TOWARDS AUTOMATED LIDAR BORESIGHT SELF-CALIBRATION

TOWARDS AUTOMATED LIDAR BORESIGHT SELF-CALIBRATION J. Skaloud a, *, P. Schaer a a TOPO Lab, Ecole Polytechnique Fédérale de Lauanne (EPFL), Station 18, 1015 Lauanne, Switzerland KEY WORDS: airborne laer canning, LiDAR, boreight, calibration, claification, roof detection ABSTRACT: Thi paper focue on practical apect when performing boreight calibration in airborne laer canning uing rigorou methodology implemented in LIBOR oftware. LIBOR technique, introduced by (Skaloud and Lichti, 2006), i baed on expreing the boreight calibration parameter within the direct-georeferencing equation eparately for each target point and conditioning a group of point to lie on a common planar urface. Although there i no need for a priori information about the plane parameter a thee are part of the unknown, good etimation require implication of variou planar feature that differ in lope and orientation. Such condition are typically fulfilled in reidential-urban area where the preence of plane in form of roof-top i abundant. Thee are identified by grouping point belonging to the ame urface into a ditinct cla eparately for each flight line and finding clacorrepondence among the flight line. We preent an automated approach for thi election proce that tem from intrinic geometry of curved urface. Thi claification i followed by additional fine-filtering for return from feature a chimney, antenna etc. The preented dicuion focue on practical example with data from continuouly-rotating and ocillating-mirror ytem. Thee finding how that good automated point election i poible and act a a pre-requiite to robut etimate of all boreight angle with accuracy that i everal time uperior to the ytem noie level. 1. INTRODUCTION In contrary to relatively well developed approache to boreight etimation between an Inertial Meaurement Unit (IMU) and frame/line-baed imagery (Cramer and Stallmann, 2002; Kruck, 2001; Skaloud and Schaer, 2003) the exiting procedure for the LiDAR-IMU mialignment, while functional, are recognized a being uboptimal and much reearch i devoted to their improvement. The adopted approache are uually baed either on phyical boundarie or cro-ection (Schenk, 2001), DTM gradient (Burman, 2000) or mimic the photogrammetric calibration approach via ignalized or intenity-deduced target point (Morin, 2002). The drawback of thee method i the lack (or implification) of aurance meaure, correlation with the unknown terrain hape or limit impoed by laer pointing accuracy and uncertainty due to beam-width. Not long ago, a more rigorou cla of calibration procedure tarted to emerge (Filin, 2003; Frie, 2006; Skaloud and Lichti, 2006). Thee type of approache model all ytematic error directly in the meaurement domain and condition group of point to reide on a common urface of known form. Thi alleviate the problem of LiDAR beam-pointing uncertainty experienced in photogrammetry-like approache while preerving the correct formulation of the obervation equation for each point eparately. It wa alo demontrated that etimating the calibration parameter together with thoe of urface doe not compromie the etimate of the boreight (Skaloud and Lichti, 2006) and the elf-calibrating cheme i indeed poible. We will exploit thi approach further with the aim of achieving it complete automation when electing and claifying the needed planar feature. The organization of the paper i a follow. After recalling the functional model for the recovery of calibration parameter we propoe an algorithm for automated detection and extraction of the planar ection of the rooftop. After that we preent a ynthei of our practical experience when applying thi approach to airborne canner of different type (i.e. ocillating or continuouly rotating mirror) and provider (e.g. Optech, Leica, Riegl). 2. ESTIMATION MODEL Following (Skaloud and Lichti, 2006) the functional model i baed on conditioning the georeferenced LiDAR target point to lie on urface of known form, particularly plane. The plane coefficient are etimated together with the calibration parameter. The a-priori unknown of a plane j are repreented T a j = 1 j 2 j 3 j 4j and the deired form of the condition ued for the parameter etimation read: Xi ui α m Y i R b v i i U i β a j, + + + = 0 Z i w i γ (1) 1 T where, g = [ X Y Z] are the coordinate of IMU-centre in m the mapping frame at time i, R = f(, r p, y) i the orientation bi matrix from the IMU body frame (b) to the mapping frame parameterized by roll (r), pitch (p) and yaw (y) obervation at time i, a i the lever-arm offet between the IMU and LiDAR meaurement center expreed in the IMU body frame, α, β and γ are the unknown boreight angle and U i the kewymmetric matrix of LiDAR vector u defined by mean of the mounting orientation matrix ( T b* range (ρ) meaurement and a: ( ρ +Δρ)inθ T b* u = [ u v w] T 0 ( ρ +Δρ)coθ ) a well a encoder (θ) and (2) * Correponding author. Tel: +41 21 693 27 55 / Fax: +41 21 693 57 40 / email: jan.kaloud@epfl.ch

Other ytem-related calibration parameter can be expreed in the Eq. (2), a it i the cae for a contant range finder offet Δρ. The Eq. (1) contain two et of unknown, firt related to the boreight and ytematic laer error and econd related to plane coefficient. The combined (or Gau-Helmert) adjutment model i ued after the linearization in etimating the correction of the parameter et ˆ δ ˆ 1, δ 2 from a relation: ame plane. The individual tep of thi proce will be preented in more detail. ( ) ( ) ( ) ( ) T T 1 T T A1 BP B A ˆ 1 A1 BP B A 2 δ1 T T T T T A ˆ 2 BP B A1 A2 BP B A2 + G PG δ c 2 T T 1 ( ) ( ) A BP B w 0 + = T T T A 0 2 BP B w G Pw + c c (3) where A 1, A 2 are the repective deign matrice of partial derivative of the functional (2) with repect to calibration and plane parameter, B i the deign matrix of partial derivative of the ame functional taken with repect to the obervation, G i the deign matrix of partial derivative of the linearized contrain impoed on the plane parameter, w i the micloure vector, P and P c are the weight matrice (often diagonal) related to obervation and the contrain, repectively. The pare tructure of the deign matrice allow formulating a contribution of individual obervation equation in uch a way that they can be added directly to the normal equation in a equential manner. Thi enable the practical efficiency when uing large LiDAR data et. 3. AUTOMATED ROOF DETECTION The decribed method for the parameter etimation wa encoded into a program baptized LiBOR. The prerequiite for it correct functioning i the planarity of the elected urface. Thi aumption (i.e. no departure greater than the noie level of urface meaurement) i indeed central to thi method. Neverthele, finding the planar feature in the natural terrain require the ue of ophiticated claification routine or viual guidance by mean of orthophoto or approximate elevation model. Our experience in thi regard ha been that finding uitable natural terrain even on uch planar urface like occer field i problematic. On the other hand, their exitence i relatively abundant within urban dataet. Moreover, urface like roof often vary in apect and lope, which i needed for good parameter de-correlation. The election of rooftop can be performed by manual fence-drawing ; however, the claification need to be done eparately for each trip. Hence, there i a practical need to automate the roof election proce completely. Such automation hould alo minimize the exitence of the outlier, i.e. point that do not belong to the urface (e.g. return from antenna, chimney, etc.). The propoed algorithm follow the global workflow depicted in Fig. 1. Firt, the vegetation i removed and the roof are identified within a reference trip (normally the trip with the bet data quality) by mean of a local covariance analyi, whoe detail will be decribed later. The location of the correponding plane in the ubequent trip i approximately etimated by matching Digital Surface Model (DSM) derived from thoe trip with that of reference. The earch i further refined for individual point by mean of covariance analyi of the neighborhood and the urface boarder are finalized by region growing. The outcome of thi proce are group of point within different trip that can be conditioned to lie on a Figure 1: Generalized workflow of roof finder algorithm 3.1 Covariance analyi The principle of local neighborhood covariance analyi i a key component for claifying the laer point cloud (Fig. 2). The etimate of a local covariance for a query point need to be preceded by patial indexing. Thi i achieved once for all point by the method of k-d tree decompoition. Local covariance are then computed for a pre-elected volume and their principle orientation i found by eigenvalue decompoition. It wa previouly reported that uch approach i computationally very efficient mean of etimating urface normal vector and local curvature directly out of untructured laer data (Bae and Lichti, 2004; Pauly et al., 2002). Figure 2: ALS point cloud of urban area with building and tree (color-coded by abolute height) 3.2 Roof detection within a trip Referring to the algorithm flow in Fig. 1 the firt tep after the covariance analyi conit in the removal of point reflected by vegetation. In general, point belonging to the ground or building can be characterized by low curvature value (urface can often be approximated by a plane), whilt canning point within vegetation and on roof edge generate high curvature value. Thee propertie allow etting up a Boolean tet baed

on a threhold on the local curvature computed out of the local terrain normal (Schaer et al., 2007). The reult of thi election are hown in Fig. 3 where point belonging to the tree and ome point on the roof edge are identified in green. Figure 6: Point clutered to roof group Figure 3: Removal of vegetation (mainly) by etting a threhold on local curvature etimate (in green) The next tep conit in removing all point belonging to the ground. By pecifying a maximum building ize and minimum building height for the area of interet, the algorithm earche for initial ground point (defined a the lowet point within a given cell, where cell ize i larger than maximum building ize). Thee point are ued a initial query point to earch for other point belonging to the ground until all point are claified (Fig. 4). Figure 7: Computation of bet fitting plane Fig. 6 how the reult of the roof clutering tep. Roof group having fewer point than a certain threhold are removed automatically (minimal number of point for one group i defined by pecifying minimal roof ize). In the lat tep, the plane parameter for each roof are computed by the leat quare matching (Fig. 7). 3.3 Roof correpondence between trip Figure 4: Removal of ground point (in red) Once the point on the ground are identified, the remaining point can be clutered to point belonging to the ame plane (thu to the ame roof). Thi i achieved by a region growing approach that compare the etimated local terrain normal. In other word, two point (pq and pj) are conidered a belonging to the ame plane when the following criteria are met (Fig. 5): TRUE if and(α qj atol, d jq dtol ) (4) on_ame_plane(pq, p j ) = q q FALSE if or(α j > atol, d j > dtol ) Where n n j q r jq = p q p j, d qj = r jq n q, α qj = aco n j nq Figure 5: Comparion of local normal to evaluate if two point belong to the ame plane Prior to calibration, the initial boreight value i often conidered a zero. Conequently, trip mimatche on the ground coordinate can reach everal meter, even for boreight approximation better than a degree. Due to the poible exitence of uch large eparation (mainly between flight line of different orientation and altitude) the proce of identifying the correponding rooftop between trip i eparated in two tep. An approximate global hift between the trip i etimated firt, and the earch i refined in the econd phae. The former employ the well known technique of rater matching by cro-correlation. Comparing the DSM of one trip to that of the reference trip yield a planar hift (ΔX, ΔY) that i applied a an approximate match. Once the roof group have been determined for the reference trip and the initial planar hift have been applied, the earch for a correponding group i initiated from the reference group centre by applying the rule tipulated in Equation 4 and the area i augmented by regional growing. 3.4 Roof finder interface To interactively control the reult of the roof finder algorithm and eventually apply correction (if neceary), the computation are guided by a Graphical Uer Interface (GUI). Within the GUI the uer can eaily adapt the proceing parameter and viualize every intermediate reult of the proce. The interface alo indicate the quality of the detected feature in term of tandard deviation and maximum out-ofplane deviation (Figure 8).

achieving good de-correlation between the etimated parameter. 4.2 Optech The firt example concern the calibration of the Optech' ALTM 3100 airborne laer canner. It canning principle employ an ocillating mirror that produce the zig-zag canning pattern. The ytem operate at elected frequencie with maximum of 100 khz, while about 75 khz were ued for the calibration. The maximum aperture i 50 degree. To reduce ome undeirable ditortion due to imperfect deign, thi aperture i often limited to 22 degree, a wa the cae for the calibration. The laer pule have an aperture of 0.3mrad (e.g. thi repreent a laer dot ize of 30cm at 1km ditance) and the ytem allow to regiter up to four return per ingle pule. They are habitually equipped with Applanix 510 navigation ytem, which in thi particular cae conit of the LTN200-A1 IMU (1deg/h FOG) and Novatel L1/L2 GPS receiver. The flight pattern wa executed twice a hown in Fig. 9, at 550 m and 1100 m above the ground. Figure 8: Uer interface of oftware for roof detection: the boundarie and the elected point for every roof are directly viualized on top of the DSM (vegetation already removed) 4. CALIBRATION EXAMPLES Laer return from 20 plane were elected to participate in the LiBOR adjutment. Some of thee were ued a check plane, i.e. plane that do not contribute to parameter etimation but are ueful for control purpoe. Thi i depicted in Fig. 10, on the out-of-plane reidual (1σ and maximum) plotted for previou and following adjutment. In the following we preent a ynthei of our experience when applying the preented adjutment methodology and automated roof-detection algorithm on data laer of different canning principle and from the market-leading manufacture like Optech, Leica and Riegl. Figure 10: Out-of-plane reidual before and after adjutment (automated plane election) The group of point per plane were firt elected manually by drawing polygon line eparately for each trip. Second election wa made automatically by the propoed procedure. The reult of boreight etimate for thee two input are compared in Table 1. A it can be een from thi table the boreight value are practically the ame for both election, albeit the latter aved coniderably the operator time. Figure 9: Typical calibration field and flight pattern 4.1 Calibration field() and flight pattern The prerequiite for the choice of the calibration field election i the preence of larger planar feature (e.g. rooftop) that vary in apect and inclination. Thi i typically the cae of an urban area, a hown in Fig. 9. The ame figure illutrate a cloverleaf flight pattern that i uually executed at two different altitude. The variation of flight orientation and height i important for Method roll Pitch yaw σ r σ p σ y [deg] [deg 10-3 ] Manual 0.058-0.031 0.038 0.2 0.2 2.5 Auto 0.058-0.031 0.031 0.1 0.1 2.0 Optech -0.054-0.035 0.000??? Table 1: Comparion of boreight etimate for Optech ALS The boreight value are alo compared to the bet etimate provided by Optech for the ame ytem. Optech boreight calibration trategy for thi particular ytem employed the cro-ection method that can relatively well etimate the boreight in roll and pitch, but i inappropriate for etimating the yaw angle. Therefore, there i a good agreement to thoe etimated by LiBOR in the roll and pitch angle, but there i a

large difference in yaw a the boreight in thi direction wa not etimated by the manufacturer. 4.3 Leica Leica ALS50 employ alo an ocillating mirror and therefore ha a imilar canning pattern to that of ALTM3100. The maximum canning frequency and aperture are 150 khz and 75 degree, repectively. The laer pule have an aperture of 0.33 mrad (e.g. thi repreent a laer dot ize of 33cm at 1km ditance). The type of navigation equipment varie with the year of fabrication. The calibration field wa again in an urban area and flight pattern wa imilar to that of Fig. 9 but at altitude level of 1000 m and 1500 m above the terrain. The combination of the flight peed, altitude and canning frequency reulted in point denitie of 2.6 pt/m 2 and 1.4 pt/m 2, repectively. The choice of the flight parameter wa not optimized for the LiBOR approach where more favorable geometry could be attained at lower flying height. Thi wa due to a compromie with the calibration requirement according to a different methodology (Morin, 2002) that wa performed imultaneouly by the ytem owner. Neverthele, thi offer a poibility to compare the reult attained by both calibration method. A hown in Table 2, the difference are practically inignificant in roll and pitch but omewhat conequential in yaw. Neverthele, the mot outtanding dicrepancy concern the range finder offet, the value of which wa aumed a calibrated (in well controlled environment of many GCP). Thi effect hould be, however, conidered cautiouly a ALS50 define biae in range meaurement eparately for each of 255 poible intenity value. Although it can be aumed that the intenity value vary only little for the rooftop of imilar kind, no detailed analyi ha been performed in thi repect. Nonethele, the correlation of the range finder offet with the ret of the etimated parameter i invetigated in the plot of Fig. 11. There it can be een that it i not ignificantly correlated to other etimated parameter, and it value hould therefore be conidered a ignificant. It relation to reidual influence of other ytematic correction applied prior to LIBOR input then cannot be ruled out. 4.4 Riegl boreight angle, Δρ followed by 4x47 plane coefficient The lat preented example concern the hort-range 2D canner (Riegl LMS Q240-x) with a canning angle of 60 and maximum range of 450 (Q240) and 650 m (Q240i) at 80% reflectance. It canning mechanim employ rotating mirror providing unidirectional and parallel canning pattern. The rate i choen a a function of deired point denity and flight parameter, typically everal point per m 2 when tranported by a helicopter. A the ytem i available to our reearch intitute the reult of calibration are available for different IMU configuration a hown in Table 3. LiDAR / IMU roll pitch yaw σ r σ p σ y [deg] [deg -3 ] Q240/LN200 0.139-0.060-0.057.7.9 9.3 Q240i/FSAS 0.445 0.150 0.025.7.7 4.0 Table 3: Boreight etimate for different ytem configuration Uing a helicopter to carry the ytem allow reducing the flying height above the terrain, which ha a favourable effect on the geometry (i.e. the inclination of the plane i larger acro the wath). To ome extent, the quality of the modelling can be judged from the ditribution of obervation reidual after the adjutment. Fig. 12 how a hitogram of the reidual for all 8- type of meaurement together with their repective RMS. It can be noticed that all hitogram are centred on zero (i.e. they are unbiaed) and their repective RMS value are fairly mall (i.e. mm or cm level in poition and range; arc-econd level for the angular quantitie). The number of reidual cloe to zero i alo reduced, which mean that the geometry i uch that mot of the plane contribute to the etimate. Overall, it can be concluded that no important parameter were omitted from the model, and that the overall etimation i in good condition. Method roll pitch yaw σ r σ p σ y Δρ σ Δρ [deg] [deg 10-3 ] [cm] Libor 1.091-0.645 0.024.1.1.1-23 1.2 Leica 1.091-0.651 0.043??? 0? Table 2: Comparion of boreight etimate for Leica ALS50 Fig. 12: Hitogram of meaurement reidual for the urban data of trong geometry 5. CONCLUSIONS Figure 11: Correlation matrix between parameter where black=0 and white=1. The order of parameter i 3 The LiBOR approach on boreight elf-calibration in airborne laer canning wa tudied in light of it practicability. After recalling it underlying adjutment principle the emphai wa given on the automation of it input, i.e. eparation and claification of planar rooftop egment per plane and trip.

The experience confirm the uitability of the preented algorithm for urban area where the building are eparated and have relatively imple roof tructure (e.g. a in Fig. 2). For a ituation where the roof landcape i complex (e.g. building are attached in varying angle or large preence of dormer window, chimney, etc.) the algorithm ha more difficultie to locate uitable planar feature. In uch a cae mall aitance can be eaily applied via the roof finder GUI by pecifying a polygon around roof border by mean of viual guidance baed on the DSM of the reference trip. On the other hand, the election of the appropriate point and the earch of rooftop correpondence in other trip remain completely autonomou. The practical example were given for intrument from three market leader in the ALS indutry. In all cae the comparion of parameter mean value and accuracy etimated by LiBOR wa either equal or uperior to that baed on the method propoed by it manufacture. Hence, the benefit of the tudied method are not only in the rigorou modeling and automation but alo in it uitability to ytem of different provider or canning principle. 6. ACKNOWLEDGMENT Pauly, M., Gro, M. and Kobbelt, L.P., 2002. Efficient implification of point-ampled urface, IEEE Conference on Viualization, Boton Schaer, P., Skaloud, J., Landtwing, S. and Legat, K., 2007. Accuracy Etimation for Laer Point Cloud including Scanning Geometry, 5th International Sympoium on Mobile Mapping Technology (MMT2007), Padua, Italy Schenk, T., 2001. Modeling and Analyzing Sytematic Error in Airborne Laer Scanner. In: C.a.E.E.a.G. Science (Editor). The Ohio State Univerity Skaloud, J. and Lichti, D., 2006. Rigorou approach to boreight elf calibration in airborne laer canning. ISPRS Journal of Photogrammetry and Remote Sening, 61: 47-59 Skaloud, J. and Schaer, P., 2003. Toward A More Rigorou Boreight Calibration, ISPRS International Workhop on Theory Technology and Realitie of Inertial/GPS/Senor Orientation, Catelldefel, Spain Thi work wa motly funded by the Swi Commiion for Innovation (CTI/KTI Project 7782 EPRP) in collaboration with Swiphoto AG. The author thank greatly to Derek Lichti for hi help in k-d tree implementation and advice on covariance analye. REFERENCES Bae, K.-H. and Lichti, D., 2004. Edge and Tree Detection from Three-dimenional Unorganied Point Cloud from Terretrial Laer Scanner, 12th Autralian Remote Sening and Photogrammetry Conference, Fremantle, Autralia Burman, H., 2000. Calibration and orientation of airborneiimage and laer canner data uing GPS and INS, Royal Intitute of Technology, Stockholm, 107 pp Cramer, M. and Stallmann, D., 2002. Sytem Calibration For Direct Georeferencing, Photogrammetric Computer Viion, ISPRS Commiion III Sympoium, Graz, Autria, pp. 6. http://www.ipr.org/commiion3/proceeding/ Filin, S., 2003. Recovery of Sytematic Biae in Laer Altimetry Data Uing Natural Surface. Photogrammetric Engineering and Remote Sening, 69(11): 1235-1242 Frie, P., 2006. Toward a rigorou methodology for airborne laer mapping., EuroCOW. on CDROM, Catelldefel, Spain, pp. 7 Kruck, E., 2001. Combined IMU and enor calibration with BINGO-F, Integrated Senor Orientation, Proc. of the OEEPE Workhop ". CD-ROM, Hannover, pp. 84-108 Morin, K., 2002. Calibration of airborne laer canner, The Univerity of Calgary, 135 pp.