FULLY AUTOMATIC IMAGE-BASED REGISTRATION OF UNORGANIZED TLS DATA

FULLY AUTOMATIC IMAGE-BASED REGISTRATION OF UNORGANIZED TLS DATA Martn Wenmann, Bors Jutz Insttute of Photogrammetry and Remote Sensng, Karlsruhe Insttute of Tehnology (KIT) Kaserstr. 12, 76128 Karlsruhe, Germany {martn.wenmann, bors.jutz}@kt.edu KEY WORDS: Laser Sannng, TLS, pont loud, regstraton, mage-based, graph-based, automaton. ABSTRACT: The estmaton of the transformaton parameters between dfferent pont louds s stll a rual task as t s usually followed by sene reonstruton, objet deteton or objet reognton. Therefore, the estmates should be as aurate as possble. Reent developments show that t s feasble to utlze both the measured range nformaton and the refletane nformaton sampled as mage, as 2D magery provdes addtonal nformaton. In ths paper, an mage-based regstraton approah for TLS data s presented whh onssts of two major steps. In the frst step, the order of the sans s alulated by hekng the smlarty of the respetve refletane mages va the total number of SIFT orrespondenes between them. Subsequently, n the seond step, for eah SIFT orrespondene the respetve SIFT features are fltered wth respet to ther relablty onernng the range nformaton and projeted to 3D spae. Combnng the 3D ponts wth 2D observatons on a vrtual plane yelds 3D-to-2D orrespondenes from whh the oarse transformaton parameters an be estmated va a RANSAC-based regstraton sheme nludng the EPnP algorthm. After ths oarse regstraton, the 3D ponts are agan heked for onssteny by usng onstrants based on the 3D dstane, and, fnally, the remanng 3D ponts are used for an ICP-based fne regstraton. Thus, the proposed methodology provdes a fast, relable, aurate and fully automat mage-based approah for the regstraton of unorganzed pont louds wthout the need of a pror nformaton about the order of the sans, the presene of regular surfaes or human nteraton. 1. INTRODUCTION The automat regstraton of pont louds aqured wth a terrestral laser sanner (TLS) s stll of great nterest. Eah pont loud represents dense and aurate 3D nformaton about surfaes of objets n the loal area around the sanner wth respet to a loal oordnate frame. However, usually multple sans from dfferent loatons have to be reorded to obtan a full sene overage. Hene, a regstraton proess has to be arred out whh transforms all pont louds nto a ommon oordnate frame. Standard approahes for alulatng the transformaton parameters between two partally overlappng pont louds are based on the Iteratve Closest Pont (ICP) algorthm (Besl & MKay, 1992) and dfferent varants of t (Rusnkewz & Levoy, 2001). The ICP algorthm mnmzes the dfferene between two pont louds. For large numbers of ponts, however, the ICP algorthm shows a hgh omputatonal effort whh s due to the teratve proessng sheme. Hene, t seems qute feasble to extrat relevant nformaton from the pont louds whh an be used for regstraton. Suh relevant nformaton may for example be derved va the dstrbuton of the ponts wthn eah pont loud by usng the normal dstrbutons transform (NDT) ether on 2D san sles (Brenner et al., 2008) or n 3D (Magnusson et al., 2007). Urban envronments or senes ontanng ndustral nstallatons usually ontan regular surfaes of whh varous types of geometr features mght arse. Smple features whh are lkely to our and useful for regstraton are lnes (Stamos & Leordeanu, 2003) derved from the range nformaton sampled as range mages. Other ommonly used features whh are extrated dretly from the pont louds are planes (Dold & Brenner, 2004; Brenner et al., 2008; Pathak et al. 2010a; Pathak et al. 2010b) or more omplex geometr features lke spheres, ylnders or tor (Rabban et al., 2007). However, all these feature types representng geometr prmtves are not suted n senes wthout regular surfaes. In addton to regular surfaes, sans n urban senes mght also ontan a typal skylne. Ths border between the sky and a set of buldngs shows speal features when usng a ylndral projeton model for samplng the range nformaton to panoram range mages overng 360 n the horzontal dreton, e.g. extrema or flat regons whh are suted for a oarse algnment of two sans (Nühter et al., 2011). As suh features strongly depend on the sene ontent, ths approah s not suted f the skylne s less dstntve and thus not suffent for regstraton purposes. In the presene of luttered senes, desrptors representng loal surfae pathes are more approprate. Suh desrptors may be