ACCURATE REGISTRATON OF MMS POINT CLOUDS OF URBAN AREAS USING TRAJECTORY

Transcription

1 IPR Annals of the Photogrammetry, Remote ensng and patal Informaton cences, Volume II-5/W2, 23 IPR Workshop Laser cannng 23, 3 November 23, Antalya, Turkey ACCURATE REGITRATON OF MM POINT CLOUD OF URBAN AREA UING TRAJECTORY. Taka a,, H. Date a,. Kana a,y. Nna b, K.Oda b, T.Ikeda b a. Graduate chool of Informaton cence and Technology, Hokkado Unversty, apporo 6-84, Japan s_taka@sdm.ss.st.hokuda.ac.jp, (hdate, kana)@ss.st.hokuda.ac.jp b Asa Ar urvey Co., Ltd, Kawasak-sh 25-4, Japan ysh.nna (kz.oda, tty.keda)@ajko.co.jp KEY WORD: Regstraton, Pont cloud, Urban, Mappng, Laser scannng ABTRACT: Recently, by Moble Mappng ystem (MM) wth laser scanners, a GP and IMU (Inertal Measurement Unt), 3D pont clouds of urban areas (MM pont clouds) are easly acqured. When the same areas are scanned several tmes by the MM, the pont clouds often have dfferences n the range of several hundreds of mllmetres. uch dfferences are caused by nertal drfts of IMU and losses of GP sgnals n urban areas. In ths paper, we propose an automatc accurate regstraton method of MM pont clouds usng a new varant of ICP (Iteratve Closest Pont) algorthm for MM pont clouds and trajectory modfcaton. Our method conssts of four steps. Frstly, some trajectory ponts are automatcally extracted by analyzng the trajectory. econdly, the dfferences of pont clouds are derved at the extracted trajectory ponts n the overlappng scan regon by our new ICP algorthm whch mnmzes pontto-plane and pont-to-pont dstances smultaneously and flters ncorrect correspondences based on a pont classfcaton by PCA (Prncple Component Analyss). Thrdly, the modfed postons and rotaton parameters at all extracted trajectory ponts are derved by a least squares method for postonng and regstraton constrants. Fnally, each pont n the pont clouds s modfed by coordnate transformatons whch are derved from lnear nterpolaton of the modfed postons and rotaton parameters of the extracted trajectory ponts. Our method was appled to MM pont clouds and trajectory ane performances were evaluated.. INTRODUCTION Moble Mappng ystem (MM) wth laser scanners, GP and IMU (Inertal Measurement Unt) contrbutes easy acqustons of 3D pont clouds of urban areas (MM pont clouds). When the same areas are scanned by MM several tmes, MM pont clouds often have dfferences n the range of several hundreds of mllmetres. uch dfferences are caused by nertal drfts n IMU and losses of GP sgnals n urban areas. Therefore, an automatc regstraton method whch accurately and effectvely modfes these dfferences s strongly requred. Many pont cloud regstraton algorthms have been proposed, for example 4PC (Ager et al., 28) and ICP (Iteratve Closest Pont) algorthm (Besl and McKay, 992, Chen and Medon., 992). The ICP s especally effectve for correctng the dfferences n MM pont clouds, because magntude of the dfferences s relatvely small compared wth the sze of pont clouds ane pont clouds have smlar poses. ICP algorthm provdes an accurate regstraton between two pont clouds by teratvely mnmzng regstraton errors whch are squared dstances between correspondng ponts n each pont clouds. Many varants of ICP about the selecton of correspondng ponts and error metrcs have been proposed (Al-Durgham et al., 2). Rusnkewcz et al. (Rusnkewcz and Levoy, 2) evaluated some varants of ICP algorthms, and concludeat ICP usng pont-to-plane dstances for error metrc (pont-toplane ICP) s more accurate than the standard ICP whch mnmzes pont-to-pont dstances. Rdene et al. (Rdene and Goulette, 29) propose a regstraton method for MM