Registration between Multiple Laser Scanner Data Sets

Transcription

1 24 Regstraton between Multple Laser Scanner Data Sets Fe Deng Wuhan Unversty Chna 1. Introducton Laser scanners provde a three-dmensonal sampled representaton of the surfaces of objects wth generally a very large number of ponts. The spatal resoluton of the data s much hgher than that of conventonal surveyng methods. Snce laser scanners have a lmted feld of vew, t s necessary to collect data from several locatons n order to obtan a complete representaton of an object. These data must be transformed nto a common coordnate system. Ths procedure s called the regstraton of pont clouds. In terms of nput data, regstraton methods can be classfed nto two categores: one s the regstraton of two pont clouds from dfferent scanner locatons, so-called par-wse regstraton (Rusnkewcz & Levoy, 2001), and the other s smultaneous regstraton of multple pont clouds (Pull, 1999; Wllams & Bennamoun, 2001). However, the global regstraton of multple scans s more dffcult because of the large nonlnear search space and the huge number of pont clouds nvolved. Commercal software typcally uses separately scanned markers that can be automatcally dentfed as correspondng ponts. Akca (2003) uses the specal targets attached onto the object(s) as landmarks and ther 3-D coordnates are measured wth a theodolte n a ground coordnate system before the scannng process. Radometrc and geometrc nformaton (shape, sze, and planarty) are used to automatcally fnd these targets n pont clouds by usng cross-correlaton, the dmenson test and the planarty test. Accordng to the automatc regstraton problems, several efforts have been made to avod the use of artfcal markers. One of the most popular methods s the Iteratve Closest Pont (ICP) algorthm developed by Besl & McKay(1992) and Chen & Medon (1992). ICP operates two pont clouds and an estmate of the algnng rgd body transform. It then teratvely refnes the transform by alternatng the steps of choosng correspondng ponts across the pont clouds, and fndng the best rotaton and translaton that mnmzes an error metrc based on the dstance between the correspondng ponts. One key to ths method s to have a good pror algnment. That means, for partally unorganzed and overlappng ponts, f there s lack of good ntal algnment, many other ICP varant don t work well because t becomes very hard to fnd correspondng ponts between the pont clouds. Also, although a consderable amount of work on regstraton of pont clouds from laser scanners, t s dffcult to understand convergence behavor related to dfferent startng condtons, and error metrcs. Many experment showed that the rate of convergence of ICP heavly reles on the choce of the correspondng pont-pars, and the dstance functon.

2 450 Laser Scannng, Theory and Applcatons There are knds of varants of ICP method to enhance the convergence behavor accordng to dfferent error metrcs, and pont selecton strateges. There are two common dstance metrcs. Frst error metrc (Besl, 1992) s the Eucldan dstance between the correspondng ponts, but t s hghly tme consumng due to the exhaustve search for the nearest pont. Another one s the pont-to-plane dstance that descrbed n (Chen,1991, Rusnkewcz & Levoy,2001), whch uses the dstance between a pont and a planar approxmaton of the surface at the correspondng pont. They found the pont-to-plane dstance to perform better than other dstance measures. If there are a good ntal poston estmaton and relatvely low nose, ICP method wth the pont-to-plane metrc has faster convergence than the pontto-pont one. However, when those condtons cannot be guaranteed, the pont-to-plane ICP s prone to fal (Gelfand et al.,2003). The teratve closest compatble pont (ICCP) algorthm has been proposed n order to reduce the search space of the ICP algorthm (Godn et al., 2001). In the ICCP algorthm, the dstance mnmzaton s performed only between the pars of ponts consdered compatble on bass of ther vewpont nvarant attrbutes (curvature, color, normal vector, etc.). Invarant features comng from ponts, lnes and other shapes and objects, moment nvarants can be appled wdely from classfcaton, dentfcaton and matchng tasks. Sharp(2002) presented the feature-based ICP method that also called ICP usng Invarant Feature(ICPIF), whch chooses nearest neghbor correspondences by a dstance metrc that represented a scaled sum of the postonal and feature dstances. Compared wth tradtonal ICP, ICPIE converges to the goal state n fewer teratons, and doesn t need for a user suppled ntal estmate. In order to overcome dfferent pont denstes, nose, and partal overlap, Trummer(2009), extendng an dea known form 2-dmensonal affne pont pattern matchng, presented a non-teratve method to optmally assgn nvarant features that are calculated from the 3-dmentonal surface wthout local fttng or matchng. Compared to Sharp, ths method doesn t use any ntal soluton. As for lne-based and plane-based lterature, Bauer(2004) proposed a method for the coarse algnment of 3D pont clouds usng extracted 3D planes that they both are vsble n each scan, whch leads to reduce the number of unknown transform parameters from sx to three. Reman unknowns can be calculated by an orthogonal rectfcaton process and a smple 2D mage matchng process. Stamos and Allen (2002) llustrated partal task for range-to-range regstraton where conjugate 3D lne features for solvng the transformaton parameters between scans were manually corresponded. Stamos and Leordeanu (2003) developed an automated feature-based regstraton algorthm whch searches lne and plane pars n 3D pont cloud space nstead of 2D ntensty mage space. The par-wse regstratons generate a graph, n whch the nodes are the ndvdual scans and the edges are the transformatons between the scans. Then, the graph algorthm regsters each sngle scan related to a central pvot scan. Habb et al. (2005) utlzed straght-lne segments for regsterng LIDAR data sets and photogrammetrc data sets though. Gruen and Akca (2005) developed the least squares approach tacklng surface and curve matchng for automatc co-regstraton of pont clouds. Hansen (2007) presented a plane-based approach that the pont clouds are frst splt nto a regular raster and made a gradual progress for automatc regstraton. Jan (2005) presented a pont set regstraton usng Gaussan mxture models as a natural and smple way to represent the gven pont sets. Rabban et al. (2007) ntegrated modelng and global regstraton where start out extractng geometrc nformaton for automatc detecton and fttng of smple objects lke planes, spheres, cylnders, and so forth, to regster the scans. In Jaw(2007),an approach for regsterng ground-based LDAR pont clouds usng overlappng

3 Regstraton between Multple Laser Scanner Data Sets 451 scans based on 3D lne features, s presented, where ncludes three major parts: a 3D lne feature extractor, a 3D lne feature matchng mechansm, and a mathematcal model for smultaneously regsterng ground-based pont clouds of mult-scans on a 3D lne feature bass. Flory(2010)llustrated surface fttng and regstraton of pont clouds usng approxmatons of the unsgned dstance functon to B-splne surfaces and pont clouds. Nowadays, most of the laser scanners can supply ntensty nformaton n addton to the Cartesan coordnates for each pont, or an addtonal camera may be used to collect texture. Therefore, further extenson can smultaneously match ntensty nformaton and geometry under a combned estmaton model. Kang (2009) presented an approach to automatc Image-based Regstraton (IBR) that refers to search for correspondng ponts based on the projected panoramc reflectance magery that converted from 3D pont clouds. In Roth (1999), a regstraton method based on matchng the 3-D trangles constructed by 2-D nterest ponts that are extracted from ntensty data of each range mage, was presented. 2. Iteratve Closest Pont (ICP) 2.1 Basc Concepts of ICP The purpose of regstraton s to brng multple mage of the surveyed object n to the same coordnate system so that nformaton from dfferent vews or dfferent sensors can be ntegrated. Let f denote the magng process, I s the mage and O s the surveyed object, we can get: I = f( O) (1) Consderng the currently used surveyng method, such as photogrammetry and laser scannng, we can say that f s an njecton. What we have known s mage fragments of the real world, and the destnaton of regstraton s then fttng all those fragments together. Mathematcally, t s to fnd the relatons between those f s. Concretely, the am of regstraton s to fnd the rgd transformaton T that can brng any par of correspondng ponts ( p, q j ) from the surfaces of two shapes P and Q representng the same pont of the surveyed object nto concdence. The rgd transformaton T s determned by EPQ (, ) = dtpuv ( (, ), q( f( uv, ), guv (, ))) dudv= 0 (2) Ω Where d s a dstance functon used to calculate the dstance between two ponts, assume d s the Eucldan dstance functon, then E( P, Q) = Tp( u, v) q( f ( u, v), g( u, v)) dudv = 0 (3) Ω Ths functon s usually used as the cost functon n regstraton algorthms. For regstraton of pont sets wth pont-to-pont dstance, t can be represented as dscrete form: 2 2 p P, q Q e = Tp q = 0 (4) j j From the dscrete representaton we can drectly get the soluton dea of regstraton problem, fndng correspondng ponts, n fact ths can be treated as an absolute orentaton

4 452 Laser Scannng, Theory and Applcatons problem wthout scalng whch has been well solved by Horn(1997). He used unt quaternon to represent the rotaton whch smplfes ths problem to a lnear one and reduces ths problem to a egenvector problem, the rotaton s estmated from fndng the largest egenvector of a covarance matrx, then translaton can be found by the dfference of the masses of two pont clouds. More generally we can extend ths to other features such as lne segments, planar patches and some even more complex basc geometrc models lke spheres, cylnders and toruses (Rabban, 2007). Regstraton s a chcken-and-egg problem, f correspondences are know an estmaton can be obtaned by mnmzng the error between the correspondences, f an ntal estmaton s known we can generate matches by transformng one pont set to the other. The frst approach s usually used for coarse regstraton and the second s for refnement. The ICP method belongs to the second approach and t s an excellent algorthm for regstraton refnement. Snce the ntroducton of ICP method (Besl & McKay, 1992, Chen & Medon, 1991), t has been the most popular method for algnment of varous 3d shapes wth dfferent geometrc representaton. It s wdely used for regstraton of pont clouds, and there have been many knds of varants of basc ICP algorthm. However the basc concepts or workflow of ICP method s the same. It starts wth two meshes and an ntal estmate of the algnng rgdbody transform, then t teratvely refnes the transform by alternately choosng correspondng ponts n the meshes through the gven ntal estmaton and fndng the best translaton and rotaton that mnmzes an error metrc based on the dstance between them. Intutvely the ICP method chooses the reference pont p and the closest pont q of surface Q as a pont par, that s why t s called teratve closest pont algorthm. The basc workflow of ICP method s as below, Input: model P and Q wth overlappng regon, ntal estmaton of the rgd transformaton T whch transform P to the coordnate system of Q ; Select reference ponts p j on P ; For every reference pont p j,transform the reference pont to the coordnate system of Q wth T, the new pont wll be p j = Tpj ; For every transformed reference pont p j, select the closest pont q on Q whch s closest to p j ; Usng the pont pars ( pj, q j) to calculate a new estmaton of the rgd transform T + 1 Iteratvely repeat ths procedure untl the dfference between the two transformaton T + 1 and T s lttle enough. Rusnkewcz & Levoy(2001) gave a Taxonomy of ICP varants accordng to the methods used n the stages of the ICP method. Salv et al.(2007) gave a survey of recent range mage regstraton methods also nclude some ICP methods. Because the ICP method has to dentfy the closest pont on a model to a reference pont, and thus affect the qualty of the pont pars and the error metrc drectly, varous defntons of closest pont such as pont-topont, pont-to-(tangent) plane and pont-to-projecton were proposed for accuracy or effcency]. As an optmzaton problem, the stablty s very mportant; knds of samplng

5 Regstraton between Multple Laser Scanner Data Sets 453 method, outler detecton method and robust estmate method were proposed for ICP method. In ths part, we wll frst dscuss the usually used pont-to-pont, pont-to-plane and pontto-projecton error metrc and ntroduce some method proposed for the mprovng of stablty of the ICP method. 2.2 Closest pont defnton and fndng As the qualty of algnment obtaned by ths algorthm depends heavly on choosng good pars of correspondng ponts n the two datasets, one of the key problems of ICP method s how to defne the closest pont, t nfluences the convergence performance and speed and accuracy of the algorthm drectly. In order to mprove the ICP method varous varants of ICP method have been developed wth dfferent defnton of closest pont. Rusnkewcz and Levoy s survey about varants of ICP ntroduced a taxonomy of some of these methods. Accordng to hm, these methods can be classfed nto several groups based on ther error metrcs, ncludng drect pont-to-pont method, methods usng normal of the ponts, such as pont-to-(tangent) plane methods. Addtonal nformaton such as range camera nformaton such as pont-to-projecton method and ntensty or colors can be used to reduce the search effort of correspondent pont pars or to elmnate the ambgutes due to nadequate geometrc nformaton on the object surface. All of these methods can be accelerated wth KD-Tree searchng (Smon, 1996), Z-buffer (Benjemaa & Schmtt, 1999) or closest-pont cachng (Smon,1996, Nshno & Ikeuch, 2002). Besl s orgnal ICP method ams at the regstraton of 3d shapes, so he proposed knds of defnton of closest pont for a gven pont on varous geometrc representatons. We focus on the pont set representaton. Let Q be a pont set wth Nq ponts, d s an Eucldean dstance calculator, the dstance of closest pont of Q to p of pont set P equals to the dstance between the closest pont q of Q to the pont p, d( p, Q) = mn d( pq, ) {1,2,, Nq } And the resdual for each par of ponts ( p, q ) s e = Tp q Besl s orgnal work used nave pont-to-pont error metrc, adoptng the Eucldan dstance between correspondng ponts as the error metrc. It belongs to explct method whch has to detect correspondng ponts on the other surface. And the problem s the low convergence speed of the algorthm for certan types of data sets and ntal estmaton. Laser scannng sensors often combned wth mage sensors, t s easy to obtan both the range and color nformaton of the surveyed object. Wek (1997) used ntensty nformaton to detect correspondng ponts between two range mages. Godn et al.(1994) frst proposed teratve closest compatble pont (ICCP) method wth addtonal ntensty nformaton, then adopted ths method wth nvarant computaton of curvatures (Godn et al., 1995), and ntroduced a method for the regstraton of attrbuted range mages (Godn et al., 2001). He gave the dstance between two attrbuted ponts n a (3+m) dmensonal space wth m addtonal attrbutes lke color (m=3). (5) (6)

