower point density would reduce the number offlight lines, an important factor in the survey costs.

In this section we work out the definition of this requirementand the way in which the requirement is verified. Section 3.1 re-views the components of the planimetric mapping accuracy anddefines the requirement to be used in overlaps between strips. InSection 3.2 it is explained how ridge lines in strip overlaps are usedfor the accuracy verification. The influence of roof tiles onto theaccuracy of ridge line locations is discussed in Section 3.3.

92 G. Vosselman / ISPRS Journal of Photogrammetry and Remote Sensing 74 (2012) 90–100

3.1. Definition of the potential planimetric mapping accuracy

The potential planimetric mapping accuracy is defined here bythree components. These are related to the uncertainty of objectoutlining in an error-free point cloud, strip offsets and the standarddeviation of remaining errors.

When outlining objects in a point cloud the accuracy of thereconstructed edges strongly depends on the type of edge (OudeElberink and Vosselman, 2011). Edges that can be defined by theintersection of two planar surfaces can be very accurate as allpoints on those surfaces contribute to the estimation of the edgelocation. Most inaccurate are height jump edges. In the worst casethe height jump edge is parallel to the scan lines of the laser scan-ner. The uncertainty in outlining is then proportional to the spac-ing between the scan lines. Assuming a homogeneous pointdistribution of p points/m2, the point spacing will be 1ffiffi

pp . In an er-

ror-free point cloud the maximum error Dpd in the outlining ofthe object related to the point density (pd) will then be half thepoint spacing.

Dpd ¼1

2ffiffiffipp ð1Þ

This is obvious if the vertical face is visible from the scanner’sperspective. In that case a line in the middle between the scan lineon the low surface and the scan line on the high surface will not befurther away than half the scan line spacing (=point spacing in caseof a homogeneous distribution) in the XY-plane. In cases where thevertical face cannot be seen from the scanner’s perspective, thehigher surface will occlude a part of the lower surface. In that casethe outline of the higher object can be obtained by constructing apolygon through the outer points of the higher surface and thendilating that polygon by half the point spacing. Assuming homoge-neous point spacing, the maximum error will again be at most halfthe point spacing.

In general the assumption of the homogeneous point spacing isvalid for scanners with polygon mirrors which were mostly used.However, in two cases it does not hold. When flying under windyconditions with a helicopter strong variations in the platform’spitch angle may occur. This leads to variations in the scan linespacing. Furthermore deviations from the average point spacingoccur on surfaces that are seen from the laser scanner’s perspectiveunder a small incidence angle. Sloped roof faces near the strip bor-der with normal vectors pointing away from the flight line there-fore often have lower point densities. No corrections for theexpected outlining accuracies have been made for these cases.

Terms describing the planimetric accuracy of the point cloudare added to the maximum outlining error in the error-free pointcloud to obtain the potential planimetric mapping accuracy. Errorsin the point cloud can be caused by many different calibration er-rors as well as noise in the sensor measurements (Skaloud andLichti, 2006; Friess, 2006). For the quality control procedure, thesources of the errors in the point cloud do not need to be identified.It only needs to be checked whether the point cloud fulfils thespecified requirements. The effects of noise and calibration errorsonto the point cloud are therefore quantified by strip offsets inX- and Y-direction and a standard deviation of all planimetric dis-tortions of the point cloud. These distortions could either be causedby noise in the sensor positioning or by the effects of sensor cali-bration errors that are not captured in the constant strip offsets.

Formally this leads to the following expression for the assumedmaximum error Emax

i that may be made when outlining objects inthe point cloud of strip i.

Emaxi ¼ Dpd þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDX2

i þ DY2i

qþ 3rXYi

ð2Þ

The first term describes the maximum outlining error in an er-ror-free point cloud as defined above. The second term is thelength of the planimetric offset vector of a strip i derived fromthe strip offsets in X- and Y-direction, DXi and DYi. The third termcontains the standard deviation of the planimetric distortions instrip i, rXYi

, multiplied by three to obtain a large confidence inter-val. It is assumed that the larger part of the local distortions of thepoint cloud is due to the noise in the platform positioning. As thedistortions may to some extent also be caused by remaining sensorcalibration errors that cannot be modelled by a strip offset, the dis-tortions may also show some systematic behaviour. Their distribu-tion may therefore deviate from a normal distribution. Still,assuming that random noise will contribute the largest compo-nent, a three sigma value is used to set the confidence interval. Itshould be emphasised that the expression in Eq. (2) is for the worstcase scenario. Strips with an acceptable maximum error will on theaverage have a much higher accuracy in the outlining of objects.