pont clouds. In ther method, MM pont clouds are dvded nto blocks and pont-to-plane ICP s appled to each block par. However n ths method, gaps between neghborng blocks may occur. In addton, when ther method s appled to multpath pont clouds, accumulated errors sometmes occur. Gressn et al. (Gressn et al., 22) propose a MM pont cloud regstraton method based on trajectory. In ther method, frstly, the dfferences are derved by an ICP algorthm at several trajectory ponts. Next, MM trajectory s modfed by the least squares method based on poston and regstraton constrants. Fnally, pont clouds are regstered accordng to the modfed trajectory. Therefore, ths regstraton method provdes a better result because t performs contnuous regstraton of pont clouds along the trajectory. However n ths method, pont-to-pont ICP algorthm s used, ane rotaton s not consdered n the regstraton process. Moreover, the accuracy of ther method has not been evaluated. In ths paper, we propose an automatc accurate regstraton method for MM pont clouds usng a new varant of ICP algorthm for MM pont clouds and trajectory modfcaton and we evaluate the regstraton accuracy of our method. Our method follows three extensons from the method proposed by Gressn et al. (Gressn et al., 22). : Adaptve extracton of trajectory ponts for calculatng dfferences based on trajectory analyss. Development of a new varant of ICP algorthm for MM pont clouds to perform an accurate regstraton. Introducng rotatons to the trajectory modfcaton and pont cloud regstraton process for accurate regstraton 2. Data et 2. OUR REGITRATION METHOD In ths paper, MM pont clouds and MM trajectory are denoted by Pand Qrespectvely. The pont cloud s a set of laser scanned ponts P = {(p, t ) p = (x, y, z ), =,, n} and each pont has a poston (x, y, z ) n a world coordnate system. Also, each pont s acqured at the GP tme t. do:.594/sprsannals-ii-5-w

2 IPR Annals of the Photogrammetry, Remote ensng and patal Informaton cences, Volume II-5/W2, 23 IPR Workshop Laser cannng 23, 3 November 23, Antalya, Turkey Trajectory ponts Pont clouds DMP The quantty of dfferences Modfed postons of trajectory tep : Dfference modfcaton ponts extracton tep 2 : Dfference calculaton by CCICP tep 3 : Dervaton of transformaton parameters Fgure. The overvew of our method tep 4 : Regstraton of pont clouds mlarly, the trajectory Q = {(q j, c j, t j ) q j = (x j, y j, z j ), c j = (θ j, φ j, ψ j ), j =,, m(m < n), t j < t j+ } s a set of ponts and each pont j has a poston (x j, y j, z j ) and roll ptch yaw angles (θ j, φ j, ψ j ) of MM. Addtonally, each pont j s acqured at the GP tme t j. In our test data, the maxmum dfferences between the overlappng pont clouds are 4mm n a vertcal drecton and 2mm n a horzontal drecton. q cstart q astart q aend Velocty changng ponts : dstance along the trajectory q oend q ostart q cend q cstart Corner ponts Trajectory ponts Canddates of DMP 2.2 Overvew of the proposed regstraton method q cend (a) (b) Fgure shows the overvew of our method. Our method conssts of the followng four steps. tep : Dfference Modfcaton Ponts extracton Dfference Modfcaton Ponts (DMPs) for trajectory modfcaton are automatcally extracted from all the gven trajectory ponts Q by analyzng acceleratons and angular velocty of MM and trajectory ntersectons. Ths step reduces the number of redundant dfference calculatons n the step2. tep 2 : Dfference calculaton by CCICP algorthm The dfferences at each DMP n the overlappng regons are derved by the CCICP (Classfcaton and Combned ICP) algorthm. The CCICP algorthm s a new varant of ICP algorthm for MM pont clouds whch mnmzes pont-toplane and pont-to-pont dstances, smultaneously, and also flters ncorrect correspondences based on pont classfcaton by PCA (Prncple Component Analyss). tep 3 : Dervaton of transformaton parameters Translaton and rotaton parameters for all DMPs are derved as least squares solutons for absolute postonng constrant, relatve postonng constrant, and regstraton constrant. tep 4 : Regstraton of pont clouds Each pont poston p n the pont cloud s modfed by coordnate transformatons whch are derved from lnear nterpolaton of the modfed postons of DMPs ane derved rotaton parameters. 2.3 Dfference Modfcaton Ponts extracton The dfferences often occur at areas where MM velocty and orentaton change drastcally. Therefore, n these areas, the dfferences are non-lnear and pont clouds may be dstorted. In addton, pont clouds at ntersectng trajectory regons should be regstered accurately. From these ponts of vew, n our method, DMPs are automatcally extracted from all gven trajectory ponts Q by analyzng acceleratons and turnng speeds of MM and trajectory ntersectons. DMP extracton conssts of followng two steps. tep A : electng Canddates of DMP Velocty changng ponts Q a are recognzed by thresholdng for lk q j q k q k l j q j (c) dst( m, n) dst(m,n):dstance along the trajectory d eq : dstance threshould Fgure 2. electng Canddates of DMP (tepa) acceleraton as follows: Q a = {q j v j v j /(t j t j ) a th }. Where a th s a threshold for acceleraton, v j s a velocty of MM at a trajectory pont j : v j = q j q j /(t j t j ). Orentaton changng ponts Q o are recognzed by thresholdng for angular velocty as follows: Q o = {q j (ψ j ψ j )/(t j t j ) ω th }. Where ω th s a threshold for angular velocty, ψ j s a yaw angle of MM at trajectory pont j. Canddates of DMP for each velocty changng pont sequence n Q a are determned by followng crteron as shown n Fgure 2(a). Let q astart, q aend be the startng and endng ponts poston of a sequence of consecutve velocty changng ponts. Canddates q cstart, q cend are selected as the farthest back and forth ponts poston from q astart, q aend wthn along trajectory ponts poston. mlarly, canddates of DMP for each orentaton changng pont sequence n Q o are determned as shown n Fgure 2(b). Moreover, trajectory ntersectons are recognzed by detectng ntersecton for lne segments l j and l k whch consst of consecutve trajectory ponts j, j + and k, k +. If l j ntersects l k, ponts j, j + and k, k + are selected as the canddate for the DMP shown n Fgure 2(c). Fnally, f the dstance of consecutve canddates m and n along the trajectory dst(m, n) exceeds the dstance threshold d eq, new trajectory ponts are selected at regular ntervals, as shown n Fgure 2(d). tep B : Determnaton of DMP and correspondences Frstly, trajectory ponts are segmented at corner ponts as shown n Fgure 3(a). econdly, the correspondng pont j of a canddate j n segment J are detected as a nearest pont wthn the dstance d c n the segments except for J and J s neghbors as shown n Fgure 3(b). Thrdly, trajectory s subdvded nto blocks at regular ntervals d (d < d eq ) (Fgure 3(c)). Fnally, q m d eq New canddates of DMP q n (d) do:.594/sprsannals-ii-5-w

3 IPR Annals of the Photogrammetry, Remote ensng and patal Informaton cences, Volume II-5/W2, 23 IPR Workshop Laser cannng 23, 3 November 23, Antalya, Turkey the set of DMPs R ane set of DMP correspondences Ω, are extracted as shown n Fgure 3(d). If one or more canddates or pars of canddates exst n a block, one canddate or par of canddates s extracted. 2.4 Dfference calculaton by CCICP algorthm 2.4. Extractng local pont clouds for ICP Our new ICP algorthm s appled to local pont clouds whch are extracted by DMPs aner GP tmes. Frstly, two trajectory ponts poston, q ps,q pe are selected as the farthest back and forth ponts poston from each DMP wthn d p along the trajectory ponts. Next, the pont wthn the tme range (t ps t t pe ) s extracted from the pont clouds CCICP algorthm The features of the CCICP algorthm are mnmzng pont-toplane and pont-to-pont squared dstances smultaneously and flterng ncorrect correspondences based on pont classfcaton by PCA. These features are shown as follows. A) Flterng ncorrect correspondences The ponts n the local pont clouds are classfed nto lnear ponts, planar ponts and scatter ponts dependng on the results of the PCA. In the ICP, lnear-planar and scatter-planar correspondences are rejected as ncorrect correspondences for accurate regstraton by the CCICP algorthm. For example, correspondng ponts on electrc cables and buldng facades or ones on utlty poles and walls are not used n the ICP. B) Mnmzng pont-to-plane and pont-to-pont dstances Pont-to-plane and pont-to-pont dstances are mnmzed smultaneously. Pont-to-plane dstance mnmzaton s appled to planar-planar correspondences, because relable normal estmatons can be performed at planar ponts. Pont-to-pont dstance mnmzaton s appled to the other correspondences. Therefore ponts on roads, buldng facades and walls are regstered accurately, and ponts on utlty poles and electrc cables are also regstered. In ths paper, pont-to-plane dstance mnmzaton problem s lnearzed and solved usng the method of Low (Low, 24). The CCICP algorthm follows fve steps. In the followng algorthm, and T ndcate a source pont cloud and a target pont cloud. p and p T ndcate a poston of pont and a poston of pont T. tep : electon ubset of for dstance calculaton and rgd transformaton dervaton s selected. The selecton s done by random samplng (a sample [% of are selected). The sampled pont set s represented by. tep 2 : Pont classfcaton Each pont n s classfed nto lnear ponts, planar ponts and scatter ponts by PCA (Demantke et al., 2). In ths method, local pont dstrbutons of each pont are evaluated by egenvalues λ, λ 2 and λ 3 ( λ λ 2 λ 3 ) and unt egenvectors e, e 2 and e 3, of the varance-covarance matrx M whch s calculated from the poston of pont and ts neghbors (ponts wthn dstance r PCA from ). In order to evaluate the local pont dstrbutons, the magntude relatons of the egenvalues are nvestgated usng the followng three values: a D = λ λ 2, a 2D = λ 2 λ 3, a 3D = λ 3. If a D s larger than the others, the local pont dstrbuton of pont s recognzed as lnear. If a 2D s larger than the others, t s d egment J+ egment K j egment J Corner ponts recognzed as planar. In ths case, egenvector e 3 s kept as the normal vector of. In addton, f a 3D s larger than the others, t recognzed as scatter. tep 3 : Matchng The pont n T whch s closest to pont s extracted as a correspondng pont of pont. If s found, t s classfed by PCA. tep 4 : Rejectng Correspondences consstng of a lnear pont and a planar pont or a planar pont and a scatter pont are rejected. A set of resultng correspondences s denoted by U, and a set of planar-planar correspondences s denoted by V. tep 5 : Mnmzng The average of pont-to-plane squared dstance E PT_PL s derved from equaton (). E PT_PL = V Trajectory ponts Canddates of DMP (a) Canddates correspondence Blocks Fgure 3. Determnaton of DMP and correspondences detecton (tepb) (Tp T p ) n (, ) V Where n = an normal vector of pont n a homogeneous coordnate system T = a transformaton matrx n a homogeneous coordnate system p T, p = postons of p T, p n a homogeneous coordnate system The averages of pont-to-pont squared dstances E PT_PT are derved from equaton (2). E PT_PT = U V (c) Tp T p 2 (, ) U V Canddates correspondence New canddates of DMP (b) Correspondence of DMP (d) In the equaton (), when rotaton angles of T (α, β, γ) about x, y, z axs are nearly zero (α, β, γ ), (Tp T p ) n n equaton () s reformulated as equaton (3). j j DMP 2 () (2) do:.594/sprsannals-ii-5-w

4 IPR Annals of the Photogrammetry, Remote ensng and patal Informaton cences, Volume II-5/W2, 23 IPR Workshop Laser cannng 23, 3 November 23, Antalya, Turkey γ β t x p x p x n x (Tp T p γ ) n = ([ α t y p [ y p [ y n ) [ y β α t z p z p z n z = a α + a 2 β + a 3 γ + n xt x + n yt y + n zt z +(p T p ) n Where a = n zp y n yp z a 2 = n xp z n zp x a 3 = n yp x n xp y t x, t y, t z = translaton parameters of T For all correspondences, equaton (3) s denoted by equaton (4) usng a matrx representaton. (3) Ax b (4) a a 2 a 3 n x n y n z a 2 a 22 a 23 n 2 Where A = [ x n 2 y n 2 z a V a V 2 a V 3 n V x n V y n V z b = [ (p p ) n (p 2 p 2 ) n 2 (p V p V ) n V x = [α β γ t x t y t z T mlarly, Tp T p n equaton (2) s reformulated as equaton (5). γ β t x Tp T p γ = [ α t y [ β α t z = A x b Where A = [ p z p y p z p x p x p x b = [ p y p y p z p z p x p y p z p y p x [ p x p y p z From equatons (4) and (5), the parameters of the coordnate transformaton x opt = (α, t ICP ), whch mnmzes E PT_PL and E PT_PT smultaneously, are derved from equaton (6). Where, α s a rotaton parameter about the x, y, z axs and t ICP s translaton parameter. x opt = arg mn [ A A x [ b 2 b x = arg mn x A x b 2 Where A = [A A U V T b = [b b U V T A = [ A A (5) (6) b = [ b b The soluton x opt s obtaned by solvng A x = b usng pseudo nverse matrx of A. At each teraton, source pont cloud s transformed by the x opt. Here f the number of teratons from step3 to step5 reaches threshold n ITTR or the sum of E PT_PT and E PL_PT s less than threshold δ E or the dfference between current and prevous sums n the teratons s less than δ ΔE, algorthm s termnated, otherwse return to step3. Therefore the amount of dfference s determned by a concatenated transformaton of x opt at each teraton. 2.5 Dervaton of transformaton parameters In order to calculate the transformaton parameters for all DMPs, the modfed poston and rotaton parameters are derved by solvng the overconstraned equatons defned by absolute postonng constrant, relatve postonng constrant, and regstraton constrant. The constrants are defned by equatons (7)-(9). Absolute postonng constrant: (j R), [ q j α = [ q j j (7) Relatve postonng constrant: (j R), [ q j α [ q j = [ q j j α j [q j (8) Regstraton constrant: (j Ω ), [ q j α = [ q j j α + [ t j ICP j (9) Where q j = a modfed poston of q j whch s derved by a least square method Ω = a set of source DMPs α j = rotaton angles around x, y, z axs whch are derved by a least square method 2.6 Regstraton of pont clouds Rotaton and translaton parameters (r, Δ ) for pont n pont clouds are derved by lnear nterpolaton of modfed poston and rotaton parameters of neghborng DMPs j and j (t j t t j ). The lnear nterpolaton s denoted by equaton () and equaton (). r = α j + t t j (α t j t j α j ) j () Δ = Δq j + t t j (Δq t j t j Δq j ) j () Where Δq j = q j q j Fnally, poston of each p n the pont clouds s modfed by the coordnate transformaton usng r and Δ. do:.594/sprsannals-ii-5-w

5 IPR Annals of the Photogrammetry, Remote ensng and patal Informaton cences, Volume II-5/W2, 23 IPR Workshop Laser cannng 23, 3 November 23, Antalya, Turkey Red:outward Blue:backward Green:trajectory DMP C A tep tep2 Fgure 4. MM pont clouds and trajectory Table 5. Used parameters Acceleraton threshold a th.5 m/s 2 Turnng speereshold ω th 8.5 deg/s Dstance threshold m Equal nterval threshold d eq 25 m DMP correspondence search dstance d c 2 m Block dvson nterval d m Pont clouds extracton dstance d p m electng rate a sample.5 % PCA search radus r PCA.3 m Lmtaton of teraton n ITTR 3 ICP error threshold δ E. -7 m 2 ICP error dfference threshold δ E. -4 m 2 earch radus of closest pont r d.7 m Fgure 6. DMPs and evaluated postons (a) Top vew of buldng façade at poston A n Fgure 6 B 3. REULT 3. Input data sets and parameters Our method was appled to urban area pont clouds and trajectory was acqured by MM (GeoMasterNeo). The trajectory s shown n Fgure 4 and consst of 2,92 ponts. mlarly, the pont clouds are shown n Fgure 4 and consst of 39,39,44 ponts. The travel dstance of MM s about 3. km. Used parameters n our experments are shown n Table 5. ome parameters, for example a th and ω th, were determned by common knowledge about runnng condton of MM, on the other hand, other parameters were determned by expermentally. 3.2 Regstraton results and error evaluaton The results of our method are shown n Fgures 6-8. Fgure 6 shows DMPs whch are extracted from trajectory ponts. The number of DMPs was 4, anat of DMP pars was 9. The left fgures n Fgure 7 show pont clouds before regstraton at the postons A-C whch are shown n Fgure 6, and rght fgures show pont clouds after regstraton. In the left fgures of Fgure 7(a) and (c), horzontal dfferences are vsble before regstraton, on the other hand, the dfferences are modfed after regstraton as shown n the rght fgures. mlarly, n the left fgure of Fgure 7(b), sgnfcant elevaton dfferences are vsble. On the other hand, dfferences are modfed as shown n the rght fgures. From these results, our method can perform vsually accurate regstraton of pont clouds. Our algorthm was mplemented on a standard PC wth Intel Core 7 3.3GHz CPU, 32GB RAM, GeForce GTX57 GPU. The computaton tme of regstraton was about 6sec. The (b) de vew of utlty pole at poston B n Fgure 6 (c) Top vew of buldng façade at poston C n Fgure 6 Fgure 7. Pont clouds before and after regstraton most of computaton tme was the dfference calculaton by CCICP, and t was about 33sec. Fgure 8 shows the amount of dfference wth color. In the fgures, the amounts of dfference are derved by calculatons of dstances between each pont n the outward pont cloud and ts closest pont n the backward pont cloud. The color bar s shown n the top of Fgure 8. If the closest pont does not exst nsde of 4 mm area from each pont, ponts are colored n black. In left fgures n Fgure 8, orgnal pont clouds have about 2-4mm dfferences. On the other hand, n the rght fgures, the dfferences are reduced to about less than mm at roads and buldng facades. Fgure 9 shows the dfferences at poston C usng another color range. In ths fgure, as a result, dfferences are less than 5mm at roads and buldng facades after regstraton. These results show that an accurate regstraton of pont clouds whch reduce the dfferences among pont clouds to less than 5mm was realzed by our method. Moreover, the accuracy of the CCICP algorthm was compared wth a standard ICP algorthm (random sample, do:.594/sprsannals-ii-5-w

6 RM of the sum of E PT_PT and E PL_PT [m RM of correspondng ponts [m IPR Annals of the Photogrammetry, Remote ensng and patal Informaton cences, Volume II-5/W2, 23 IPR Workshop Laser cannng 23, 3 November 23, Antalya, Turkey (a) Poston A n Fgure 6 (b) Poston B n Fgure 6 Dfferences 4[mm no rejecton, pont-to-pont, and a quaternon based soluton method). To evaluate CCICP algorthm, a pont clouat conssted of about 5.3M ponts and another pont clouat conssted of about 5.9M ponts were used. The regstraton parameters are the same as the ones shown n Table 5. Fgure shows changes of two RM values of correspondng pont dstances at each teraton of the ICP. In ths fgure, the RM of CCICP s 4% smaller than one of the standard ICP, ans means that our ICP realzes more accurate regstraton than the standard ICP. The processng tmes were 78.3sec for CCICP and 83.3sec for a standard ICP. It was estmateat the man dfference of the processng tmes was caused by a dfference of the soluton methods for mnmzaton problem. Coordnate transformaton parameters of our ICP was derved by solvng smultaneous equaton usng pseudo-nverse matrces. On the other hane parameter of the tandard ICP was derved by a quaternon based method. Fnally, the effectveness of the rotaton was evaluated as shown n Fgure usng the same pont clouds and settngs for accuracy evaluaton. Fgure shows RM values whch were derved from the sum of E PT_PT and E PL_PT. In ths fgure, the RM of CCICP wth rotaton s smaller than that of ts CCICP wthout rotaton. Therefore, ntroducng the rotaton to CCICP s effectve for accurate regstraton of MM pont clouds. (c) Poston C n Fgure 6 Fgure 8. Colored dfferences before and after regstraton.2 Dfferences [mm Fgure 9. Detaled dfferences at poston C 4. CONCLUION In ths paper, an automatc accurate regstraton method of MM pont clouds usng CCICP algorthm for MM pont clouds and modfyng trajectory s proposed. The performance of the method s evaluated by applyng t to MM pont clouds and a trajectory. Our method can reduce the dfferences among pont clouds to less than 5mm at roads or buldng facades on average. Also, ts computaton tme was about 6sec for our test data ncludng 4M ponts and 2.2K trajectory ponts. Moreover, the accuracy of CCICP algorthm was also evaluated. It s concludeat our ICP algorthm was more accurate than the standard ICP algorthm. Future work ncludes automatc parameter determnaton. REFERENCE CCICP tandard ICP Ager, D., Mtra, N., and Cohen, D., Ponts Congruent ets for Robust Parwse urface Regstraton. ACM Transactons on Graphcs, 27(3), pp. -. Al-Durgham, M., Detchev, I., Habb, A., 2. Analyss of Two Trangle-Based Mult- urface Regstraton Algorthms of Irregular Pont Clouds. In IPR Workshop - Laser cannng 2, 33 (Part 5/W2), pp Besl, P. and McKay, N. D., 992. A method for regstraton of 3D shapes. IEEE Trans. on PAMI, 4(2), pp Iteraton Fgure. Comparng RM values at each.25.2 CCICP wthout rotaton CCICP wth rotaton Iteraton Fgure. Effectveness of rotaton Chen, Y. and Medon, G., 992. Object Modelng by Regstraton of Multple Range Images. Image and Vson Computng, (3), pp Demantke, J., Mallet, C., Davd. N., Vallet, B., 2. Dmensonalty based scale selecton n 3D LDAR Pont Cloud. The Internatonal Archves of the Photogrammetry Remote ensng and patal Informaton cences, 38 (Part 5/W2), (on CDROM). Gressn, A., Cannelle, B., Mallet, C., Papelard, J. P., 22. Trajectory-based Regstraton of 3D Ldar Pont Clouds Acqured wth a Moble Mappng ystem. Internatonal ocety for Photogrammetry and Remote ensng Annals, (3), pp Low, K. L., 24. Lnear Least-quares Optmzaton for Pont-to-Plane ICP urface Regstraton. Techncal Report, Department of Computer cence, Unversty of North Carolna at Chapel Hll, TR4-4. Rdene, T., Goulette, F., 29. Co-regstraton of DM and 3D Pont Clouds Acqured by a Moble Mappng ystem. pecal Issue on Moble Mappng Technology, pp Rusnkewcz., Levoy M., 2. Effcent varants of the ICP algorthm. Proceedngs of Internatonal Conference on 3-D Dgtal Imagng and Modelng, pp do:.594/sprsannals-ii-5-w