derved from geometr urvature or normal vetors of the loal surfae (Bae & Lht, 2004; Bae & Lht 2008). Further approahes whh are sutable for more omplex senes are based on extratng speal feature ponts n the range mages n order to support the regstraton proess (Barnea & Fln, 2008; Steder et al., 2010). Currently, most of the terrestral laser sanners an not only measure the dstane to 3D sene ponts but also apture ether o-regstered amera mages or panoram refletane mages representng the respetve energy of the baksattered laser lght. Therefore, several approahes are based on the use of 2D magery as the mages provde addtonal nformaton about the loal area around the sanner whh mght not always be represented n the range measurements. Hene, the regstraton of two pont louds an be supported by usng relable feature orrespondenes between the respetve amera or refletane mages. For ths purpose, dfferent knds of features an be used, but most of the urrent mage-based approahes are based on the use of feature ponts or keyponts. Many of the magebased approahes use SIFT features to detet dstntve 2D feature ponts by whh pont orrespondenes between two mages an be deteted. These features an be extrated from the o-regstered amera mages (Bendels et al., 2004; Al- Manasr & Fraser, 2006; Barnea & Fln, 2007) or from the refletane mages (Böhm & Beker, 2007; Wang & Brenner 2008; Kang et al., 2009). For all pont orrespondenes, the respetve feature ponts are projeted nto 3D spae and thus lead to a muh smaller set of 3D ponts used for regstraton. In ths paper, a method for a fully automat regstraton of a large number of unorganzed sans s proposed. Reahng a 55

hgh level of automaton also nludng the sortng of the sans s essental as most of the urrent approahes are based on parwse regstraton for whh an already known order of the sans s assumed. For parwse regstraton, a modfaton of a fast and automat mage-based regstraton approah whh has been publshed reently (Wenmann et al., 2011) and whh s also suted for senes wthout regular surfaes s presented. In ontrast to ths approah, only those orrespondenes wth relable range nformaton are used and, nstead of a refnement step, an ICP-based fne regstraton s ntrodued. Thus, besdes beng very fast, the proposed algorthm does nether depend on a pror nformaton about the order of the sans nor on the presene of regular surfaes. The paper s organzed as follows. In Seton 2, the proessng han of the proposed algorthm s outlned. As t wll be shown, the algorthm an be dvded nto the two major steps of organzng the TLS data and arryng out a suessve parwse regstraton whh are presented n Seton 3 and Seton 4 n detal. In Seton 5, the performane of the proposed algorthm s proved by proessng 11 pont louds of a benhmark TLS data set. The apablty of the proposed method s dsussed n Seton 6 wth respet to auray, relablty and performane. Fnally, onlusons and suggestons for future work are outlned n Seton 7. nformaton. Coverng 360 n the horzontal dreton and 90 n the vertal dreton wth a sngle shot measurement auray of 12mm and an angular resoluton of 0.12 up to a range of approxmately 200m, eah san returns 2.25 mllon 3D ponts from a regular san area of 3000 x 750 ponts beng represented as panoram refletane mage (Wang & Brenner, 2008). The refletane and range nformaton derved from the san at san poston 01 are vsualzed n Fgure 2. In order to hek the qualty of the automatally alulated regstraton results, aurate referene values are needed. The provded referene values are based on the use of artfal targets and a manual algnment whh yelds an expeted auray of the san postons n the low mllmeter range. For testng the proposed algorthm, a subset onsstng of 11 uprght sans wth a spang of approxmately 5m s used. 2. METHODOLOGY The regstraton approah proposed n ths paper ams at reahng a hgh level of automaton and smultaneously gettng fast, relable and aurate results. As llustrated n Fgure 1, the approah an be dvded nto two major parts. The frst part deals wth the organzaton of unorganzed pont louds whh s later requred for a suessve parwse regstraton. Hene after the aquston of TLS data, speal features have to be extrated whh are sutable for organzng the sans. The seond part fouses on the regstraton of the pont louds. Usng relable 3D ponts derved va the prevously extrated features and ntrodung ther projetons onto a vrtual plane yelds 3D-to-2D orrespondenes. These are used for reevng a oarse regstraton of the pont louds whh s followed by a fne regstraton n order to mprove the auray of the results. The sheme of ths brefly summarzed methodology s presented n detal n Seton 3 and Seton 4. 3. ORGANIZATION OF TLS DATA The urrent regstraton approahes address a fully automat regstraton of dfferent sans of a sene. To further nrease the level of automaton, the proposed algorthm frst organzes the sans automatally, whh yelds a struture for suessve parwse regstraton. Ths s done by onsderng the reorded sans (Seton 3.1), extratng dstntve features and feature orrespondenes between the sans (Seton 3.2) and usng a graph-based approah (Seton 3.3). 3.1 Data Set and Referene Values In the followng, the qualty of the proposed regstraton approah s demonstrated wth a benhmark TLS data set provded by the Unversty of Hanover. Ths set onssts of 12 uprght sans and 8 tlted sans whh were aqured n the German ty of Hanover n an area alled Holzmarkt, and the respetve referene values for the relatve orentaton between the sans. The sans were reorded wth a Regl LMS-Z360 sanner and ontan nformaton about the 3D oordnates of objet ponts as well as the orrespondng refletane Fgure 1. Proessng han of the proposed approah. 3.2 Feature Extraton One several sans have been aqured, the next step onssts of extratng dstntve features. Here, the Sale Invarant Feature Transform (SIFT) (Lowe, 2004) s utlzed for detetng suh dstntve keyponts n an mage derved from the TLS data and extratng loal feature desrptors whh are nvarant to mage salng and mage rotaton, and robust wth respet to mage nose, hanges n llumnaton and small hanges n vewpont. These desrptors allow for loatng orrespondenes between dfferent mages and, fnally, to derve ommon mage objets. As the desrptors are represented as vetors, they an be ompared by onsderng Euldean dstanes. An effetve measure desrbng the dstntveness of a keypont an be derved from the rato of the Euldean dstanes of a desrptor belongng to a keypont n one mage to the nearest neghbor and the seond nearest neghbor n the other mage. Ths rato has to be below a gven threshold t des, whh an vary between 0 and 1. For pratal purposes and dfferent applatons, dstntve features arse when usng a threshold between t des = 0.6 and t des = 0.8. As the feature orrespondenes used for 56

regstraton should be relable, a threshold of t des = 0.66 s used. Ths means that the dstane of a desrptor belongng to a SIFT feature n mage to the nearest neghbor n mage j s only about 2/3 of the dstane to the seond nearest neghbor. (a) (b) Fgure 2. Vsualzaton of the aptured TLS data: (a) refletane and (b) range nformaton. In order to hek the smlarty of the sans, the number of SIFT features between mage pars from all avalable postons s alulated and stored n the onfuson matrx C. For ths purpose, the same san IDs are used as n the provded data set. The dagonal elements C(,) represent the total number of SIFT features extrated n the respetve refletane mage. As an be seen n Table 1, the onfuson matrx s not neessarly symmetr whh depends on the alulated rato of the Euldean dstanes of a feature desrptor to the nearest and seond nearest neghbor. If, for a feature desrptor derved from mage, the nearest neghbor and the seond nearest neghbor n mage j are a lttle more dstntve as requred, ths rato s below the threshold t des and thus meets the onstrant. In the reverse ase, when omparng a feature desrptor derved from mage j to feature desrptors derved from mage, t mght our that the nearest neghbor and the seond nearest neghbor are more smlar whh auses a rato above the threshold t des. 3.3 Organzng Large Numbers of Sans by Smlarty When dealng wth a large number of sans, t mght be desrable to reah a hgh level of automaton. Ths wll also nlude automatally sortng the sans for parwse regstraton so that the error between estmated and real poston s mnmal. Therefore, a graph-based algorthm s proposed here. Any set of unorganzed pont louds an dretly be represented as a graph, where the nodes represent the sans and the edges are weghted wth the total number of SIFT orrespondenes between the respetve sans. In the most general ase, every node s onneted wth every other node whh results n a omplete graph. As mentoned before, the onfuson matrx C s not neessarly symmetr and therefore, a dreted graph s used nstead of an undreted graph. Hene, the entry C(,j) of the onfuson matrx represents the weght of an undretonal edge from node to node j. The frst step towards organzng the pont louds onssts of an ntalzaton whh an be done va seletng a defned ntal san. Alternatvely, t would be possble to use other rterons f only the relatons between the sans are of mportane, e.g. the node from whh the edge wth the maxmum weght wthn the graph starts. Ths ntal set ontanng exatly one node s then teratvely expanded untl t ontans all nodes of the graph. Eah teraton starts wth searhng undretonal edges from the atual set of nodes to the remanng nodes and the edge wth the maxmum weght leads to the node by whh the atual set s expanded. Resultng from the seleted onnetons, a struture an be generated whh represents the order of the sans for the automat parwse regstraton. For the gven onfuson matrx C (Table 1), the resultng struture for a suessve parwse regstraton proess s shown n Fgure 3. Fgure 3. Resultng sheme for suessve parwse regstraton: The sans are labeled wth ther ID and the onnetons used for further alulatons are labeled wth the number of deteted SIFT orrespondenes between the respetve refletane mages. 4. REGISTRATION OF TLS DATA After alulatng the order of the sans by hekng the smlarty of the respetve refletane mages, a parwse regstraton of suessve sans an be arred out. For ths purpose, the already alulated 2D SIFT features leadng to San ID 01 02 03 05 06 08 09 11 15 17 19 01 4986 217 63 45 33 58 41 28 44 62 39 02 229 5663 319 100 59 80 43 48 35 46 38 03 88 308 5967 253 120 56 47 68 57 38 56 05 70 114 277 6200 484 78 58 68 131 68 84 06 31 70 124 466 6682 169 68 56 477 134 71 08 86 96 53 78 163 6867 205 64 328 404 99 09 39 34 37 56 68 158 5571 330 78 577 656 11 17 24 37 40 44 41 277 4061 24 134 408 15 61 40 59 129 503 344 82 30 7154 211 53 17 53 56 34 60 121 379 590 169 240 6159 361 19 21 25 43 51 54 84 629 482 42 344 4852 Table 1. Number of SIFT orrespondenes between the refletane mages of dfferent sans wthn the hosen subset. The values an be summarzed n the onfuson matrx C and the entry C(,j) of ths matrx denotes the number of pont orrespondenes found when all desrptors derved from mage are ompared to the nearest neghbor and the seond nearest neghbor derved from mage j. 57

orrespondenes have to be projeted to 3D spae, and the relablty of the alulated 3D ponts has to be heked wth respet to range nformaton (Seton 4.1) before regstraton. The followng regstraton s based on 2D projetons of the relable 3D ponts onto a vrtual plane (Seton 4.2), and dvded nto a oarse regstraton (Seton 4.3) and a fne regstraton (Seton 4.4). 4.1 3D Pont Estmaton As SIFT features are determned wth subpxel auray, the respetve 3D nformaton has to be nterpolated as the measured values are only avalable on the regular san raster. A relable 3D pont orrespondng to a SIFT feature an however only be generated, f all of the four nearest ponts on the san raster ontan vald range nformaton. The measured ponts whh arse from objets n the sene wll probably provde a smooth surfae whereas ponts orrespondng to the sky or ponts along edges of the objets mght be very nosy. Therefore, ponts have to be dsarded f they do not le on the surfae of any objet n the sene. The provded sans are already fltered wth respet to mnmum values of the baksattered energy (Fgure 4a). Addtonally, the proposed algorthm onsders the standard devaton σ of the values wthn a 3 x 3 neghborhood of eah pxel n the range mage n order to avod unrelable range nformaton at edges of sene objets. If the standard devaton σ of the respetve range values s larger than a predefned threshold t std whh s seleted to t std = 0.1m, the range nformaton of the enter pxel s not relable, otherwse the range nformaton of the enter pxel s assumed to be relable (Fgure 4b). Combnng these onstrants yelds a 2D onfdene map M C whh s llustrated n Fgure 4. (a) (b) onto a 2D mage plane of a vrtual amera n order to use powerful algorthms of omputer vson applatons. The respetve transformaton an be desrbed va [ ] x = K R t X (1) where the matrx K s the albraton matrx of a vrtual amera, and the matrx R and the vetor t desrbe the rotaton and the translaton of ths vrtual amera wth respet to the loal oordnate frame of the laser sanner. In the regstraton proess, R refers to the loal oordnate frame so that the vrtual amera has the same orentaton as the laser sanner and looks nto the horzontal dreton (Wenmann et al., 2011). Besdes, the poston of the vrtual amera s assumed to equal the loaton of the laser sanner and therefore, the translaton vetor s set to t = 0. As a onsequene of ntrodung a vrtual amera plane, any parameters an be used for the foal lengths of the amera n x- and y- dreton as well as for the oordnates of the prnpal pont. Furthermore, the mage plane has not neessarly to be lmted on a fnte area and all ponts behnd the amera may also be nluded by mappng them onto the vrtual plane va symmetr onstrants as they represent the 2D projetons onto the vrtual plane of a seond amera lookng n the opposte dreton. Thus, nstead of reatng synthet amera mages and usng these for regstraton (Forkuo & Kng, 2004), only a few ponts are projeted wth subpxel auray. 4.3 Coarse Regstraton usng EPnP and RANSAC One 3D-to-2D orrespondenes are known, the problem of pose estmaton s the same as when usng a amera nstead of a laser sanner. Reently, the Effent Perspetve-n-Pont (EPnP) algorthm has been proposed as a non-teratve method to estmate the exteror orentaton or pose of a amera from a set of n orrespondenes between 3D ponts X of a sene and ther 2D projetons x onto the mage plane (Moreno-Noguer et al., 2007; Lepett et al., 2009). The EPnP algorthm s based on the dea of expressng the n known 3D sene ponts X as a weghted sum of four vrtual and non-oplanar ontrol ponts C j for general onfguratons. The weghts α j reman unhanged when transferrng ths relaton to amera oordnates and therefore, the ponts X an be expressed va the ontrol ponts C j whh leads to w x 4 = αj j 1 = = j = 1 K X K C (2) for = 1,, n, where K desrbes the amera matrx. The salar projetve parameters w an be substtuted by () Fgure 4. Confdene map for the san at san poston 01: (a) nformaton fltered wth respet to refletane, (b) nformaton fltered wth respet to the standard devaton σ usng a threshold value of t std = 0.1m and () the resultng onfdene map M C. The relable ponts are shown n green, the unrelable ones n red. 4.2 Perspetve Plane Projeton The refletane mages have been sampled usng a spheral projeton. For the regstraton, however, t s useful to get the oordnates of the extrated and relable 3D ponts X projeted w 4 = αjz j (3) j= 1 va the Z oordnates of the ontrol ponts. Conatenatng the resultng equatons for all n 3D-to-2D orrespondenes yelds a T T T T T lnear system M x = 0 wth x = C 1, C2, C3, C 4 and a 2n x 12 matrx M. The soluton x then leads to the amera oordnates X. One the world oordnates and the amera oordnates of the 3D ponts are known, the rotaton and translaton parameters algnng both oordnate systems an be retreved va standard methods (Horn et al., 1988). As the EPnP algorthm onsders all 3D-to-2D orrespondenes wthout hekng ther relablty, the qualty of the regstraton results 58

an be nreased by ntrodung further onstrants. The RANSAC algorthm (Fshler & Bolles, 1981) provdes a good possblty for elmnatng outlers and thus reahng a more robust pose estmaton. Ths ombnaton of EPnP and RANSAC s based on randomly seletng small, but not mnmal subsets of seven orrespondenes for estmatng the model parameters, and hekng the whole set of orrespondenes for onsstent sample ponts (Moreno-Noguer et al., 2007; Lepett et al., 2009). 4.4 Fne Regstraton usng Outler Removal and ICP The results from the prevous oarse regstraton provde a good a pror algnment whh s requred for usng the ICP algorthm n order to get a fne regstraton. However, the RANSAC algorthm only onsders the qualty of the 3D-to-2D orrespondenes. Hene, the qualty of the 3D ponts has to be onsdered separately. Ths s done by elmnatng those 3D-to- 3D orrespondenes for whh at least one 3D pont arses from perod shapes of façades and thus from ambgutes n the sene va geometr onstrants (Wenmann et al., 2011). The resultng ponts used for fne regstraton are very relable as they have been heked wth respet to the relablty of ther range nformaton, the qualty of the 3D-to-2D orrespondenes and the qualty of the 3D-to-3D orrespondenes. Therefore, the ICP algorthm s expeted to yeld very aurate results. 5. EVALUATION The frst part of the presented approah an easly be verfed f the nodes belongng to the sans are projeted onto the referene postons of the respetve sans n the sene, whh s done n Fgure 5. Fgure 5. Sans sorted wth respet to ther referene poston n the nadr vew of the sene: The streets are olored n brght gray, buldngs n dark gray. One the sans are sorted, a suessve parwse regstraton an be arred out. Between the refletane mages of the sans 01 and 02, a total number of 217 SIFT orrespondenes has been deteted (Table 1) of whh 89 are relable wth respet to the range nformaton of the orrespondng SIFT features. The respetve 3D ponts of those relable SIFT orrespondenes are projeted to 3D spae usng blnear nterpolaton. If for one san, the absolute transformaton parameters wth respet to the world oordnate frame are known whh s assumed for san poston 01, the 3D world oordnates of the alulated 3D ponts an easly be determned. For a new san, the orrespondng 2D features wth relable range nformaton are also projeted to 3D spae and bakprojeted onto a vrtual plane assgned to the loal oordnate frame whh yelds 2D observatons. Establshng 3D-to-2D orrespondenes from the 3D nformaton derved from the frst san and the 2D observatons derved from the new san allows for usng the EPnP algorthm whh has been extended by the RANSAC algorthm for an nreased robustness. Subsequently, a onssteny hek wth respet to 3D dstanes between the 3D ponts transformed nto a ommon oordnate frame va the oarse estmate of the transformaton parameters s arred out. After ths geometr outler removal, the remanng 3D-to-3D orrespondenes (29 between the sans 01 and 02) are used for an ICP-based fne regstraton. As shown n Fgure 6, the absolute poston errors after oarse regstraton are n the range between 12mm and 49mm, and the fne regstraton yelds aurate results wth absolute poston errors between 9mm and 32mm. Fgure 6. Absolute error between referene and estmated postons for oarse (dotted lne wth damonds) and fne regstraton (sold lne wth squares). 6. DISCUSSION The presented regstraton approah was tested n Matlab on a standard PC wth 2.83GHz. Although the ode s not fully optmzed wth respet to a possble parallelzaton on multple ores and thus only one ore s used, the average tme requred for parwse regstraton s about 13s. Of ths tme, about 5s are needed for alulatng the SIFT orrespondenes, about 7s for oarse estmaton usng a RANSAC-based sheme nludng EPnP and only 1s for onssteny heks and ICP on two relatvely small subsets eah onsstng of approxmately 100 ponts. If the ICP algorthm s used for larger subsets, the omputatonal effort nreases hghly. Conernng auray and performane, the proposed approah s omparable to other mage-based approahes (Wang & Brenner, 2008; Wenmann et al., 2011). As the approah fouses on usng only relable nformaton onernng range, 3D-to-2D orrespondenes and 3D-to-3D orrespondenes, the estmated transformaton parameters are very relable whh an be seen when omparng them to the referene values (Fgure 6). The approah s suted for both urban envronments and senes ontanng vegetaton and does nether depend on regular surfaes nor human nteraton. However, one onstrant onernng the sene arses as pont-lke features have to be extrated. Hene, the sene has to be well-strutured whh s assumed n all mage-based approahes usng SIFT features. As the total number of SIFT orrespondenes dereases wth an nreasng dstane between the respetve san postons whh an be seen when onsderng the entres n the onfuson matrx (Table 1) and the referene postons (Fgure 5), the presented approah as well as other mage-based approahes wll not lead to optmal results for larger dstanes between the sans. For ths purpose, approahes based on geometr prmtves (Brenner et al., 2008; Rabban et al., 2007) mght be 59

more robust n dret omparson, but they assume that regular surfaes an be found n the sene and thus less general senes. 7. CONCLUSION AND OUTLOOK In ths paper, a fully automat regstraton approah s presented whh s based on both the range nformaton and the refletane nformaton of terrestral laser sans. Automatally sortng any number of unorganzed sans by means of ther smlarty and then arryng out a suessve fast and aurate parwse regstraton, the approah provdes a powerful framework suted for typal envronments. The approah has been suessfully appled to a benhmark TLS data set ontanng mllons of ponts and been dsussed onernng auray, relablty and performane. For future work, the approah ould be extended by ntrodung a fnal global regstraton over all sans or at least onsderng those parts of the onfuson matrx arsng from the smlarty of a new san to all of the already regstered sans. Ths mght mprove the qualty of the estmated transformaton parameters and yeld an even further nreased robustness. 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