Whether a dataset fulfils the formulated requirement on the po-tential planimetric mapping accuracy can only be verified in thepresence of many ground control points. To limit the need forground control points, the relative accuracy will be verified inoverlaps between strips. Hence, the acceptance criterion shoulddepend on the discrepancies between the strips. We therefore needto relate the permissible offsets between strips and the standarddeviation of the discrepancies to the error definition for a singlestrip (Eq. (2)). An offset (DXij,DYij) between two strips i and j isthe difference of the offsets of the two single strips w.r.t. the refer-ence coordinate system. For the acceptance test it needs to be as-sumed that the two overlapping strips contribute in equal partsto the discrepancies in the overlap. In reality this will in generalnot be the case (one strip will be more displaced than the otherand two strips may also be displaced in the same direction), butas the differences only cannot provide any evidence for anotherdistribution of the errors, the equal distribution, which will resultin the most tolerant acceptance test, needs to be assumed.

Hence, the offset of a strip w.r.t. the reference coordinate sys-tem is estimated as half the offset between two overlapping strips.ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDX2

i þ DY2i

q¼ 1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDX2

ij þ DY2ij

qð3Þ

Likewise, the standard deviation of the planimetric strip distor-tions is obtained from the standard deviation of the planimetricdiscrepancies in the strip overlap rXYij

.

rXYi¼ 1

2

ffiffiffi2p

rXYijð4Þ

Substituting Eqs. (3) and (4) into Eq. (2), this leads the followingtest statistic for checking the planimetric accuracies in stripoverlaps.

Emaxi ¼ Dpd þ

12

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDX2

ij þ DY2ij

qþ 3

2

ffiffiffi2p

rXYij ð5Þ

3.2. Using ridge lines

To estimate the offsets and noise in the planimetry use is madeof corresponding horizontal ridge lines in strip overlaps. Ridgelines can be reconstructed very accurately by fitting planes to thepoints on the two adjacent roof faces and intersecting these planes(Oude Elberink and Vosselman, 2011). Locally, i.e. on a roof plane,the points are strongly correlated as the used sensor platform ori-entations will be based on only a few GPS/IMU observations.Hence, platform positioning noise will lead to a locally systematictransformation of the point cloud. The offsets between the ridgelines can be used to estimate the standard deviations of the plani-metric distortions. To be able to distinguish between height and

G. Vosselman / ISPRS Journal of Photogrammetry and Remote Sensing 74 (2012) 90–100 93

planimetric accuracy it is required that the plane intersection linesare horizontal. This would not be possible with the use of slopedintersection lines or sloped planes.

The X- and Y-components of the offset between two strips(DXij, DYij) are estimated following (Vosselman, 2008). Let ðXk

i ; Yki Þ

be the midpoint of ridge line k in strip i and let

X cos akj þ Y sinak

j � dkj ¼ 0 ð6Þ

describe the corresponding ridge line k in strip j. The distance be-tween the midpoint k in strip i and the corresponding ridge linein strip j is then given by

Xki cos ak

j þ Yki sinak

j � dkj ð7Þ

After applying an offset (DXij, DYij) to the points in strip i thedistance between the shifted midpoint and the correspondingridge line becomes

ekij ¼ ðX

ki þ DXijÞ cos ak

j þ ðYki þ DYijÞ sin ak

j � dkj ð8Þ

The offsets (DXij, DYij) are estimated by minimising the squaresum of the remaining distances ek

ij. The standard deviation of thedistances between the ridge lines is then estimated as

reij ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPk ek

ij

� �2

K � 2

vuutð9Þ

with K as the number of used ridge lines. This standard deviation iscaused by noise in the platform positioning and the non-constantdeformations between the strips.

3.3. Influence of roof tiles

In the quality control procedure in the Netherlands the abovestandard deviation of the distances between ridge lines is assumedto be equivalent to the standard deviation of the planimetric dis-tortions, i.e. rXYij

¼ reij. This is correct if the deviations of the indi-

vidual points from the fitted roof planes have no significantinfluence on the estimation of the ridge lines. These deviationsfrom a perfect plane are caused by noise (primarily ranging noise)

Fig. 1. The influence of roof tiles rtiles in m on the estimation of a single ridge line as funangles. The horizontal dashed line is used for the ridge line selection discussed in Sectio

as well as by the structure of roof tiles. When the gable roofs se-lected for the quality control have a large number of points on bothroof faces and a good intersection angle, as is recommended prac-tice, the influence of the point noise and roof tiles can be ignored.

These conditions, however, reduce the number of suitable ridgelines and thereby reduce the number of strip overlaps in which suf-ficient ridge lines are available to verify the planimetric accuracy.In this section we therefore further analyse the influence of rooftiles onto the accuracy of the ridge line estimation. After this anal-ysis we can better select suitable roof tiles as well as correct thestandard deviation of the distances between ridge lines for the con-tribution by the roof tiles. Let the influence of roof tiles on the esti-mation of a single ridge line k in the overlap between strips i and jbe denoted by rk

tilesij. Hence, the influence of roof tiles onto the var-

iance of the distance between two lines extracted for ridge k is2rk

tilesij

2. Then the variance of the planimetric distortions in the strip

overlap can be obtained by subtracting the average variance of theroof tile influence from the variance of the distances between the Kcorresponding ridge lines, i.e.

r2tilesij¼ 1

K

XK

k¼12rk

tilesij

2 ð10Þ

r2XYij¼ r2

eij� r2

tilesijð11Þ

A first indication that roof tiles may influence the accuracy ofplane fitting is obtained from the residuals. From the dataset de-scribed in Section 5.1 several subsets were selected with pointson sloped roofs and on horizontal pavement (roads, parking lots).The standard deviation of the residuals after plane fitting on thepavement point sets was consistently 1.0 cm. This corresponds tothe ranging accuracy of most airborne laser scanners. For the se-lected sloped roofs the standard deviations varied between 2.5and 3.0 cm.

To analyse the influence of the roof tiles onto the estimation of aridge line, 10 large gable roofs were selected with five differentintersection angles of the roof faces (20�, 30�, 45�, 70� and 90�).For each of the intersection angles the noise caused by the roof tilesis determined as a function of the number of points N per roof face.The derived functions shown in Fig. 1 are based on fitting the

ction of the number of points N per roof face for five different roof face intersectionn 4.2.

Fig. 2. Segmentation of two roof planes without (a) and with (b) reconsideration ofassignments of points to surfaces.

94 G. Vosselman / ISPRS Journal of Photogrammetry and Remote Sensing 74 (2012) 90–100

function affiffiffiffiNpþ b to standard deviations obtained for different val-

ues of N at intervals of 10 points per roof face. For each roof and foreach value of N 100 subsets were created by randomly subsam-pling the complete point sets. Ridge lines were estimated for eachsubset and the standard deviation of the perpendicular (signed)distances between the ridge lines and the midpoint of the firstridge line was calculated. This standard deviation is used to de-scribe the variation in the ridge line location due to the roof tilestructure. Note that this variation only depends on the numberof points on a roof face and not on the size of the roof face. WhenN points are equally distributed over a large roof face, the planeorientation estimate is more accurate than for N points on a smallroof face. In the ridge line estimation this effect is, however, exactlyoffset by the fact that for a large roof face the point of gravity of theN points is further away from the ridge line than for a small roofface.

Given a set of gable roofs in an overlap, the roof face intersec-tion angles and the number of points on the roof faces are usedto look up the roof tile influence per ridge line from Fig. 1 by inter-polation. Eqs. (10) and (11) are then used to correct the variance inthe ridge line offsets for the roof tile influence.

4. Extraction of suitable ridge lines

To evaluate the potential planimetric mapping accuracy in na-tional or regional projects with the method described above thou-sands of ridge lines need to be extracted. Interactive selection ofsuitable gable roofs would still be feasible, but automation is pre-ferred to reduce the costs. A procedure to automatically extractridge lines from the point clouds should, however, be very reliableand result in precisely estimated ridge lines. Small errors in theridge line extraction may already lead to an overestimation ofthe standard deviation of the planimetric errors and may conse-quently lead to incorrect rejection of delivered data. In this sectionwe describe a procedure that aims to keep the errors in the ridgeline extraction significantly smaller than the expected platformpositioning noise and that minimises the need for user interaction.In Section 4.1 we describe the procedure to extract ridge lines froma point cloud. Section 4.2 then details the post-processing and cri-teria used to select the accurately defined ridge lines that can beused for the quality assessment. Incorrectly accepted ridge linesare interactively eliminated following the procedure explained inSection 4.3.

4.1. Ridge line extraction

After determining which strips overlap each other, the area ofeach overlap is split into parts such that the point data in a partcan be dealt with in computer memory. Each part of a strip overlapis processed independently at the expense that occasionally a ridgeline across borders of strip parts may be missed or be extractedtwice. In every part of a strip overlap the two point clouds originat-ing from the two strips are segmented separately. For this segmen-tation into planar sets of points we use the surface growingalgorithm as previously applied in various other studies (OudeElberink and Vosselman, 2009b; Pu and Vosselman, 2009; Rutzin-ger et al., 2011).

The algorithm starts by randomly selecting a point that is notyet assigned to a planar segment. Next, a 3D Hough transform isapplied to the 20 nearest points to determine whether the localneighbourhood of the selected point contains a plane. If this isthe case, a least squares estimate of the plane parameters is ob-tained and further neighbouring points are added to this seed sur-face if they are within some perpendicular distance to the plane.The plane parameters are updated every time the number of points

in the surface has grown by 10%. Points are only considered neigh-bouring if they belong to the 20 nearest neighbours of a point thatis already assigned to the planar surface and if the distance to sucha point is less than three times the point spacing. The latter condi-tion is used to minimise the risk that planar segments on roof facesare extended to points in nearby vegetation. For the allowed per-pendicular distance to a plane a threshold of 10 cm was used to en-sure that slightly curved surfaces break up into smaller planarsegments. If the neighbourhood of the initially selected point doesnot contain a seed surface or when the segment cannot be grownany further, a next unassigned point is selected at random.

Points that are located near intersection lines of adjacentplanes, e.g. ridge lines, can be within the threshold distance to bothplanes. When the first surface is grown points that are closer to thesecond surface will have been assigned to the first surface. To avoidbiases in the plane estimation caused by these points, their assign-ment to the first surface is reconsidered when growing the secondsurface. For this the points in the neighbourhood of the point to bereconsidered are selected. A point of the first surface is assigned tothe second surface if the root mean square sum of the distances ofthe neighbouring points to the second plane is smaller than that tothe first plane. The resulting improvement in the assignment isdemonstrated in Fig. 2.

After the segmentation intersection lines of adjacent sloped sur-faces are calculated. Points within a distance from the intersectionline of three times the point spacing are used to determine the endpoints of the ridge line. For both surfaces the projections of thesenearby points onto the intersection line define an interval on theintersection line with support for a ridge line hypothesis. Whenthe intervals corresponding to the two surfaces overlap for at least2 m, the ridge line is kept for a further analysis of its suitability forthe planimetric accuracy assessment.

4.2. Selection of suitable ridge lines

A first requirement to be checked is the successful detection ofthe same ridge line in the two strips. Ridge lines extracted from thetwo strips are considered to be measurements the same ridge if thedistance between the lines is less than 1 m and if both roof faces ofone strip have corresponding roof faces in the other strip such thatthe surface normal directions do not differ by more than 5�.

With the first condition it is assumed that the maximum plani-metric error between ridge lines will be less than 1 m as we wouldotherwise miss a correct measurement. It also assumes that therewill be no buildings with two accurately defined ridge lines withina 1 m distance. A suitable value for this distance threshold dependson the point precision and density. For the dataset used in theexperiments the threshold did not lead to confusion. All ridge off-sets were clearly smaller than 1 m and no buildings were detectedwith two ridge lines within 1 m.

The condition on the differences in surface normal directions isneeded to detect cases as in Fig. 3 where the roof of a larger dormerintersects the roof plane near the ridge. In one strip one may havedetected this intersection line whereas the ridge line may havebeen extracted in the overlapping strip. Without checking the

Fig. 3. The intersection line between a dormer and a roof plane in one strip (lightpoints) may be close to the ridge line detected in the overlapping strip (dark points).

G. Vosselman / ISPRS Journal of Photogrammetry and Remote Sensing 74 (2012) 90–100 95

surface normal directions the two lines may be considered corre-sponding if they are within a 1 m distance.

To distinguish between planimetric and height accuracy theridge lines should be horizontal. By requiring a maximum ridgeline slope (e.g. 5�), sloped ridge lines as found on hip roofs areeliminated.

The above conditions are used to identify correctly correspond-ing horizontal ridge lines. Further processing steps and conditionsare used to ensure that the estimated ridge lines have little biasand a small standard deviation.

Biases in the estimation of ridge lines can, e.g., be caused bynon-planarity of the extracted roof faces as in the example ofFig. 4. The right side of the roof consists of two faces under a slightangle. The segmentation in one strip (dark points) correctly identi-fied these two faces and only used the upper planar face for the cal-culation of the ridge line. In the other strip (light points) the bentwas not noticed and the points of the two faces were grouped intoone segment. Consequently, the plane and ridge line estimation inthis strip will be slightly biased. As such a bias in the estimation ofthe ridge line does not necessarily have an impact on the planimet-ric accuracy assessment. A biased estimation may be allowed if it isassured that the bias is approximately the same in both strips andtherefore eliminated in the measurement of the distance betweenthe two extracted ridge lines. To avoid different biases in case ofnon-planar segments it is important that the points used for theplane estimation cover the same area. We therefore only use apoint for the plane estimation if the corresponding segment inthe overlapping strip contains a nearby point (e.g. within threetimes the point spacing). In the case of Fig. 4 this effectively elim-inates the points on the right most face that was not included inthe segment in the other strip. The ridge lines determined in bothstrips are then based on data obtained over the same area and thedifference between the estimated ridge lines will no longer bebiased by non-planar surfaces.

A further concern is that roof tiles could lead to an underestima-tion of the data accuracy. Knowing the roof plane intersection an-gle and the number of points on the roof faces, the uncertaintycaused by the roof tiles can be obtained from the functions inFig. 1 for every extracted ridge line. Although a correction cannow be made for the roof tile influence, it is still advisable to onlyuse ridge lines that can be estimated well. If one would use ridgelines derived from gable roofs with small slopes and just a few

Fig. 4. Different segmentations in the two strips may lead to differences in theestimated ridge line locations. Here the data of one strip (light points) is under-segmented because of an undetected surface bent on the right side of the ridge.

dozen points, the uncertainty caused by the roof tiles would belarger than the typical platform positioning noise of some 3 cm.In that case r2

tilesij> r2

XYij. It would then become questionable

whether the correction of the variance of the distances betweenridge lines r2

eijfor the large influence by roof tiles would still lead

to an accurate estimation of r2XYij

. To avoid such extreme correc-tions, ridge lines are only used in the accuracy analysis if r2

tiles con-tributed less than 25% to the overall ridge line variation r2

eij. With

an assumed sensor positioning noise rXYijof 3 cm, this leads to a

maximum of 1.24 cm for the allowed influence of the roof tiles.Based on this criterion (horizontal dashed line in Fig. 1), one canderive the minimum number of points on the roof faces for the var-ious roof face intersection angles. This minimum number of pointsper roof face is used as a further criterion to select the ridge linesfor the accuracy analysis. Fig. 1 shows that gable roofs with a 90�plane intersection angle can already be used with 40 points perroof face, whereas roofs with a 20� intersection angle require atleast 290 points per roof face to obtain an acceptable roof tile influ-ence. As the analysis of the roof tile influence used a minimumintersection angle of 20�, roof faces intersecting under an evensmaller angle were not used.

4.3. Outlier analysis

After the above selection of suitable ridge lines the strip offsetand standard deviations are computed as described in Section 3.2.Despite the strict criteria defined above, occasionally incorrectlyestimated ridge lines are selected that may have an influence onthe accuracy estimation. To eliminate those ridge lines the lineswith the largest residuals in the offset estimation are inspectedby an operator together with the local point cloud in a 3D viewer.An operator can typically decide within a few seconds whether theridge line estimation may be biased. Thus even checking a fewhundred ridge lines does not take much time. After removing theoutliers, the strip offsets and standard deviations are recomputed.

5. Results and analysis

The described methods have been applied to the first part of thenational high point density survey in the Netherlands. This datasetis described in Section 5.1. In Section 5.2 we analyse the procedureto extract the highly accurate ridge lines. Various aspects of theplanimetric quality analysis are described and discussed in Sec-tion 5.3. The extracted ridge lines can, of course, also be used toanalyse the height accuracy. This is described in Section 5.4.

5.1. Data set

The dataset used in the experiments was acquired by Fugro Aer-ial Mapping in 2007. The survey covered the area of the regionalwater authority Zeeuwse Eilanden consisting of the (partly former)islands of Walcheren, Noord- and Zuid-Beveland, Tholen, andSchouwen-Duiveland in the province of Zeeland located in thesouth-west of the Netherlands (Fig. 5). The 100,000 ha of this areawere surveyed at a height of 375–400 m in 589 strips with a widthof 430–460 m and a 100 m strip overlap. Flights were planned witha 10 points/m2 point density. Because of the strip overlaps, a num-ber of additional strips to cover small gaps and multiple echoes invegetation the total dataset contained 20 billion points, corre-sponding to an average point density of 20 points/m2.

5.2. Extracted ridge lines

The 589 strips resulted in 1664 strip overlaps. Many of thosestrip overlaps were very small as a result of cross strips along the

Fig. 5. Data coloured by strip number over the area of the regional water authority Zeeuwse Eilanden (left) in the south-west of the Netherlands (right). (For interpretation ofthe references to colour in this figure legend, the reader is referred to the web version of this article.)

96 G. Vosselman / ISPRS Journal of Photogrammetry and Remote Sensing 74 (2012) 90–100

coast line and interrupted flight lines with overlapping heads andtails. The 1289 strip overlaps equal or larger than 10 ha have beenanalysed. With a 100 m strip overlap this corresponds to 1 km inlength.

The methods described in Section 4 were used to extract theridge lines in the overlaps. The criterion was used that the influ-ence of the roof tiles should be less than 25% of the expected plat-form positioning noise of 3 cm. This leads to a required minimumnumber of points on the roof faces that varies with the roof faceintersection angle (cf. the intersections with the horizontal dashedline in Fig. 1). Next to this criterion (termed flexible in Table 1 andlater figures), ridge lines were also selected based on fixed valuesfor the minimum number of points and minimum roof plane inter-section angle. The numbers of extracted ridge lines in the overlapsare shown in Table 1. It is obvious from the table that the flexibilityto use both well intersecting roof planes with a low number ofpoints as well as roof planes with many points but a unfavourableintersection angle leads to a very large increase in the number ofridge lines that can be used for the planimetric accuracy analysis.

The statistics in Fig. 6 show that this selection strategy alsoleads to a larger number of strip overlaps with at least 10 extractedridge lines required for the accuracy analysis. With an interval of20 ha the figure shows the percentage of overlaps with 10 or moreridge lines for the four ridge line selection strategies as a functionof the strip overlap size. Even with the best selection strategy aminimum of 10 ridge lines could only be extracted in 403 (31%)out of the 1289 strip overlaps larger than 10 ha. This low numberis, however, caused by the very large number of relatively smallstrip overlaps that are created by cross strips and re-flown stripparts. For normal strip overlaps the results are much better. Thesestrip overlaps are typically longer than 10 km. With a strip overlapof 100 m, this results in an overlap size of 100 ha. Of all strip over-laps larger than 100 ha 79% contains at least 10 ridge lines when

Table 1Number of extracted ridge lines as a function of required number of points and roofface intersection angle.

Minimum number ofpoints per roof face

Minimum roof faceintersection angle

Number of extractedridge lines

Flexible Flexible 28,69350 70� 11,618100 45� 11,325150 30� 8779

extracted with the flexible criteria. For the fixed minimum valuesthis is between 50% and 54%. Although the planimetric accuracycannot be analysed in all strip overlaps, the large number of over-laps that can be checked will give a good impression on the overallrelative planimetric quality of the dataset.

Strip offsets and sensor positioning noise have been estimatedin all strip overlaps with at least 10 accurately extracted ridgelines. The point clouds around all extracted lines with a residuallarger than 25 cm were inspected in a point cloud viewer. Only fiveof these 86 potential outliers did not correspond to correctly esti-mated ridge lines. In four cases dike profiles were mistaken as ga-ble roofs. In one case the frame of a roof window was extracted inone strip whereas the nearby and parallel plane of surroundingroof tiles was taken from the other strip. These five extracted lineswere removed as observations for the strip offset and sensor posi-tioning noise estimation, although the ridges of the dikes wouldprobably not have led to significant errors in this estimation. Themanual inspection of the outliers did not take more than a fewminutes.

5.3. Planimetric accuracy analysis

For the Dutch laser scanning survey the defined error Emaxi

should not exceed 0.50 m. At first sight this may seem rather toler-ant. Yet, taking into account that the last component of the errordefinition contains a three sigma confidence interval, there is notmuch room for large errors. For example, if a strip offset of15 cm occurred in a survey with 10 points/m2, the maximum al-lowed standard deviation of the platform positioning is only0.06 m. This 0.06 cm should not just account for positioning noise,but also for non-constant strip deformations caused by e.g. IMU-drift.

Fig. 7 shows the frequencies of the estimated strip offsets andsensor positioning uncertainty. Strip offsets are 16 cm on the aver-age with a close to uniform distribution between 0 and 30 cm.After correction for these offsets, a standard deviation is derivedfrom the remaining residuals. Corrected for the influence of rooftiles, sensor positioning noise is estimated in every strip overlap.The results in the right graph of Fig. 7 show that the large majorityof the estimates are below 5 cm. The average standard deviation is3.0 cm. Without a correction for the roof tile influence this wouldonly be a little higher (3.1 cm).

The estimated offsets and standard deviations are used to com-pute the maximum error Emax

i that may occur when mapping in the

Fig. 6. Percentage of strip overlap with at least 10 ridge lines for the four ridge line selection criteria as a function of the strip overlap size. The numbers between brackets arethe numbers of strip overlaps within each 20 ha class interval.

Fig. 7. Frequencies of estimated offsets between overlapping stripsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDX2

ij þ DY2ij

q(left) and the estimated sensor positioning uncertainty in a strip rXYi

(right) in the 403evaluated overlaps.

Fig. 8. Frequencies of the estimated potential mapping accuracy Emaxi with and without correction for the roof tile influence in the 403 evaluated strip overlaps.

G. Vosselman / ISPRS Journal of Photogrammetry and Remote Sensing 74 (2012) 90–100 97

point cloud of a strip (cf. Eq. (5)). In open areas the point densitywithin a strip is 10 points/m2. Dpd therefore amounts to 0.16 m(cf. Eq. (1)). The results are presented in Figs. 8 and 9. 393 out ofthe 403 checked overlaps pass the test on the theoretical maxi-mum planimetric mapping error (Emax

i 6 0:50 m, green in Fig. 9).In five overlaps the error is a higher than allowed but still below0.60 m (yellow in Fig. 9). In five further overlaps the error is evenhigher, with a maximum value of 0.92 m (red in Fig. 9). According

to the survey company, these errors were caused by a malfunction-ing IMU. Obviously, there’s a correlation between the evaluationsof neighbouring overlaps that have one strip in common. If the sys-tem performance is flawed in one strip, this will affect the analysisin the overlaps with the strips to the left and right.

The colour coded overlaps in Fig. 9 vary in width. The thin over-laps are the regular overlaps of about 100 m in width. The thickoverlaps appear in areas where strips have been re-flown to ensure

Fig. 9. Planimetric quality control in overlaps by checking the error Emaxi (Eq. (5)). Green: Emax

i 6 0:50 m, yellow: 0:50 m < Emaxi 6 0:60 m, red Emax

i > 0:60 m, grey: insufficientridge lines to compute check the planimetric quality.

Fig. 10. Frequencies of the estimated height offsets between strips and the height standard deviation in the 403 evaluated strip overlaps.

98 G. Vosselman / ISPRS Journal of Photogrammetry and Remote Sensing 74 (2012) 90–100

complete coverage. Fig. 9 confirms the conclusion drawn fromFig. 6 that sufficient ridge lines can be extracted in the large major-ity of the normal (i.e. longer) overlaps.

The effect of the correction for the roof tile influence on the esti-mated maximum planimetric mapping error can be analysed fromFig. 8. Without a correction the standard deviation computed fromthe distances between the ridge lines is taken as the estimate forthe standard deviation of the planimetric distortions. With a cor-rection this standard deviation is reduced by estimated roof tileinfluences according to Eqs. (10) and (11). Fig. 8 shows that the dis-tribution of the estimated maximum error slightly shifts to lowervalues in case of a correction for the roof tile influence. It did, forthis particular block, however, not lead to a different outcome ofan acceptance test (Emax

i 6 0:50 m).

5.4. Height accuracy analysis

The horizontal ridge lines have been extracted for the purposeof analysing the planimetric accuracy of a point cloud. They can,

of course, also be used to analyse the height accuracy, althoughone may typically prefer to use horizontal surface patches in stripoverlaps for this purpose. The horizontal accuracy was analysedhere as a kind of side product making use of the extracted ridgelines.

Fig. 10 shows the height offsets between strips as well as theheight standard deviations estimated from the height differencesbetween corresponding ridge lines after removing the height offsetbetween two strips. The product specifications allow a maximumsystematic height error of 0.05 m and a maximum height standarddeviation of 0.05 cm. This is achieved in 397 out of the 403 evalu-ated strip overlaps. Only in one strip overlap the height offsets (of0.11 m) between the strips is larger than twice the maximum sys-tematic height error. In six overlaps the estimated height standarddeviations is higher than 0.05 m. The rejected strip overlaps areclearly related to those rejected in the analysis of the planimetricaccuracy. Four out of the six overlaps included a strip of the over-laps with a poor planimetric accuracy. One further overlapincluded a strip that was captured around the same time as a strip

G. Vosselman / ISPRS Journal of Photogrammetry and Remote Sensing 74 (2012) 90–100 99

with poor planimetric accuracy and thus is also likely to have beenaffected by the malfunctioning IMU.

6. Discussion

This paper presented a method to check the planimetric qualityof accurate airborne laser scanning surveys which makes use ofridge lines in strip overlaps. This procedure has been successfullyused for the nationwide survey of the Netherlands. Within thisproject ridge line extraction and computation of the test statisticshas been done by the companies conducting the laser scanningsurveys. After delivery of the point clouds and the test statistics,the latter were checked by an independent party in a few randomlyselected strip overlaps.

The method in use has been extended in this paper with ananalysis of the influence of roof tiles on the ridge line accuracy. Itwas shown that the number of overlaps that can be checked canbe considerably increased when steep gable roofs with a few pointsand close to flat gable roofs with many points can also be used forridge line extraction.

The survey over the area of the regional water authority Zee-uwse Eilanden contained a large number of relatively short flightlines because of the shapes of the islands and many re-flown stripparts. In other regions one may therefore expect longer flight lines.This will increase the number of overlaps in which the planimetricquality can be verified.

A clear requirement for the applicability of the developed pro-cedure is the availability of gable roof buildings. For the Nether-lands, the pilot area of the Zeeuwse Eilanden was a kind of worstcase scenario. With 138 inhabitants per km2 the province of Zee-land is one of the least densely populated areas in the Netherlands.In other parts of the Netherlands one will therefore typically findmore buildings and less strip overlaps that cannot be checked.Compared to most other countries, the Netherlands is, however,densely populated. For areas in other countries, the lower avail-ability of building roofs will therefore likely restrict the usage ofthe proposed quality analysis procedure to the relatively denselypopulated areas.

As mentioned earlier, the analyses in the strip overlaps only as-sess the relative planimetric accuracy. Although good results inthese analyses may give confidence that the data is of good quality,the procedure cannot completely eliminate the need for an abso-lute planimetric accuracy assessment. Ground control points thatcan be measured accurately in the point clouds will still be neededfor this part of the quality assessment.

In recent years significant progress has been achieved in obtain-ing high point density point clouds by dense image matching (Hir-schmüller, 2008; Furukawa and Ponce, 2010). This triggers thedebate whether point clouds generated from imagery are thecheaper alternative to point clouds obtained by laser scanning (Le-berl et al., 2010; Haala, 2011). While dense matching is success-fully used for the generation of 3D city landscapes andorthophoto production (Irschara et al., 2012), the ability of laserscanning to measure points on the ground in forested areas maybe hard to improve. For nationwide surveys primarily aiming athigh quality digital terrain models in all types of terrain laser scan-ning has proven its value. The improved quality control procedureas described in this article has been successfully used to keep pacewith the increasing accuracy and point density delivered by laserscanners.

Acknowledgement

The author would like to thank the AHN Steering Committee formaking available the data of the regional water authority ZeeuwseEilanden.

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