6 454 Laser Scannng, Theory and Applcatons m x x λ a a = 1 d( pq, ) = ( p q ) + ( p q ) Where p x and q x are postons of the two ponts, p a and q a are the th components of the addtonal attrbutes. Johnson & Kang(1997) took both the dstance and the ntensty or color dfference nto account. He found the closest pont n a space wth sx freedoms, three for coordnates n the Eucldan space, and three for the color space. The dstance between two p p p p p p correspondng pont p wth poston ( x1, x2, x 3) and color ( c1, c2, c 3) and q wth poston q q q q q q ( x1, x2, x3) and color ( c1, c2, c 3) s (7) 1 p q 2 p q 2 p q α p q α p q α p q d( p, q) = [( x x ) + ( x x ) + ( x x ) + ( c c ) + ( c c ) + ( c c ) ] (8) where α = ( α1, α2, α3) are scale factors that wegh the mportance of color aganst the mportance of shape. In order to elmnate the effect of shadng whch nfluence the ntensty of the color. Johnson and Kang employ the YIQ color model whch separate ntensty ( Y ) from hue ( I ) and saturaton( Q ) and make the scale of the Y channel one tenth the scale of the I and Q channels. Let ( c1, c2, c3) = ( y,, q), then α = ( α1, α2, α3) = (0.1,1,1) However the pont-to-pont error metrc doesn t take the surface nformaton nto account, ths pont-pont dstance based error metrc suffers from the nablty to slde overlappng range mages (Nshno & Ikeuch,2002), and may converges to a local mnmum wth a nose data set. Pottman & Hofer(2002) dd a research on squared dstance functon to curves and surfaces, accordng to ther work the pont-to-pont dstance s only good when the two surface are algned wth a long dstance after the ntal transformaton. As we have mentoned, a good ntal estmaton s essental to avod runnng nto a local mnmum poston for ICP regstraton method, that means the dstance between the two surfaces should be close. Pottman and Hofer ndcated that the pont-to-tangent plane dstance s exactly the second order Taylor approxmant of the dstance between the two surfaces. In order to get a better regstraton result, pont-to-plane metrc s wdely used (Chen & Medon 1991; Dora et al.,1997). Chen and Medon employ a lne-surface ntersecton method whch can be subsumed n pont-to-(tangent) plane methods. They treat the ntersecton pont of the lne l passng through the pont p drectng to the normal of the surface P at p as the closest pont. l= { a n ( p a)} p The green ponts ndcate the real poston of the correspondence, the red one s the dentcal pont obtaned from correspondng method. For pont-to-pont metrc, t s the closest pont to p. The calculatng for pont-to-plane metrc s much more complex, we have to get the pont q whch s the ntersecton of the normal vector at p of surface P and the surface Q, then the dstance from the pont p to the tangent plane of Q at pont q as the metrc. The pont-to-projecton metrc can be get easly from the projecton of pont p onto surface Q from the scannng staton of Q. (9)

7 Regstraton between Multple Laser Scanner Data Sets 455 Fg. 1. From left to rght are pont-to-pont pont-to-plane and pont-to-projecton metrc. And the resdual for each par of ponts ( p, q ) s e = ( Tp q ) n p By embeddng the surface nformaton nto the error metrc n ths way, pont-plane dstance metrc based methods tend to be robust aganst local mnma and converge quckly wth an accurate estmaton. However the computaton of pont-plane dstance s too expensve, gven that we have gotten the ntal estmaton, we can take the advantage of the nformaton to accelerate the closest pont fndng process, then pont-to-projecton methods usng vewng drecton to fnd the correspondence are proposed for effcency (Benjemaa & Schmtt, 1999; Neugebauer, 1997; Blas & Levne, 1995 ). The prncpal dea of Blas and Levne s ponts-to-projecton method s to frstly project the pont p backward to a 2D pont p Q on the predefned range mage plane of the destnaton surface scanned at staton O Q, and then p Q s forward projected to the destnaton surface Q from the staton OQ to get q. The obvous drawback of ths method s that the closest pont between the two surfaces obtaned can t represent the closeness of the two surfaces, consequently resultng n bad accuracy. Park & Subbarao (2003) ntroduced the contractve projecton pont algorthm whch take the advantage of both the pont-to-plane metrc s accuracy and pont-to-projecton metrc s effcency. He projects the source pont to the destnaton surface then re-project the projecton pont to the normal vector of the source pont, by teratvely applyng the normal projecton the pont wll converge to the ntersecton pont of pont-to-plane method. As the Fg. 2 showed, frst project p 0 onto a mage plane vewed from the staton O Q, then fnd the ntersecton pont q p 0 of the lne of sght from O Q to p 0 and the surface Q, and project ths pont onto the normal of the pont p 0 of surface P to get the pont p 1. Iteratvely do forward projecton and normal projecton to p we can get the approxmate correspondence of p 0. Assume M Q s the perspectve projecton matrx of vew Q to the mage plane I Q, T Q s the transformaton matrx from the camera coordnate system of vew Q to the world coordnate system, I Q s a 2d mage plane wth respect to the data set Q whch can be treated as a range mage vewed from staton O. Frst back project p 0 onto the mage plane, (10) Q P = M T p q 1 Q Q 0 (11)

8 456 Laser Scannng, Theory and Applcatons Fg. 2. Fndng the closest pont wth the Park and Subbarao s method. (a) (b) (c) (d) (e) (f) Fg. 3. The algnment wth pont-to-pont ICP method. (a),(b)and (c) are ntal transformed wth the ntal estmaton of the transformed used as nput n the ICP algorthm; (d) and (e) are algned wth the pont-to-pont ICP method, (f) s algned wth the pont-to-plane ICP method.

9 Regstraton between Multple Laser Scanner Data Sets 457 Then forward-project the pont P q onto the surface Q, we get pont q p 0. In fact q p 0 s nterpolated from the range mage I Q. Next s the so called normal projecton whch project the pont q onto the normal vector ˆp at p 0 to get the pont p 1, p 0 p ˆ ˆ 1 = p 0 + ( q p 0) p p (12) p0 By teratng the smlar projectons to p 1, p wll converge to the ntersecton pont q s of pont-to-plane method f goes to nfnty. Expermentally ths method s fast for both parwse regstraton and mult-vew regstraton problems. 2.3 Technques for stablty Though we can fnd correspondng ponts through above methods, the qualty of algnment obtaned by those algorthms depend heavly on choosng good pars of correspondng ponts. If the nput datasets are nosed or bad condtoned, the correspondence selecton methods and the outler detecton methods play a very mportant role n the regstraton problem. In fact correspondence selecton and outler detecton essentally mean to the same thng whch keep good matches and elmnate bad matches. Frst, we wll gve some detals of Gelfand et al. s method (Gelfand et al., 2003) to analyze geometrc stablty of pont-to-pane ICP method based on 6x6 co-varance matrxes. By decompose the rgd transformaton T nto rotaton R and translaton t, the resdual of pont-to-plane error metrc can be wrtten as e = ( Tp q ) n = ( Rp + t q ) n = ( r p + t q ) n p p p Where r s a (3 1) vector of rotatons around the x, y, and z axes, and t s the translaton vector. Replace the functor d n formulaton (1) nstead of (13) then we can get k E= (( Rp + t q ) n ) k = 1 = 1 2 = (( p q ) n + r ( p n ) + t n ) 2 T T Gven an ncrement ( Δ r Δt T T ) to the transformaton vector ( r t ), the pont-to-plane dstance wll correspondngly changed by (13) (14) T T p n Δ d = [ Δ r Δt ] n By lnearzng the resdual functons, we wll get the covarance matrx (15) Τ T ( pn 1 1) ( n1) pn 1 1 pn k k C = n1 nk (16) Τ T ( pn k k) ( nk) Formulaton (15) tells us f p n s perpendcular to r and n s perpendcular to t, the dstance to plane wll always be zero, that means the error functon (14) wll not change.

10 458 Laser Scannng, Theory and Applcatons Ths wll cause problems when usng the covarant matrx to calculate the transformaton T T vector ( r t ), because certan types of geometry may lead the matrx to be a sngular one whch means the answer wll not be unque. So Gelfand et al. used the condton number of the covarance matrx as a measure of stablty, and gave some smple shapes below whch may cause problems. Fg. 4. Unstable shapes and the correspondng number and types of nstablty. The orgnal and early ICP methods (Besl & McKay, 1992, Chen & Medon, 1991) usually chose all avalable ponts, some unformly subsample the avalable ponts (Turk, 1994), others use random samplng method (Masuda et al.,1996). If too many ponts are chosen from featureless regons of the data, the algorthm converges slowly, fnds the wrong pose, or even dverges, so color nformaton s also used for pont pars selecton (Wek, 1997). Normal-space samplng s another smple method of usng surface features for selecton (Johnson & Kang, 1997), t frst buckets the ponts accordng to the normal vectors n angular space, then sample unformly across the buckets. Rusnkewcz & Levoy(2001) suggested another Normal-space samplng method whch select ponts wth large normals nstead of unformly samplng. As sldng between datasets can be detected by analyzng the covarance matrx used for error mnmzaton (Guehrng, 2001), the adopton of weghtng methods based on the contrbuton of pont pars to the covarance matrx s reasonable. Dora et al(1997) mproved Chen s method by weghtng the resduals of those pont pars, extended t to an optmal weghted least-squares framework to weaken the contrbuton of the resdual of outlers to the error functon, as a pont-to-plane method, the dervatve of the standard devaton of pont-to-plane dstance s a good choce for the weghtng factor. Smon(1997) teratvely adds and removes pont-pars to provde the best-condtoned covarance matrx, Gelfand et al. brought ths method to the covarance-based samplng method. Assume L and x (=1,,6) are correspondng egenvalues and egenvectors of covarance matrx C, n s the p

11 Regstraton between Multple Laser Scanner Data Sets 459 normal vector at p, and v = [ p np, n ] p. Then, the magntude of v xk represent the error the par of ponts wll brng n. The covarance-based samplng ams to mnmze the sum of ths value to all of chosen pars over the sx egenvector. That s when choosng the nth par we have to guarantee n mn{ V max{ v xk,( k = 1,,6)}} (17) = 1 Methods wth thresholds are also proposed. The dstance thresholder of Schutz et al.(1998) regards the pont pars whose dstance s much greater than the dstance s between the centers of masses of the two pont clouds as outlers, that s f 2 j Tp q > ( c s), then the pont par ( p, q ) s an outler, where c s an emprcal threshold. Assumng the dstances j between correspondng pont pars are dstrbuted as a Gaussan, Zhang(1994) ntroduced a statstcal outler classfer whch examnes the statstcal dstrbuton of unsgned pont par dstances to dynamcally estmate the threshold to dstngush whch pars are outlers. Dalley & Flynn (2002) dd a comparson between orgnal pont-to-pont ICP, pont-to-pont ICP wth Schutz s and Zhang s classfer and pont-to-plane ICP, he found that pont-topont ICP wth Zhang s outler detecton method s sometmes even better than pont-toplane ICP method. Generally the selecton methods of pont pars, the outler detecton methods and threshold methods mprove the stablty of ICP method to certan condtons, ths problem s far from well done, snce no general method has been proposed to sut all of these bad condtons. The ultmate soluton of these problems s to mprove the qualty of the datasets Feature based regstraton The commonly used features for regstraton n 2D mages are feature ponts, whch are easy to fnd wth varous corner pont detecton methods, such as the very popular method Scalenvarant feature transform (SIFT)(Lowe, 2004). Contrarly pont features of pont cloud are hard to detect, nstead lne and plane features whch can be easly extracted are wdely used n feature based regstraton method. Lne features are usually extracted from the ntersecton of plane features, plane features can be easly automatcally extracted from pont clouds wth scan lne or surface growng methods (Vosselman et al.,2004, Stamos, 2001). If we can found the matchng between those features automatcally the regstraton process can be automated wthout ntal estmaton or supply ntal estmaton for other algorthms, ths s very mportant because fne regstraton methods such as ICP usually need ntal estmaton, f we can provde an ntal transformaton to the fne regstraton process, the whole procedure wll be automated. Stamos s group used automatcally extracted lne features to do range-range mage regstraton and range-2d mage regstraton (Stamos & Leordeanu, 2003, Stamos, 2001, Chao & Stamos, 2005), they also proposed a crcular feature based method (Chen & Stamos, 2006). He et al.(2005) ntroduced an nterpretaton tree based regstraton method wth complete plane patches. Von Hansen(2007) grouped surface elements to large planes then adopted a generate-and-test strategy to fnd the transformaton. Dold & Brenner(2006) and Pathak et al.(2010) brought geometrc constrants nto the matchng of plane matches of the plane based regstraton method, and Makada et al.(2006) proposed an extended Gaussan mage based method to

12 460 Laser Scannng, Theory and Applcatons estmate the rotaton automatcally. Jaw & Chuang(2007) ntroduced a framework to ntegrate pont, lne and plane features together, and compared the ntegrated method wth algorthms usng such features separately, he found that the ntegrated method s much more stable than those separated ones. Rabban et al.(2007) goes even far more, he ntegrated the modelng and regstraton together, smultaneously determned the shape and pose parameters of the objects as well as the regstraton parameters. In ths chapter we wll gve the functonal and stochastc models of pont, lne, and plane features based regstraton, and some of ther propertes. 3.1 Pont features Gven a par of pont features ( p, q), Apply a rgd transformaton T wth a 3 3 rotaton R and translaton t = ( t t t ) T, we can get the mathematc model x y z ν = Rp + t q = 0 In ths model pont pars ( p, q) are measurements, R and t are parameters we need to estmate, so ths equaton can be treated as an adjustment of condton equatons wth unknown parameters. To solve ths problem we need at least three pont pars, one for translaton the other two for rotaton. Gven one pont par ( p1, q1), we can fx the pont p 1 wth the pont q 1, then the pont cloud P can rotate about p 1, f another par was known we ( p2, q2) can rotate p 2 to q 2, at ths tme the pont cloud P can rotate about the lne l cross p 1 and p 2, the thrd par ( p3, q3) wll algn the pont cloud P concdent wth Q by rotatng about the lne l and fx p 3 to q 3. There are varous representaton of rotaton, such as Euler angle, ( ϕ, ωκ, ) system, roll-ptchyaw system, rotaton matrx, and quaternon system. Rotaton matrx s the usually used representaton for analyss, but t has nne elements, because there are only three freedoms for a rotaton, there are sx nonlnear condtons between the nne elements to form an orthogonal matrx whch s troublesome n calculaton. The frst three methods represent the rotaton wth three angles; the dfference between them s lttle n calculatng process, so we wll dscuss them together as an angle system. The last quaternon method has been proven very useful n representng rotatons due to several advantages above other representatons; the most mportant one s that t vares contnuously over the unt sphere wthout dscontnuous jumps. The pont feature based method s the specal case n absolute orentaton wthout scalng, Horn [14] adopted quaternon representaton of rotaton nto t and reduced t to a lnear problem. Any rotaton can be represented as a quaternon q = [ q0 q1 q2 q3], as rotaton n 3 R has only three freedom, so the quaternon must be constraned by q = q + q + q + q =. The relaton between the quaternon and the rotaton matrx s (18) 2 2 2q0 + 2q1 1 2qq 1 2 2qq 0 3 2qq qq R = 2q1q2+ 2q0q32q0+ 2q2 1 2q2q3 2q0q qq 1 3 2qq 0 22qq qq 0 12q0+ 2q3 1 Horn found that the matrx (19)

13 Regstraton between Multple Laser Scanner Data Sets 461 Sxx Sxy S xz n T M = pq = Syx Syy Syz (20) = 1 Szx Szy Szz Whose elements are sum of product of matched pont pars contans all the nformaton requred to solve the least square problem. Sxx + Syy + Szz Syz Szy Szx S xz Let N = Syz Szy Sxx Syy Szz Sxy + Syx, the result unt quaternon wll be the Sxy Syx Szx + Sxz Sxx + Syy Szz egenvector correspondng to the most postve egenvalue. Once the rotaton s solved, the translaton can be solved by calculatng the drecton from the mass of the rotated movng pont set to the mass of the fxed pont set. The lnear soluton doesn t take the error of measurements nto account, for better accuracy we wll ntroduce the least square method below. No matter whch representaton s used, by takng the frst-order partal dervatves of Eq. 18 wth respect to the parameters, we can generally lnearze Eq. 18 then adopt a least square method to get ths problem solved. Because the coordnates of the feature ponts are also measurements whch are not accurate, takng ths nto consderaton we can even refne them by addng them to the parameters needed refned and take the frst-order partal dervatves wth respect to them. The ntal value of the transformaton can be obtaned from the lnear dea ntroduced above, then for every par of ponts the general form of the lnearzed functonal model s A V + B x ˆ + e = 0 (21) or or where V s the ncremental parameter vector of the coordnates of the par of ponts, ˆx s the ncremental parameter vector of the parameters of the transformaton, e s the error vector of every par of ponts. Gven n pont pars the functonal model and statstcal model wll be A V + B xˆ + e = 0 (22) 3n 6 6n 1 3n 6or3n 7 6 1or n 3n σ0 3n 3n σ0 3n 3n D = Q = P (23) where σ 0 s the mean error of unt weght along x, y, z drectons for each par of ponts, Q s the covarance matrx, P can be regarded as the weght matrx of each par of ponts whch ndcate the matchng degree along the three drecton, f we assume the weght of all of the drectons of a par of ponts ( p, q) s the same, e.g. w, the weght matrx for each correspondence wll be P = dag( w, w, w ), the matrx P wll be P = dag( P, P,, P n ) (24) 1 2 Apply condton adjustment wth unknown parameters, we can get xˆ = N B N e where 1 T 1 bb aa T T 1 aa, bb aa N = AQA N = B N B (25)

14 462 Laser Scannng, Theory and Applcatons 3.2 Lne features Lne segments are very common n survey especally man-made features, they are more obvous and the matches between lne features are more ntutve. Because the lmtaton of the resoluton of the scanner, we can t fnd accurate pont-to-pont matches n the datasets, the lne feature based method gets out of the hard work of fndng pont-to-pont match because of more accurate and robust lne features. The general expresson of lne s the ntersecton of two plane, however wth such an expresson ths problem can be extended to the plane based method, so we choose sx parameters ( x0 y0 z0 n ) T x ny n z to defne the lne, three ( n n n for the unt vector of the drecton whch has one constrant, the ) T x y z other three (x0 y0 z Τ 0) for poston of the lne. Lnes n x x y y z z n n n 3 R can be represented as = =,( nx + ny + nz = 1) (26) x y z For each lne correspondence, there are two constrants, the frst one s the transformed unt P P P T drecton must be the same, secondly the already known pont ( x0 y0 z 0 ) on the lne feature l P detected from pont set P should be on the correspondng lne lq extracted from pont set Q. n Q = Rn P (27) ' Q Q Q x x x0 y y0 z z0 = =, where xq = y' = Rx Q Q Q Q + t nx ny n z z' As the lne feature correspondences are conjugate, we can get another functon (28) ' P P P x x x0 y y0 z z0 T, where x P y' = = = = R ( xp t ) (29) P P P nx ny n z z ' If we regard n P and n Q as ponts, we can estmate the rotaton wth Horn s method drectly just lke the pont based method, and then the translaton can be also calculated drectly from Eq. 28 and Eq.29. For teratve least square method, the lnearzed functonal model and statstc model are A V + B xˆ + e = 0 (30) 7n 12 12n 1 7n 6or7n 7 6 1or n 7n σ0 7n 7n σ0 7n 7n D = Q = P (31) For lne feature based method, we need at least 2 pars of nondegenerate lne whch are not parallel to get the transformaton solved, gven the frst lne correspondence, we can fx the lne of the movng pont cloud to the correspondng lne of the fxed pont cloud, the movng pont cloud can stll move along ths lne and rotate about ths lne, once the other nonparallel lne correspondence s gven, the movng pont cloud s algned to the fxed one.

15 Regstraton between Multple Laser Scanner Data Sets Plane features Plane s the most common feature n scene, and generally used n regstraton, for t s much more drect and accurate than pont and lne features. Just lke what we have mentoned above, the lne features based method also leads to the plane features based, snce the lne features are usually extracted from the ntersecton of detected planes, that s to say the general expresson of lne feature wth the ntersecton of two plane s more accurate. Each plane can be defned by three ponts or a plane equaton wth four parameters. usually there are numerous pont measurements on each plane, estmatng the functon of the plane and applyng them for the regstraton s much more reasonable. The functon of a plane can be represented as where ( nx, ny, n z) s the unt normal of the plane. nx x + ny y + nz z + d= 0 (32) P P P P For each par of plane match, ( nx, ny, nz, d ) from the movng pont cloud P and Q Q Q Q ( n, n, n, d ) from the fxed pont cloud Q, we can get x y z n Q P Rn = 0 (33) P Q ( P d d + Rn ) t = 0 Just lke the lne feature based method, the rotaton can be also estmated drectly, to get the translaton, we can brng Eq. 33 to Eq.34, then P Q Q d d + n t = 0 Whch s a lnear functon whch can be solved drectly; we can use t to get an approxmate estmaton of the transformaton. The lnearzed functonal model and statstc model of plane based method are 6n 8 8n 1 6n 6or7n 7 6 1or (34) (35) A V + B xˆ + e = 0 (36) n 6n σ0 6n 6n σ0 6n 6n D = Q = P (37) We need at least two nonparallel planes to estmate the rotaton, and from Eq. 34 we can see that we need at least three planes n nondegenerate mode to estmate the translaton. Gven a plane correspondence we can fx these two planes together, then the movng pont cloud can rotate about the norm of the plane and translate on the plane, once the other correspondence s gven the rotaton s determned, but the movng pont cloud can stll translate along the ntersecton lne of the frst two planes, so we need the thrd plane correspondence to get ths resolved. Measurements for each correspondence Mnmal number of correspondences Num of functons for each correspondences Pont based 6(3 for each pont) 3 3 Lne based 12(6 for each lne) 2 7 Plane based 8(4 for eanch plane) 3 6 Table 1. Summary and comparson of pont, lne and plane based regstraton

16 464 Laser Scannng, Theory and Applcatons (a) (b) (c) (d) Fg. 5. The regstraton of ground laser based and arborne laser based pont clouds of the cvl buldng of Purdue Unversty. (a) s the plane patches extracted from obtaned by a ground laser; (b) s the plane patches extracted from obtaned by a arborne laser. There s a great deal of dfference of resoluton between the two pont cloud, the resoluton of ground laser based s at least ten tmes hgher than the arborne laser based one. (c) s the ntal estmaton from the approxmate lnear method; (d) s the refned algnment wth pont-toplane ICP method. 3.4 Automatc matchng of feature We have ntroduced the basc concepts of feature based regstraton, however there s stll a problem, whch s how to automatcally get correspondng features. Pont features are the smallest elements n the 3D space, but they are so unversal wth lttle constrants and nformaton that t s the very dffcult to automatcally fnd pont matches. Lne feature s also very dffcult to fnd pont matches, because the lne are always extracted from the ntersecton of planes, thus the matchng between lne features can be deduced to plane matchng problem. Whle planes have much nformaton, ncludng the plane equaton and the ponts on ths plane, so t can restran the matchng much better than pont and lne features. Most of the automatc feature correspondence fndng method use an exhaustvely traversng method whch takng all of the possble matches nto consderaton wth some methods lke geometry constrants(he et al.,2005), colors or ntensty(rabban et al., 2007), statstc based method(pathak et al.,2010) to cut off those obvous error matches and prune the searchng space. We wll generally ntroduce some of these methods below. In He s work, he proposed a method wth a nterpretaton tree and knds of geometrc constrants to generate plane correspondences. The nterpretaton tree ncludes all of the

17 Regstraton between Multple Laser Scanner Data Sets 465 possble correspondences between two pont sets. The th layer of the nterpretaton tree are all possble features n pont set P correspondng to feature q n pont set Q. The geometrc constrants they ntroduced nclude area constrant, co-feature constrant and two matched feature constrant. The area constrant ensures the correspondng planes have almost the same area, and the co-feature constrant make the angle between a feature and ts father s smlar and ensure the dfference of dstance between the two features wthn a proper threshold. The two matched feature constrant assume the centrods of the correspondng planes are dentcal ponts, then two plane matches s enough for the regstraton; however t can t sut n such condtons where the planes are occluded and ncomplete. But stll we can generalze ths constrant to three matched feature constrant accordng to the property descrbed above, and stop the growng of the branch of the tree whch has more than three matches. Dold added boundary length constrant, boundng box constrant and Mean ntensty value constrant to He s method. Boundary length constrant clams that the length of the boundary derved from the convex hull should be nearly the same, the rato of the edges of the boundng box wth one edge along the longest edge of the boundary s also proposed as an smlarty between two correspondng planes, what s more, ntensty nformaton s also used n Dold s work. Pathak ntroduced a statstc based method; the greatest dfference between ths method to the geometrc based method above s the use of the covarance of the plane parameters and the covarance of the estmated transformaton. The constrant or test used for prunng the searchng space nclude sze smlarty test, gven translaton agreement test, odometry rotaton agreement test, plane patch overlap test, cross angle test and parallel consstency test. The sze smlarty test s acheved by the use of the covarance matrx of the plane parameters whch s proportonal to the number of ponts n the plane. Gven translaton agreement test, odometry rotaton agreement test need the ntal value of the translaton and rotaton parameters whch s not always avalable n practce, plane patch overlap test s to ensure that the estmated relatve pose of the pont sets have overlapped area, the cross angle test s smlar wth the geometrc constrant whch ensure the smlarty of the angle between the correspondences, and the last parallel consstency test really can be classfed to the cross angle test as a specal stuaton where the cross angle should be zero. Sze smlarty test employs a threshold based method, each of the other tests generates a welldesgned dstrbuton, and uses an confdence nterval to determne whether the correspondence s usable or not. Thorough ntroducton and dervaton of ths method can be found n Pathak s work(pathak et al., 2010). Makada et al.(2006) proposed a relable and effcent method whch extended Gaussan mages (EGI)(Horn, 1987). The rotaton estmate s obtaned by exhaustvely traversng the space of rotatons to fnd the one whch maxmzes the correlaton between EGIs. t seems tme consumng, but actually mproves the effcency by the use of the sphercal harmoncs of the Extended Gaussan Image and the rotatonal Fourer transform. Generally, the process s tme-consumng, but by the use of the sphercal harmoncs of the Extended Gaussan Image and the rotatonal Fourer transform come up wth by Makada, the effcency s mproved remarkably. Once the rotaton s estmated, the translaton can also be estmated by maxmzng the correlaton between two pont sets. Another specal method proposed by Ager et al.(2008) adopted the nvarablty of certan ratos under affne transformaton, and hence rgd transformaton. Ths method extract all sets of coplanar 4-ponts from a pont set that are approxmately congruently related by

18 466 Laser Scannng, Theory and Applcatons rgd transforms to a gven planar 4-ponts, and then test f the conjugate four-ponts satsfy the nvarablty of the such ratos. Fg. 6. e s the ntermedate pont e of the four-ponts {a,b,c,d}, the ratos r 1 and r 2 s nvarant under rgd transformaton. 4. Least square 3D surface matchng The Least Squares Matchng(LSM) concept had been developed n parallel by Gruen (1984, 1985), Ackermann (1984) and Pertl (1984) for mage matchng whch has been wdely used n Photogrammetry due to ts hgh level of flexblty, powerful mathematcal model and ts hgh accuracy. Gruen and Akca(2005) ndcated that f 3D pont clouds derved by any devce or method represent an object surface, the problem should be defned as a surface matchng problem nstead of the 3D pont cloud matchng, and generalzed the Least Squares (LS) mage matchng method to sut the surface matchng msson. Ths method matches one or more 3D search surfaces to a 3D template surface through the mnmzng of the sum of squares of the Eucldean dstances between the surfaces. The unknown parameters are treated as stochastc quanttes n ths model wth pror weghts whch can be used to elmnate gross erroneous and outlers, and ths can mprove the estmaton very much. The unknown parameters of the transformaton are estmated by the use of the Generalzed Gauss Markoff model of least squares. Because most of the pont clouds n applcaton just represent the surface of the scene, many regstraton mssons can be treated as surface matchng tasks. In ths part we wll gve an ntroducton of the mathematcal model of Least Square 3D surface matchng whch can be used for pont cloud regstraton. 4.1 Mathematcal model Each surface can be represented of a functon of three bases of the 3D world. For generalzaton the conjugate overlappng regons of the scene n the left and rght surface can be represented as f ( xyz,, ) and gxyz (,, ) no matter the representaton of the surface s pont cloud, trangle mesh, or any other methods. The msson s to make the two surfaces dentcal to each other, that s f( x, y, z) = g( x, y, z) (38) Assume the errors caused by the sensor, the envronment and the measure method are random errors, we can get the observaton functon as

19 Regstraton between Multple Laser Scanner Data Sets 467 f ( xyz,, ) exyz (,, ) = gxyz (,, ) (39) The sum of squares of the Eucldean dstances between the template and the search surface elements can be used as the goal functon of the least square mnmzaton. 2 d = mn (40) Though the relaton between two pont clouds usually s a rgd transformaton wthout scalng, Gruen and Akca use a seven-parameter smlarty transformaton to express the relatonshp of the conjugate surfaces. However the sole and core even the representaton of ths method wll not change, the only dfference s the parameter space. Addng a scalng parameter to the rgd transformaton, the smlarty transformaton wll be x t x r11 r12 r13 x0 y = t + srx = t + s r r r y 0 y z t r z 31 r32 r 33 z 0 The formulaton (39) can be lnearzed by Taylor expanson g ( x, y, z) g ( x, y, z) g ( x, y, z) f ( xyz,, ) exyz (,, ) = g( xyz,, ) + dx+ dy+ dz x y z x x z wth dx = dp, dz = dp, dz = dp p p p (41) (42) (43) Where p= [ t, t, t, s, ϕ, ωκ, ] T s the parameter vector, get Eq. 41, 42 and 43 together we wll x y z obtan the lnearzed observaton functons. exyz (,, ) = gdt + gdt + gdt + ( ga + ga + ga ) dm x x y y y y x 10 y 20 y 30 = ( g a + g a + g a ) dϕ + ( g a + g a + g a ) dω x 11 y 21 y 31 x 12 y 22 y 32 = ( ga + ga + ga ) dκ x 13 y 23 y 33 (44) Then the general form of the observaton model and the statstcal model wll be e= Ax l (45) σ0 D= σ Q= P (46) Untl ths step, we can say that t s almost the same wth the pont-to-pont method, or pont-to-pont ICP because t also needs to fnd the correspondences wth the ntal estmaton, and then teratvely mprove the estmaton of the transformaton. To accelerate the searchng of closest pont, Akca and Gruen(2006) proposed an boxng structure, whch parttons the search space nto boxes, and correspondence s searched only n the box contanng the pont and ts neghbors. What makes ths method dfferent from the ICP method s that the unknown transformaton parameters are treated as stochastc quanttes usng proper a pror weghts.

20 468 Laser Scannng, Theory and Applcatons e = Ix l (47) b b σ0 b σ0 b b D = Q = P (48) where I s an dentty matrx, l b s a fcttous observaton vector for the system parameters. The ncremental vector and the standard devaton of the parameters can be got by T 1 T xˆ ( A PA Pb) ( A Pl Pbl b) = + + (49) 2 T T ˆ σ ˆ ˆ 0 = ( v Pv+ vbpbvb)/ r, where v= Ax l, vb = Ix lb (50) Generally the contrbuton of ths method s the generalzed mathematcal model whch can sut to any knd of representaton of the surface and the method of treatng the unknown parameters as stochastc quanttes whch establshed the control of the estmatng of the parameters. 5. References Ackermann, F., Dgtal mage correlaton: performance and potental applcaton n photogrammetry. Photogrammetrc Record, 11 (64), Ager, D., N. J. Mtra and D. Cohen-Or, 2008, 4-ponts Congruent Sets for Robust Surface Regstraton, ACM Transactons on Graphcs, vol.27,3, pp.1-10 Akca, Devrm. 2003, FULL AUTOMATIC REGISTRATION OF LASER SCANNER POINT CLOUDS, ETH, Swss Federal Insttute of Technology Zurch, Insttute of Geodesy and Photogrammetry, vol.1, pp Akca, D. and A. Gruen, Fast correspondence search for 3D surface matchng. ETH, Edgenösssche Technsche Hochschule Zürch, Insttute of Geodesy and Photogrammetry. Bauer, J., K. Karner, A. Klaus, R. Perko, 2004, Robust Range Image Regstraton usng a Common Plane, Proceedngs of 2004 WSCG. Benjemaa, R., Schmtt, F., Fast global regstraton of 3D sampled surface usng a multz-buffer technque. Image and Vson Computng 17, pp Bentley, J.L. Multdmensonal bnary search trees used for assocatve searchng. Comm. of the ACM 1975, 18(9), Besl, P.J., McKay, N.D., A method for regstraton of 3-D shapes. IEEE Transactons on Pattern Analyss and Machne Intellgence 14 (2), Blas, G. and M. Levne, 1995, Regsterng Multvew Range Datato Create 3D Computer Objects, Trans. PAMI, Vol. 17, No. 8. Chen, Y. and Medon, G. 1991, Object Modelng by Regstraton of Multple Range Images, Proc.IEEE Conf. on Robotcs and Automaton. Chen, Y. and Medon, G., Object Modelng by Regstraton of Multple Range Images,Image and Vson Computng, 10(3), pp Chen Y., Y.Shen, D. Lu. A Smplfed Model of Three Dmensonal-Datum Transformaton Adapted to Bg Rotaton Angle, Geomantc and Informaton Scence of Wuhan Unverst, 2004,12,pp:

21 Regstraton between Multple Laser Scanner Data Sets 469 Dalley, G. and P. Flynn, 2002, Par-wse range mage regstraton: a study n outler classfcaton, Comput. Vs. Image Und, 87 (1 3), pp Dold, C. and C. Brenner, 2006, Regstraton of terrestral laser scannng data usng planar patches and mage data, Internatonal Archves of Photogrammetry and Remote Sensng, pp Dora, C., Weng, J. & Jan, A.K Optmal regstraton of object vews usng range data. IEEE Trans.on Pattern Analyss and Machne Intellgence 19(10), pp Flory, S. and M. Hofer, 2010,Surface Fttng and Regstraton of Pont Clouds usng Approxmatons of the a Unsgned Dstance Functon, Computer Aded Geometrc Desgn, Vol.27(1), pp:66-77 Gelfand, N.; Ikemoto, L.; Rusnkewcz, S.; Levoy, M., 2003, Geometrcally stable samplng for the ICP algorthm, 3-D Dgtal Imagng and Modelng(3DIM). Proceedngs. Fourth Internatonal Conference on 3D Dgtal Imagng and Modelng, pp Chao, C. and Stamos, I., 2005, Sem-Automatc Range to Range Regstraton: A Feature- Based Method. In Proceedngs of the Ffth nternatonal Conference on 3-D Dgtal Imagng and Modelng (June 13-16, 2005), 3DIM. IEEE Computer Socety, Washngton, DC, pp Chen, C.C. and I. Stamos, 2006, Range Image Regstraton Based on Crcular Features, 3DPVT, pp Godn, G., D. Laurendeau, R. Bergevn, A Method for the Regstraton of Attrbuted Range Images. In: Proc. of Thrd Int. Conference on 3D Dgtal Imagng and Modelng, Quebec, pp Godn,G., M. Roux and R. Barbeau, 1994, Three-dmensonal regstraton usng range and ntensty nformaton, Proc. SPIE Vdeonetrcs III, vol. 2350, pp Godn, G. and P. Boulanger, 1995, Range mage regstraton through nvarant computaton of curvature, Proc. ISPRS Workshop From Pxels to Sequences, Zurch, Swtzerland, pp Gruen, A., Adaptve least squares correlaton concept and frst results. Intermedate Research Project Report to Heleva Assocates, Inc. Oho State Unversty, Columbus, Oho, pp Gruen, A., Adaptve least squares correlaton: a powerful mage matchng technque. South Afrcan Journal of Photogrammetry, Remote Sensng and Cartography, 14 (3), Gruen A. and D. Akca, 2005, Least squares 3D surface and curve matchng, ISPRS Journal of Photogrammetry & Remote Sensng 59 (2005) Guehrng J., 2001, Relable 3D surface acquston, regstraton and valdaton usng statstcal error models. Proc. 3DIM. Habb, A., Mwafag, G., Mchel, M., and Al-Ruzouq, R., Photogrammetrc and LIDAR Data Regstraton Usng Lnear Features, Photogrammetrc Engneerng & Remote Sensng, Vol. 71, No. 6, pp Hansen, V. W., Regstraton of Aga Sanmarna LIDAR Data Usng Surface Elements, ISPRS Journal ofphotogrammetry and Remote Sensng. He, W., Ma, W. and Zha, H., Automatc regstraton of range mages based on correspondence of complete plane patches, Proceedngs of the Fth Internatonal

22 470 Laser Scannng, Theory and Applcatons Conference on 3-D Dgtal Imagng and Modelng, Ottawa, Ontaro, Canada, pp Horn, B.K.P., 1987, Closed-form Soluton of Absolute Orentaton usng Unt Quaternons, Journal of the Optcal Socety A, 4, pp Horn, B. K. P., 1987 Extended gaussan mages, IEEE, pp Jaw, J.J., and T.Y. Chuang, Regstraton of LIDAR Pont Clouds by means of 3D Lne Features, JCIE Journal of the Chnese Insttute of Engneers. Jan B. and B. C. Vemur, 2005, A Robust Algorthm for Pont Set Regstraton Usng Mxture of Gaussans, Tenth IEEE Internatonal Conference on Computer Vson (ICCV'05) Vol. 2, Bejng, Chna,October 17-October 20 Johnson, A. and Hebert, M., 1997, Surface Regstraton by Matchng Orented Ponts, Proc. 3DIM. Johnson, A. and S. Kang, 1997, Regstraton and Integraton of Textured 3-D Data, Proc. 3DIM. Kang, Z.; Zlatanova, S. Automatc regstraton of terrestral scan data based on matchng correspondng ponts from reflectvty mages, Proceedng of 2007 Urban Remote Sensng Jont Event, Pars, France, Aprl, 2007,pp Kang, Z.; Zlatanova, S.; Gorte, B. Automatc regstraton of terrestral scannng data based on regstered magery, Proceedng of 2007 FIG Workng Wee; Hong Kong SAR, Chna, May, Kang, Z.; Zlatanova, S. A new pont matchng algorthm for panoramc reflectance mages. Proc of the 5th Internatonal Symposum on Multspectral Image Processng and Pattern Recognton (MIPPR07). Wuhan, Chna, November, 2007, pp F Kang, Z., J. L, L. Zhang, Q. Zhao, and S. Zlatanova, 2009,Automatc regstraton of terrestral laser scannng pont clouds usng panoramc reflectance mages, Sensors, 2009,9, pp: , do: /s Lowe, D. G., 2004, Dstnctve Image Features from Scale-Invarant Keyponts, Internatonal Journal of Computer Vson, 60, 2, pp Masuda, T., K. Sakaue, and N.Yokoya, 1996, Regstraton and Integraton of Multple Range Images for 3-D Model Constructon, Proc. CVPR Makada, A., A. IV Patterson, and K. Danlds, 2006, Fully automatc regstraton of 3d pont clouds. In CVPR 06: Proceedngs of the 2006 IEEE Computer Socety Conference on Computer Vson and Pattern Recognton, pp Neugebauer, P., 1997, Geometrcal clonng of 3d objects va smultaneous regstraton of multple range mages, In Proc. Int. Conf. on Shape Modelng and Applcaton, pp Nshno, K., K. Ikeuch, Robust smultaneous regstraton of multple range mages, The 5th Asan Conference on Computer Vson (ACCV2002), pp Park, S. and M.Subbarao, An accurate and fast pont-to-plane regstraton technque. Pattern Recogn. Lett. 24, 16, pp Pathak,K., A. Brk, N. Vaskevcus and J. Poppnga. 2010, Fast regstraton based on nosy planes wth unknown correspondences for 3-d mappng. IEEE, 26, pp Pertl, A., Dgtal mage correlaton wth the analytcal plotter Plancomp C-100. Internatonal Archves of Photogrammetry and Remote Sensng, 25 (3B),

23 Regstraton between Multple Laser Scanner Data Sets 471 Pottman, H. and M. Hofer., 2002, Geometry of the squared dstance functon to curves and surfaces. Venna Insttute of Technology Techncal Report No.90. Pull, K., Multvew regstraton for large data sets. Proceedngs of 3-D Dgtal Imagng and Modellng (3DIM), pp Rabban T., S. Djkman, F. Heuvel, and G. Vosselman, An Integrated Approach for Modellng and Global Regstraton of Pont Clouds, ISPRS journal of Photogrammetry and Remote Sensng, Vol. 61, pp Roth, G., Regstraton two Overlappng Range Images, Proc. of Second Int. Conference on 3D Dgtal Imagng and Modelng, Ottawa, pp Rusnkewcz, S., Levoy, M., Effcent varant of the ICP algorthm. Proceedngs of 3-D Dgtal Imagng and Modellng (3DIM), pp Salv, J., C. Matabosch, D. Fof, and Forest, A revew of recent range mage regstraton methods wth accuracy evaluaton. Image Vson Comput, 25, pp Schutz,C., T. Jost and H. Hugl, 1998, Sem-automatc 3d object dgtzng system usng range mages, n: Proceedngs of the Thrd Asan Conference on Computer Vson, vol. 1, pp Sharp, G., S. Lee, and D. Wehe. ICP regstraton usng nvarant features. IEEE Transactons on Pattern Analyss and Machne Intellgence, 24(1):90 102, Smon, D. A., 1996, Fast and Accurate Shape-Based Regstraton, Ph.D. Dssertaton, Carnege Mellon Unversty. Stamos, I., 2001, Geometry and Texture Recovery of Scenes of Large Scale: Integraton of Range and Intensty Sensng. Doctoral Thess.a Stamos, I. and M. Leordeanu, Automated Feature-based Range Regstraton of Urban Scenes of Large Scale, Proceedngs of IEEE Computer Socety Conference on Computer Vson and Pattern Recognton, Vol. 2, pp Stamos, I. and P.K. Allen, Geometry and Texture Recovery of Scenes of Large Scale, Computer Vson and Image Understandng, Vol. 88, No. 2, pp Trummer, M., H. Suesse, and J. Denzler, 2009 Coarse Regstraton of 3D Surface Trangulatons Based on Moment Invarants wth Applcatons to Object Algnment and Identfcaton, IEEE Internatonal Conerence on Computer Vson (ICCV) 2009, pp: Tuhn K. Snha, Davd M. Cash, Robert J. Wel, Robert L. Galloway, and Mchael I. Mga, 2002,Cortcal Surface Regstraton Usng Texture Mapped Pont Clouds and Mutual Informaton, Lecture Notes n Computer Scence: Medcal Image Computng and Computer-Asssted Interventon - MICCAI Turk, G. and Levoy, M. 1994, Zppered Polygon Meshes from Range Images, Proc. SIGGRAPH Vosselman,G.,Gorte,B.G.H., Sthole,G., Rabban,T., 2004, Recgnsng structure n laser scanner pont clouds. The nternatonal Arhves of Photogrammetry, Remote Sensng and Spatal Informaton Sences, vol.46,part8/w2, pp Wek, S Regstraton of 3-D partal surface models usng lumnance and depth nformaton. Proc.of IEEE Int. Conf. on 3DIM: , Ottawa, pp Wllams, J., Bennamoun, M., Smultaneous regstraton of multple correspondng pont sets. Computer Vson and Image Understandng 81 (1),

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25 Laser Scannng, Theory and Applcatons Edted by Prof. Chau-Chang Wang ISBN Hard cover, 566 pages Publsher InTech Publshed onlne 26, Aprl, 2011 Publshed n prnt edton Aprl, 2011 Ever snce the nventon of laser by Schawlow and Townes n 1958, varous nnovatve deas of laser-based applcatons emerge very year. At the same tme, scentsts and engneers keep on mprovng laser's power densty, sze, and cost whch patch up the gap between theores and mplementatons. More mportantly, our everyday lfe s changed and nfluenced by lasers even though we may not be fully aware of ts exstence. For example, t s there n cross-contnent phone calls, prce tag scannng n supermarkets, ponters n the classrooms, prnters n the offces, accurate metal cuttng n machne shops, etc. In ths volume, we focus the recent developments related to laser scannng, a very powerful technque used n features detecton and measurement. We nvted researchers who do fundamental works n laser scannng theores or apply the prncples of laser scannng to tackle problems encountered n medcne, geodesc survey, bology and archaeology. Twenty-eght chapters contrbuted by authors around the world to consttute ths comprehensve book. How to reference In order to correctly reference ths scholarly work, feel free to copy and paste the followng: Fe Deng (2011). Regstraton between Multple Laser Scanner Data Sets, Laser Scannng, Theory and Applcatons, Prof. Chau-Chang Wang (Ed.), ISBN: , InTech, Avalable from: InTech Europe Unversty Campus STeP R Slavka Krautzeka 83/A Rjeka, Croata Phone: +385 (51) Fax: +385 (51) InTech Chna Unt 405, Offce Block, Hotel Equatoral Shangha No.65, Yan An Road (West), Shangha, , Chna Phone: Fax: