A Survey of Rigid 3D Pointcloud Registration Algorithms

Transcription

1 AMBIEN 2014 : he Fourh Ieraoal Coferece o Ambe Compug, Applcao, Servce ad echologe A Survey of Rgd 3D Pocloud Regrao Algorhm Be Belleke, Vce Spruy, Rafael Berkve, ad Maare Wey CoSy-Lab, Faculy of Appled Egeerg Uvery of Awerp, Belgum be.belleke@uawerpe.be Abrac Geomerc algme of 3D pocloud, obaed ug a deph eor uch a a me-of-flgh camera, a challegg ak wh mpora applcao roboc ad compuer vo. Due o he rece adve of cheap deph eg devce, may dffere 3D regrao algorhm have bee propoed leraure, focug o dffere doma uch a localzao ad mappg or mage regrao. I h urvey paper, we revew he ae-of-he-ar regrao algorhm ad dcu her commo mahemacal foudao. Sarg from mple deermc mehod, uch a Prcpal Compoe Aaly (PCA) ad Sgular Value Decompoo (SVD), more recely roduced approache uch a Ierave Cloe Po (ICP) ad vara, are aalyzed ad compared. he ma corbuo of h paper herefore co of a overvew of regrao algorhm ha are of ere he feld of compuer vo ad roboc, for example Smulaeou Localzao ad Mappg. Keyword 3D pocloud; PCL; 3D regrao; rgd raformao; urvey paper I. INRODUCION Wh he adve of expeve deph eg devce, roboc, compuer vo ad ambe applcao echology reearch ha hfed from 2D magg ad Laer Imagg Deeco Ad Ragg (LIDAR) cag oward real-me recoruco of he evrome baed o 3D pocloud daa. O oe had, here are rucured lgh baed eor uch a he Mcroof Kec ad Au Xo eor whch geerae a rucured po cloud, ampled o a regular grd, ad o he oher had, here are may me-of-flgh baed eor uch a he Sofkec Dephee camera yeld a urucured pocloud. hee pocloud ca eher be ued drecly o deec ad recogze objec he evrome where ambe echology bee ued, or ca be egraed over me o compleely recoruc a 3D map of he camera urroudg [1], [2], [3]. I he laer cae however, po cloud obaed a dffere me ace eed o be alged, a proce whch ofe referred o a regrao. Regrao algorhm are able o emae he ego-moo of he robo by calculag he raformao ha opmally map wo pocloud, each of whch ubjec o camera oe. hee regrao algorhm ca be clafed coarely o rgd ad o-rgd approache. Rgd approache aume a rgd evrome uch ha he raformao ca be modeled ug oly 6 Degree Of Freedom (DOF). No-rgd mehod o he oher had, are able o cope wh arculaed objec or of bode ha chage hape over me. Regrao algorhm are ued dffere feld ad applcao, uch a 3D objec cag, 3D mappg, 3D localzao ad ego-moo emao, huma body deeco. Mo of hee ae-of-he-ar applcao employ eher a mple Sgular Value Decompoo (SVD) [4] or Prcpal Compoe Aaly (PCA) baed regrao, or ue a more advace erave cheme baed o he Ierave Cloe Po (ICP) algorhm [5]. Recely, may vara o he orgal ICP approach have bee propoed, he mo mpora of whch are o-lear ICP [6], geeralzed ICP [7], ad o-rgd ICP [8]. he choce for oe of hee algorhm geerally deped o everal mpora characerc uch a accuracy, compuaoal complexy, ad covergece rae, each of whch deped o he applcao of ere. Moreover, he characerc of mo regrao algorhm heavly deped o he daa ued, ad hu o he evrome elf. o our kowledge, a geeral dcuo of each of he above mehod o avalable leraure. A a reul dffcul o compare hee algorhm objecvely. herefore, h paper we dcu he mahemacal foudao ha are commo o he mo wdely ued 3D regrao algorhm, ad we compare her regh ad weakee dffere uao. h paper ouled a follow: Seco II brefly dcue everal mpora applcao doma of 3D regrao algorhm. I Seco III, rgd regrao formulaed a a lea quare opmzao problem; Seco IV expla he mo mpora rgd regrao algorhm whch are PCA, SVD, ICP po-o-po, ICP po-o-urface, ICP o-lear ad Geeralzed ICP; Fally, Seco V provde a dcuo of he dffere characerc of each of hee mehod a real world eg; Seco VI coclude he paper. II. APPLICAION DOMAINS Impora applcao doma of boh rgd ad o-rgd regrao mehodologe are roboc, healhcare, augmeed realy, ad more. I hee applcao he commo goal o deerme he poo or poe of a objec wh repec o a gve vewpo. Wherea rgd raformao are defed by 6 DOF, o-rgd raformao allow a hgher umber of DOF order o cope wh o-lear or paral rechg or hrkg of he objec. A. Roboc Sce he roduco of expeve deph eor uch a he Mcroof Kec camera, grea progre ha bee made he roboc doma oward Smulaeou Localzao Ad Mappg (SLAM) [9], [10], [11], [12]. he recoruced map repreeed by a e of pocloud whch are alged by mea of regrao ad ca be ued for obacle avodace, map explorao, auoomou vehcle corol, ec.[3], [13], [14]. Furhermore, deph formao ofe combed wh a Copyrgh (c) IARIA, ISBN:

2 AMBIEN 2014 : he Fourh Ieraoal Coferece o Ambe Compug, Applcao, Servce ad echologe radoal RGB camera [2], [15] order o grealy faclae real-world problem uch a objec deeco cluered cee, objec rackg ad objec recogo [16]. B. Healhcare ypcal applcao of o-rgd regrao algorhm ca be foud healhcare, where a of-body model ofe eed o be alged accuraely wh a e of 3D meaureme. Applcao are cacer-ue deeco, hole deeco, arefac recogo, ec. [8], [17]. Smlarly, o-rgd raformao are ued o oba a mul-modal repreeao of a cee, by combg MRI, C, ad PE volume o a gle 3D model [8]. III. DEFINIIONS Rgd regrao ca be approached by defg a co fuco ha repree he curre machg error. h co fuco he mmzed ug commo opmzao echque. If he dace bewee correpodg po each 3D pocloud eed o be mmzed, h ca be mplfed o a lear lea-quare mmzao problem by repreeg each po ug homogeeou coordae. I h eco, we brefly roduce he lea-quare opmzao problem ad dcu he cocep of homogeeou raformao ce hee form he ba of 3D regrao algorhm. A. Lea-Square Mmzao A rgd raformao defed by oly 6 DOF, wherea may oy obervao,.e., po coordae, are avalable. herefore, he umber of parameer of ay co fuco for h problem much maller ha he umber of equao, reulg a ll-poed problem whch doe o have a exac oluo. A well kow echque o oba a accepable oluo uch cae, o mmze he quare of he redual error. h approach called lea-quare opmzao ad ofe ued for fg ad regreo problem. Wherea a lear lea-quare problem ca be olved aalycally, h ofe o he cae for o-lear lea-quare opmzao problem. I h cae, a erave approach ca be ued by eravely explorg he earch pace of all poble oluo he dreco of he grade vecor of he co fuco. h lluraed by Fgure 1, where he co fuco f(d) of he ICP regrao algorhm mmzed eravely. he co fuco h cae repree he um of he quared Eucldea dace bewee correpodg po of wo pocloud daae. Error f(d) Ierao m f(d) Fgure 1. ICP Lea quare approach. B. Homogeeou raformao A homogeeou raformao hree dmeo pecfed by a 4 4 affe raformao marx [18]. h marx ued o projec each po Carea pace wh repec o a pecfc vewpo. I he followg, le v 1 = (x 1, y 1, z 1, 1) be a po whoe bae defed by vewpo oe ad le v 2 = (x 2, y 2, z 2, 1) be a po whoe bae defed by vewpo wo. he poble o expre v 2 relave o he bae of vewpo oe a v 1 = v 2, where a affe raformao marx defed by (1). h lluraed more clearly by Fgure 2. r 1,1 r 1,2 r 1,3 1,4 r = 2,1 r 3,1 r 2,2 r 3,2 r 2,3 r 3,3 2,4 3,4 (1) a 4,1 a 4,2 a 4,3 a 4,4 he raformao marx how by (1) repree a affe raformao f a 4,1 = a 4,2 = a 4,3 = 0 ad a 4,4 0. Affe raformao are coruced wh a 3 3 roao marx R ad colum vecor repreeg a ralao. IV. y v 1 Fgure 2. homogeeou raformao. REGISRAION ALGORIHMS Boh rgd ad o-rgd regrao algorhm ca be furher caegorzed o parwe regrao algorhm ad mulvew regrao mehod. Parwe regrao algorhm calculae a rgd raformao bewee wo ubeque po cloud whle he mul-vew regrao proce ake mulple po cloud o accou o correc for he accumulaed drf ha roduced by parwe regrao mehod. I he ex eco, we dcu fve wdely ued rgd regrao algorhm. Each of hee mehod re o emae he opmal rgd raformao ha map a ource po cloud o a arge po cloud. Boh PCA algme ad gular value decompoo are parwe regrao mehod baed o he covarace marce ad he cro correlao marx of he pocloud, whle he ICP algorhm ad vara are baed o eravely mmzg a co fuco ha baed o a emae of po correpodece bewee he pocloud. A. Prcpal Compoe Aaly PCA ofe ued clafcao ad compreo echque o projec daa o a ew orhoormal ba he dreco of he large varace [19]. he dreco of he large varace correpod o he large egevecor of he covarace marx of he daa, wherea he magude of h varace defed by he correpodg egevalue. z v 2 x Copyrgh (c) IARIA, ISBN:

3 AMBIEN 2014 : he Fourh Ieraoal Coferece o Ambe Compug, Applcao, Servce ad echologe herefore, f he covarace marx of wo pocloud dffer from he dey marx, a rough regrao ca be obaed by mply algg he egevecor of her covarace marce. h algme obaed a follow; Fr, he wo po cloud are ceered uch ha he org of her orgal bae cocde. Pocloud ceerg mply correpod o ubracg he cerod coordae from each of he po coordae. he cerod of he pocloud correpod o he average coordae ad hu obaed by dvdg he um of all po-coordae by he umber of po he pocloud. Sce regrao baed o PCA mply alg he dreco whch he pocloud vary he mo, he ecod ep co of calculag he covarace marx of each po cloud. he covarace marx a orhogoal 3 3 marx, he dagoal value of whch repree he varace whle he off-dagoal value repree he covarace. hrd, he egevecor of boh covarace marce are calculaed. he large egevecor a vecor he dreco of he large varace of he 3D pocloud, ad herefore repree he pocloud roao. I he followg, le A be he covarace marx, le v be a egevecor of h marx, ad le λ be he correpodg egevalue. he egevalue decompoo problem he defed a: ad furher reduce o: Ax = λx (2) x(a λi) = 0. (3) I clear ha (3) oly ha a o-zero oluo f A λi gular, a coequely f deerma equal zero: de(a λi) = 0 (4) he egevalue ca mply be obaed by olvg (4), wherea he correpodg egevecor are obaed by ubug he egevalue o (2). Oce he egevecor are kow for each pocloud, regrao acheved by algg hee vecor. I he followg, le marx y repree he raformao ha would alg he large egevecor of he arge pocloud wh he y-ax. Le marx y repree he raformao ha would alg he large egevecor of he ource pocloud wh he y- ax. he he fal raformao marx ha alg he ource pocloud wh he arge pocloud ca be obaed ealy, a lluraed by Fgure 3. uch ha ceer correpod o he ceer of he arge pocloud. B. Sgular Value Decompoo PCA baed regrao mply alg he dreco of he large varace of each pocloud ad herefore doe o mmze he Eucldea dace bewee correpodg po of he daae. Coequely, h approach very eve o ouler ad oly work well f each pocloud approxmaely ormally drbued. However, f po correpodece bewee he wo pocloud are avalable, a more robu approach would be o drecly mmze he um of he Eucldea dace bewee hee po. h correpod o a lear lea-quare problem ha ca be olved robuly ug he SVD mehod [4]. Baed o he po correpodece, he cro correlao marx M bewee he wo ceered pocloud ca be calculaed, afer whch he egevalue decompoo obaed a follow: M = USV (5) he opmal oluo o he lea-quare problem he defed by roao marx R a: R = UV (6) ad he ralao from arge pocloud o ource pocloud defed by: = c R c (7) C. Ierave Cloe Po Wherea he SVD algorhm drecly olve he lea-quare problem, hereby aumg perfec daa, Bel ad Mc. Kay [5] roduced a mehod ha eravely dregard ouler order o mprove upo he prevou emae of he roao ad ralao parameer. her mehod called ICP ad lluraed cocepually by Fgure 4. Source arge Correpodece SVD raform Ierao Fgure 4. ICP overvew cheme. Oupu Y y y Fgure 3. PCA algme from ource o arge. Fally, he cerod of he arge daa added o each of he raformed coordae o ralae he alged pocloud, X he pu of he ICP algorhm co of a ource pocloud ad a arge pocloud. Po correpodece bewee hee pocloud are defed baed o a eare eghbor approach or a more elaborae cheme ug geomercal feaure or color formao. SVD, a explaed he prevou eco, ued o oba a al emae of he affe raformao marx ha alg boh pocloud. Afer regrao, h whole proce repeaed by removg ouler ad redefg he po correpodece. wo wdely ued ICP vara are he ICP po-o-po ad he ICP po-o-urface algorhm. hee approache oly dffer her defo of po correpodece ad are decrbed more deal he ex eco. Copyrgh (c) IARIA, ISBN:

4 AMBIEN 2014 : he Fourh Ieraoal Coferece o Ambe Compug, Applcao, Servce ad echologe 1) ICP po-o-po: he ICP po-o-po algorhm wa orgally decrbed [1] ad mply oba po correpodece by earchg for he eare eghbor arge po q of a po p j he ource pocloud. he eare eghbor machg defed erm of he Eucldea dace merc: î = arg m p q j 2, (8) where [0, 1,..., N], ad N repree he umber of po he arge pocloud. Smlar o he SVD approach dcued eco IV-B, he roao R ad ralao parameer are emaed by mmzg he quared dace bewee hee correpodg par: ˆR,ˆ = arg m R, N (Rp + ) q 2 (9) =1 ICP he eravely olve (8) ad (9) o mprove upo he emae of he prevou erao. h lluraed by Fgure 5, where urface alged o urface ug ICP erao. Ierao 1 Ierao p 1 p 3 p 2 q 1 q 1 p 1 p 2 p 3 Fgure 5. ICP algme baed o a po o po approach. 2) ICP po-o-urface: Due o he mplc defo of po correpodece, he ICP po-o-po algorhm propoed by [20] raher eve o ouler. Iead of drecly fdg he eare eghbor o a ource po p j he arge pocloud, oe could ake he local eghborhood of a correpodece caddae q o accou o reduce he algorhm evy o oe. he ICP po-o-urface algorhm aume ha he po cloud are locally lear, uch ha he local eghborhood of a po co-plaar. h local urface ca he be defed by ormal vecor, whch obaed a he malle egevecor of he covarace marx of he po ha urroud correpodece caddae q. Iead of drecly mmzg he Eucldea dace bewee correpodg po, we ca he mmze he calar projeco of h dace oo he plaar urface defed by he ormal vecor : ( N ) ˆR,ˆ = arg m ((Rp + ) q ) (10) ˆR,ˆ =1 h lluraed more clearly by Fgure 6. Ierao 1 Ierao p 1 p 3 p 2 q 1 q 1 p 1 p 2 p 3 Fgure 6. ICP algme baed o a po o urface approach. 3) ICP o-lear: Boh he po-o-po ad poo-urface ICP approache defed a dffereable, covex, quared co fuco, reulg a mple lear lea-quare opmzao problem, kow a a L2-opmzao, ha ca be olved umercally ug SVD. However, L2-opmzao kow o be hghly eve o ouler becaue he redual are quared. A approach ha olve h problem kow a L1-opmzao where he um of he abolue value of he redual mmzed ead of he quare. However, he L1 co fuco o-dffereable a he org whch make dffcul o oba he opmal oluo. A a comprome bewee L1 ad L2 opmzao, he o called Huber lo fuco ca be ued a how by (11). he Huber lo fuco quadrac for mall value ad hu behave lke a L2 problem hee cae. For large value however, he lo fuco become lear ad herefore behave lke a L1 co fuco. Moreover, he Huber lo fuco mooh ad dffereable, allowg radoal umercal opmzao mehod o be ued o effcely ravere he earch pace. { e 2 () = 2 /2 f k k 2 (11) /2 f > k where k a emprcally defed hrehold ad he dace meaure. he ICP o-lear algorhm ue he Huber lo fuco ead of a ave quared lo fuco o reduce he fluece of ouler: where ˆR,ˆ = arg m ˆR,ˆ N e 2 () (12) =1 = (Rp ) q (13) o oba he opmal emae ˆR,ˆ (12), he Leveberg- Marquard algorhm (LMA) [6] ued. he LMA mehod a erave procedure mlar o he well kow grade dece ad Gau-Newo algorhm, ha ca quckly fd a local mmum o-lear fuco. 4) Geeralzed ICP: A major dadvaage of he radoal po-o-po ICP algorhm, ha aume ha he ource pocloud ake from a kow geomerc urface ead of beg obaed hrough oy meaureme. However, Copyrgh (c) IARIA, ISBN:

5 AMBIEN 2014 : he Fourh Ieraoal Coferece o Ambe Compug, Applcao, Servce ad echologe due o dcrezao error uually mpoble o oba a perfec po-o-po machg eve afer full covergece of he algorhm. he po-o-urface ICP algorhm relaxe h cora by allowg po offe alog he urface, order o cope wh dcrezao dfferece. However, h approach ll aume ha he ource pocloud repree a dcrezed ample e of a kow geomerc urface model ce offe alog he urface are oly allowed he arge pocloud. o olve h, Segal e al.[7] propoed he Geeralzed ICP algorhm whch perform plae-o-plae machg. hey roduced a probablc erpreao of he mmzao proce uch ha rucural formao from boh he ource pocloud ad he arge pocloud ca be corporaed ealy he opmzao algorhm. Moreover, hey howed ha he radoal po-o-po ad po-o-urface ICP algorhm are merely pecal cae of he Geeralzed ICP framework. Iead of aumg ha he ource pocloud obaed from a kow geomerc urface, Segal e al. aume ha boh he ource pocloud A = {a } ad he arge pocloud B = {b } co of radom ample from a uderlyg ukow pocloud  = {â } ad ˆB = {ˆb }. For he uderlyg ad ukow pocloud  ad ˆB, perfec correpodece ex, wherea h o he cae for he oberved pocloud A ad B, ce each po a ad b aumed o be ampled from a ormal drbuo uch ha a N (â, C A) ad b N (ˆb, C B). he covarace marce CA ad C B are ukow. If boh pocloud would co of deermc ample from kow geomerc model, he boh covarace marce would be zero uch ha he A =  ad B = ˆB. I he followg, le be he affe raformao marx ha defe he mappg from  o ˆB uch ha ˆb = â. If would be kow, we could apply h raformao o he oberved ource pocloud A, ad defe he error o be mmzed a d = b a. Becaue boh a ad b are aumed o be draw from depede ormal drbuo, d whch a lear combao of a ad b, alo draw from a ormal drbuo: d N (ˆb â, C B + C A ) (14) = N (0, C B + C A ) (15) he opmal raformao marx ˆ he he raformao ha mmze he egave log-lkelhood of he oberved error d : ˆ = arg m log (p(d )) = arg m d (C B + C A ) 1 d (16) Segal e al. howed ha boh po-o-po ad po-oplae ICP are pecfc cae of (16), oly dfferg her choce of covarace marce C A ad C B ; If he ource po cloud aumed o be obaed from a kow geomerc urface, C A = 0. Furhermore, f po he arge po cloud are allowed hree degree of freedom, he C B = I. I h cae, (17) reduce o: ˆ = arg m d d = arg m d 2, (17) whch deed exacly he opmzao problem ha olved by he radoal po-o-po ICP algorhm. Smlarly, C A ad C B ca be choe uch ha obag he maxmum lkelhood emaor correpod o mmzg he poo-plae or he plae-o-plae dace bewee boh po cloud. V. RESULS & DISCUSSION I h eco, we llurae he performace dfferece bewee a ave PCA baed approach, a correpodece baed SVD approach, ad he ICP po-o-po regrao approach. o allow for a far comparo, we ue he publcly avalable daae propoed by Pomerlau e al. [21]. Fgure 7 how he machg error ploed aga he umber of erao for he ICP po-o-po algorhm (darkgray) whou pre-algme, ad for he ICP po-o-po algorhm (lgh-gray) where he daa ha bee pre-alged ug he SVD approach. I he laer cae, a mple eareeghbor machg wa ued o defe po correpodece, afer whch he SVD algorhm wa ued o olve he leaquare problem. h reul clearly how he mporace of a rough al algme before applyg he ICP algorhm. Error (cm) # Ierao Fgure 7. Comparo bewee PCA, SVD ad geeral po o po ICP Furhermore, fgure 7 how he reul of a gle SVD baed lea-quare erao, ad he reul obaed ug he PCA baed regrao approach. I clear ha he PCA baed approach yeld he large machg error, due o he fac ha doe o corporae correpodece formao, uch ha h mehod hghly eve o ouler. O he oher had, a mple PCA or SVD baed approach exremely compuaoal effce, wherea he erave ICP cheme ofe oo compuaoally expeve for real-me applcao. However, Fgure 7 how ha covergece ca be reached quckly f a rough al algme avalable. Fally, mpora o oe ha reul of he vara of ICP uch a po-o-plae ad plae-o-plae grealy deped o he pu daa. If he ource pocloud doe o coa much oe, whle he arge pocloud moly mooh ad pece-we plaar, he po-o-plae algorhm ouperform Copyrgh (c) IARIA, ISBN:

6 AMBIEN 2014 : he Fourh Ieraoal Coferece o Ambe Compug, Applcao, Servce ad echologe he radoal po-o-po mehod. O he oher had f he geomerc rucure he cee are moly quadrac or polyomal, he radoal ICP po-o-po algorhm yeld beer reul. Smlarly, f a lo of oe oberved he ource pocloud, ICP plae-o-plae ouperform ICP poo-plae. VI. CONCLUSION I h paper we provded a overvew of x ae-ofhe-ar rgd 3D regrao algorhm commoly ued roboc ad compuer vo. We dcued he mahemacal foudao ha commo o each of hee algorhm ad howed ha each of hem repree dffere approache o olve a commo lea-quare opmzao problem. Furhermore, we ued a publcly avalable daae o compare he reul of hee algorhm ad cocluded ha he reul are exremely daa depede uch ha he choce for a pecfc algorhm hould maly deped o he applcao ad pu daa. [16] S. Savaree, 3D geerc objec caegorzao, localzao ad poe emao, 2007 IEEE 11h Ieraoal Coferece o Compuer Vo. IEEE, 2007, pp [17] W. R. Crum, No-rgd mage regrao: heory ad pracce, Brh Joural of Radology, vol. 77, o. uppl 2, Dec. 2004, pp. S140 S153. [18] J. Kay, Iroduco o Homogeeou raformao & Robo Kemac, Rowa Uvery Compuer Scece Deparme, o. Jauary, 2005, pp [19] B. Draper, W. Yambor, ad J. Beverdge, Aalyzg pca-baed face recogo algorhm: Egevecor eleco ad dace meaure, Emprcal Evaluao Mehod..., 2002, pp [20] K. Low, Lear lea-quare opmzao for po-o-plae cp urface regrao, ech. Rep. February, [21] F. Pomerleau, S. Magea, F. Cola, M. Lu, ad R. Segwar, rackg a deph camera: Parameer explorao for fa ICP, 2011 IEEE/RSJ Ieraoal Coferece o Iellge Robo ad Syem. IEEE, Sep. 2011, pp REFERENCES [1] R. B. Ruu, Semac 3D Objec Map for Everyday Mapulao Huma Lvg Evrome, KI - Külche Iellgez, vol. 24, o. 4, Aug. 2010, pp [2] R. A. Newcombe, A. J. Davo, S. Izad, P. Kohl, O. Hllge, J. Shoo, D. Molyeaux, S. Hodge, D. Km, ad A. Fzgbbo, KecFuo: Real-me dee urface mappg ad rackg, h IEEE Ieraoal Sympoum o Mxed ad Augmeed Realy. IEEE, Oc. 2011, pp [3] C. Kerl, J. Surm, ad D. Cremer, Dee vual SLAM for RGB- D camera, 2013 IEEE/RSJ Ieraoal Coferece o Iellge Robo ad Syem. IEEE, Nov. 2013, pp [4] S. Marde ad J. Guva, Improvg he Performace of ICP for Real- me Applcao ug a Approxmae Neare Neghbour Search, 2012, pp [5] P. J. Bel ad N. D. McKay, Mehod for regrao of 3-D hape, P. S. Scheker, Ed., Apr. 1992, pp [6] S. Fao, U. Caella, ad A. Fuello, Accurae ad Auomac Algme of Rage Surface, 2012 Secod Ieraoal Coferece o 3D Imagg, Modelg, Proceg, Vualzao & ramo. IEEE, Oc. 2012, pp [7] A. V. Segal, D. Haehel, ad S. hru, Geeralzed-ICP, Proceedg of Roboc: Scece ad Syem, Seale, 2009, p. 8. [8] D. Ruecker, L. I. Sooda, C. Haye, D. L. Hll, M. O. Leach, ad D. J. Hawke, Norgd regrao ug free-form deformao: applcao o brea MR mage. IEEE raaco o medcal magg, vol. 18, o. 8, Aug. 1999, pp [Ole]. Avalable: hp:// [9] F. Edre, J. He, N. Egelhard, J. Surm, D. Cremer, ad W. Burgard, A evaluao of he RGB-D SLAM yem, 2012 IEEE Ieraoal Coferece o Roboc ad Auomao, vol. 3, o. c. IEEE, May 2012, pp [10] J. Aula, Y. Pello, J. Salv, ad X. Lladó, he SLAM problem: a urvey. CCIA, 2008, pp [11] P. F. I. N. D. E. Carrera, MADRID RGB-D SLAM Auhor : Jorge García Bueo, o. Ocober, [12] K. Berger, S. Meer, R. Nar, ad D. Koderma, A ae of he ar repor o kec eor eup compuer vo,... ad Deph Imagg. Seor..., [13] J. Sprckerhof ad A. Nücher, A Explc Loop Clog echque for 6D SLAM...., 2009, pp [14] A. Huag ad A. Bachrach, Vual odomery ad mappg for auoomou flgh ug a RGB-D camera, Ieraoal..., 2011, pp [15] M. Ruhke, L. Bo, D. Fox, ad W. Burgard, Compac RGBD Surface Model Baed o Spare Codg. AAAI, Copyrgh (c) IARIA, ISBN: