SDF Tracker: A Parallel Algorithm for On-line Pose Estimation and Scene Reconstruction From Depth Images

Transcription

1 SDF Tracker: A Parallel Algorthm for On-lne Pose Estmaton and Scene Reconstructon From Depth Images Danel R. Canelhas, Todor Stoyanov, Achm J. Llenthal Center of Appled Autonomous Sensor Systems (AASS), Örebro Unversty, Sweden Abstract Ego-moton estmaton and envronment mappng are two recurrng problems n the feld of robotcs. In ths work we propose a smple on-lne method for trackng the pose of a depth camera n sx degrees of freedom and smultaneously mantanng an updated 3D map, represented as a truncated sgned dstance functon. The dstance functon representaton mplctly encodes surfaces n 3D-space and s used drectly to defne a cost functon for accurate regstraton of new data. The proposed algorthm s hghly parallel and acheves good accuracy compared to state of the art methods. It s sutable for reconstructng sngle household tems, workspace envronments and small rooms at near real-tme rates, makng t practcal for use on modern CPU hardware. I. INTRODUCTION Work has been done n recent years to leverage the power of parallel hardware archtectures to produce practcal realtme solutons for detaled and accurate scene reconstructon (e.g. [1] ). These methods have the potental to open new doors to robotc applcatons n whch carefully planned nteracton wth the physcal envronment s necessary. The benefts ganed from the use of parallel computatonal hardware depend on the data structure used to represent the envronment and the methods used to update and mantan t. In ths paper we present a hghly parallel algorthm for camera pose-estmaton and scene reconstructon, made possble by usng a dstance functon as the representaton of choce. We mplement a truncated sgned dstance functon (TSDF) as an mplct functon defned over a 3D space by means of dscrete samples on a cubc lattce (also referred to as voxels). At any pont n space, the functon evaluates to a scalar value that represents the sgned dstance of that pont to the nearest surface n the envronment. Evdently, closer to a surface, the absolute dstance returned by the functon decreases. The sgned part of the returned value ndcates f a pont s behnd (negatve) or n front (postve) of a surface. Thus the TSDF provdes a means for dstngushng between ponts nsde and outsde of objects. More detal on the TSDF s gven n Secton II. The motvaton for usng a TSDF as a 3D representaton n our applcaton s that t provdes an accurate reconstructon of surfaces, whle smultaneously provdng a metrc for the msalgnment of new data respectve to prevously observed parts of the envronment and encodes the approxmate gradent drecton towards the closest surface. The TSDF representaton s useful to more general robotc applcatons, snce the values contaned n the voxels can be used to quckly and accurately compute nformaton such as surface poston, orentaton and curvature. Such features may be relevant to crtcal robotc tasks e.g., grasp plannng, navgaton, object detecton and collson avodance [2]. In ths artcle, we propose a 6 DoF ego-moton estmaton system that uses depth mages as nput to mantan an updated 3D map of the envronment whle smultaneously trackng the camera pose. The proposed algorthm s conceptually smple and trvally parallelzed. The map s updated on-lne and fuses multple measurements nto a sngle consstent model, averagng out nose assocated wth the nput. We make avalable an open-source reference mplementaton 1 usng OpenMP 2 as a package for the Robot Operatng System (ROS) [3] and provde quanttatve results on a well-known RGB-D (color and depth mages) dataset wth known ground truth [4]. Ths work s related to the Knect Fuson algorthm proposed by Newcombe et al. [5] by operatng n the same problem doman.e. that of smultaneous pose trackng of a structured lght sensor and data fuson nto a consstent denosed model represented as a TSDF. The core of our data regstraton algorthm s qute dfferent however and care should be taken not to confuse the two. The proposed method operates drectly n the TSDF for the purpose of regstraton, rather than usng t to obtan denosed depth mages from a vrtual sensor, lookng at the model. We argue that ths leads to some benefts n the regstraton step. For nstance, snce the proposed method uses TSDF representaton drectly to regster new measurements, t does not depend on the defnton of explct correspondences between vertces computed from depth mages. Snce new data s regstered drectly to the model, the latter s the same, regardless of vewpont and does not suffer from occlusons nherent to perspectve projectons. The proposed algorthm, lke other dense methods, uses all the avalable data from each nput depth mage. It does so n a parallel fashon, allowng for both accurate regstraton and hgh qualty scene reconstructon at an update frequency of up to 16 Hz (dependng on the amount of memory used to represent the reconstructed volume), runnng on a laptop computer usng a quad-core CPU. The accuracy of the envronment mappng and ego-moton 1 Moble Robotcs and Olfacton Lab at the Center for Appled Autonomousls Sensor Systems (AASS) at Örebro Unversty, Sweden. ROS packages from the AASS Research Center at Örebro Unversty the OpenMP Archtecture Revew Board, The OpenMP API specfcaton for parallel programmng, (accessed 2012/09)

2 estmaton s comparable to current dense reconstructon methods employng commodty structured lght sensors. We show that even though our algorthm may accumulate drft over tme, t compares well to modern SLAM-based methods that operate on sparse features. Furthermore, our algorthm runs near real-tme on a system wthout a GPU. The next secton provdes a revew of the TSDF as a 3D representaton, followed by detals of the camera pose estmaton algorthm. We present results on an RGB-D benchmark for hand-held SLAM algorthms and fnalze wth a few concludng remarks. II. 3D REPRESENTATION The propertes of and methods related to the 3D TSDF representaton are very well documented n the work of Curless and Levoy [6] and more recently revewed n the work of Newcombe et al. [5]. For ths reason we wll only brefly defne the representaton, for the convenence of our readers, and refer to these publcatons for further detals. The representaton used n ths work s a TSDF, based on projectve measurements. The TSDF s a voxel-based data structure (a 2D llustraton s provded n Fg. 1, and a real example gven n Fg. 2) n whch each cell n a 3D grd stores an approxmate dstance to the nearest surface. For any gven voxel, ts dstance value s computed as the dfference n depth between ts coordnates and the coordnates of the nearest measured surface pont. The comparson s made n the frame of reference of the camera. The resultng dstance assumes postve values for voxels located n the free space observed n front of surfaces and negatve values for voxels that are stuated behnd observed surfaces. The dfference n sgn s then used to defne a regon of zero dstance, whch mplctly represents the actual surface of objects. The dstance values are truncated at pre-defned postve and negatve lmts, D max and D mn, respectvely. The truncaton s justfed because t lmts the mpact of new observatons n the envronment to requre only local changes. Furthermore, a true sgned dstance functon cannot be computed wth certanty from partal observatons, snce there s no nformaton as to how far the negatve sde should extend on the unseen sde of surfaces. To accurately represent a surface usng a TSDF, at least one non-truncated voxel s needed on both sdes of a surface. In ths non-truncated regon t s then possble to nterpolate between a negatve (nsde) and postve (outsde) voxel to obtan an estmated locaton for the surface (represented by zero). However, n ths work the TSDF s not only used to represent the surface, but also drectly model the error of a gven pont wth respect to the current model, and provde a gradent towards the surface. To estmate ths gradent, our method typcally requres the number of nontruncated voxels on ether sde to be larger than strctly needed for surface representaton. The thckness of ths nontruncated regon needs to be related to the amount of physcal camera movement that s expected between frames. It s mportant to note that the thckness on ether sde need not be symmetrc and should preferably be kept small on Fg. 1. Ths fgure llustrates how a TSDF s generated from a depth mage. The coordnates of each voxel are projected nto the mage plane and ts depth (or z-value ) relatve to the camera s compared wth that of the nearest pxel n the depth mage. The result of ths comparson s wrtten nto the voxel. Postve (green) values are truncated to a pre-defned maxmum. Negatve (red) values less than a pre-defned mnmum are not stored. Whte cells are those that have not yet been observed by the sensor. the negatve sde, snce t sets a lmt for the mnmum dmensons of reconstructed objects. To mprove the qualty of the surface reconstructon and provde some robustness to outlers, each voxel stores not only a sgned dstance, but also a weght w that relates how often or wth how much certanty the value nsde the voxel has been estmated. As been suggested by the cted publcatons, a unform weght can be used, producng a rollng average, or be related to an error model of the depth camera. In ether case, the update of the weght and dstance values s done as follows [6], D n (x) n+1 = D n(x)w n (x) + ˆD n (x)ŵ(x), (1) w(x) n + ŵ(x) w(x) n+1 = mn(w(x) n + ŵ(x), w max ), (2) where D n (x) n+1 s the updated dstance at locaton x based on the estmate ˆD n (x). The weght w(x) n s the accumulated sum (up to a lmt w max ) of weghts ŵ(x), assocated wth the dstances estmated for a partcular poston n the voxel grd. Lmtng the value of w allows for the model to change n order to represent new confguratons of the envronment and react robustly to dynamc elements. The volume update can be effcently done n parallel, snce no connectvty s assumed between voxels. A. Notaton III. ESTIMATION OF CAMERA POSE A formal defnton of a depth mage s as a scalar functon z n (M) that assgns a depth to all pxels of each of the n = 0... N depth mages n a vdeo stream. The doman of z n s defned on the 2D mage plane M R 2. Formally, z n : M R +.

3 dot to denote a vector wrtten n homogeneous coordnates, e.g., u = [ u 1 ], defnng an optmzaton objectve as, Fg. 2. Left: 3D Reconstructon Rght: 2D slce through the TSDF, red/green ndcate negatve/postve sgn, brghtness ndcate absolute value (brghter s hgher). Unseen areas are marked as whte. Gven z n (M), and knowng the parameters of the depth camera, 3D surface ponts can be computed. Let s n (M) be the projecton of a depth mage pxel nto 3D. Formally, s n : R 2 R R 3, s n (m) = m 1 c x f x z n (m) m 2 c y f y z n (m) z n (m), (3) where m = (m 1, m 2 ) M represents an mage pxel and c x, c y, f x, f y R represent the prncpal pont and focal lengths of a pnhole camera model. The defnton of a 3D rgd-body transformaton, T R 4 4 SE(3) used n regstraton of ponts s, [ ] R t T = 0 T (4) 1 where R R 3 3 SO(3) s a 3D rotaton matrx, t R 3 s a translaton vector and 0 T s a zero vector of approprate dmensons. Close to T = I, wth I beng a 4 4 Identty matrx, we can accurately represent T as T = e ˆ, where e s the matrx exponental functon, R 6 se 3 s a vector representng angular and lnear veloctes,.e. = [ ω 1 ω 2 ω 3 v 1 v 2 v 3 ] T (5) and ˆ R 4 4 s the matrx, ˆ = (6) Wth these defntons, T can be expressed as a functon of, as long as t remans n the neghbourhood of = 0. B. Objectve Functon In order to defne an approprate objectve functon, we examne a measure of error as the sum of squared dstances between correspondng ponts n 3D, from two consecutve mages,.e., E = s n (m ) s n+1 (m ) 2. (7) To brng these ponts nto algnment, a transformaton s appled to one of the two sets. For convenence we wll use a mn. ṡ n (m ) T ()ṡ n+1 (m ) 2. (8) Let D n (x) be the TSDF, generated from the past n depth mages, as descrbed n Secton II (for ths work the updatng of D n (x) s done through a smple rollng average over past measurements). Usng, D n (x), the above objectve can be approxmated as, mn. D n (T ()ṡ n+1 (m )) 2. (9) In other words, we are mnmzng the sum of squared pontto-model dstances, over the space of transformatons of the ponts relatve to the model. C. Soluton We obtan the soluton of the optmzaton problem defned at (9) by lnearzng the objectve functon by means of a frst-order power-seres approxmaton around = 0,.e., D n (T ()ṡ n+1 (m )) D n (T ()ṡ n+1 (m )) =0 + D n (T ()ṡ n+1 (m )) =0. (10) The assumpton that we are close to = 0 holds as long as the nter-frame movement s small, whch s true, granted that the camera speed or the tme taken to process each depth mage s not excessve. Notng that T = I for = 0, (10) smplfes to, D n (T ()ṡ n+1 (m )) D n (ṡ n+1 (m )) + D n (ṡ n+1 (m )). (11) In (11) we dentfy the Jacoban matrx as, J(m ) = D n (ṡ n+1 (m )), (12) and return to (9) to plug the new defntons back nto the objectve. mn. D n (ṡ n+1 (m )) + J(m ) 2. (13) Expandng the square and smplfyng the algebrac expresson we end up wth, mn. T J(m ) T J(m )+ 2 T J(m )D n (ṡ n+1 (m )) + D n (ṡ n+1 (m )) 2. (14) Carryng out the sum over the pxels n M for the terms dependent on, we can defne the followng matrx and vector, respectvely, H = J(m ) T J(m ), (15)

4 g = J(m )D n (ṡ n+1 (m )). (16) Dfferentatng (14) wth respect to and equatng the resultng expresson to zero, we fnd the optmal soluton by, = H 1 g. (17) The set of ponts are transformed by T ( ) and the process s repeated for several teratons. The estmated transform represents the ncremental change between the last known poston and the current poston. Though t s not strctly necessary for convergence, we terate usng a coarse-tofne sub-samplng on the nput depth mage, as ths provdes sgnfcant speed-ups n the regstraton by provdng a fast ntal algnment [7]. A fxed number of teratons are performed on each level of detal, or untl the change n the optmzaton parameter falls below some pre-defned threshold. To mprove the basn of convergence for the soluton, we scale the contrbuton of each measurement, based on a weghng functon. Ths produces the teratvely reweghed least-squares algorthm, changng (15) and (16) to g w = H w = w(d n (ṡ n+1 (m )))J(m ) T J(m ), (18) w(d n (ṡ n+1 (m )))J(m )D n (ṡ n+1 (m )). (19) The weghng functon w(x) characterzes an M-estmator [8] for whch a sensble choce s the Huber estmator [9]. It can be defned as, { 1.0 f x <= k w(x) = k x otherwse, (20) where k s a small constant (e.g. a tenth of the sze of one voxel). It may also be benefcal to extend ths weghng functon to nclude an error model of the sensor, e.g. reducng the nfluence of measurements made at greater dstance. Lastly, we note that addng a small cost related to the norm of the parameter vector tself (a regularzer), has benefts n stuatons where the soluton would otherwse tend to oscllate around the mnmum or lead to very naccurate results. Ths typcally happens when the soluton s not adequately constraned by the geometry seen n the envronment. Addng T W nto (12), where W R 6 6 s a dagonal matrx attrbutng cost to the norm of each ndvdual component of, results n, H w,r = W + w(d n (ṡ n+1 (m )))J(m ) T J(m ), (21) where W = αi, I beng the 6 6 Identty matrx and α a lnearly ncreasng functon of the number of the current soluton teraton. Large values for α wll tend to dampen the amount of change made to the parameter vector at each teraton and such dampenng s only nterestng once the Input: z n+1 (M) Measurements Compute surface ponts Pose Estmaton mnmzaton of sum of sgned dstances squared Fg. 3. s n+1 (M) D n (x) T n+1 ( ) Reconstructon Integrate measurements nto TSDF Man components of the system, and nformaton flow soluton s close to optmal. To summarze, a hgh-level overvew of the system s provded n Fg. 3. D. Lmtatons A general downsde of dense volumetrc scene representatons are the large memory requrements for storage at hgh resoluton. Recent work (e.g. [10],[11]) has been done to mtgate ths by allowng the reconstructed volume to move, provdng pose estmaton across larger dstances, but mantanng the dense surface reconstructon restrcted to a smaller space around the current sensor locaton. Other approaches, based on non-unform dvsons of space (rather than a fxed-sze cubcal lattce) have been proposed (e.g. [12]) and can also be used to ncrease the represented space, wthout addtonal memory use. Snce our method uses the TSDF to represent algnment error, t needs a dstance functon that s truncated at larger values than methods that smply use the TSDF as a scene representaton. The justfcaton for the larger truncaton values s that gven the moton between two consecutve vdeo frames, the surface ponts measured n the second frame need to be wthn a regon where numercal dervatves can be computed (see Eq.(12)). Snce the truncaton occurs at larger values, the method s unable to reconstruct detals as fne as what would be possble usng separate representatons for trackng and mappng. Apart from these lmtatons, the proposed method may lose track of the pose f the assumpton that we are close to the soluton does not hold or f the currently vewed geometry does not offer enough varaton to constran all sx degrees of freedom, causng H to be close to sngular. E. Related Work The presented method s a fast approach to solvng the mpled regstraton problem of camera-trackng. It s smlar to one presented by Ftzgbbon as Fast ICP usng the dstance transform (FICP) [9]. However, the full Eucldean dstance transform (EDT) used by FICP s too costly to compute

5 TABLE I COMPARATIVE RESULTS, THE PROPOSED ALGORITHM (OURS), AN OPEN-SOURCE IMPLEMENTATION OF THE KINECT FUSION ALGORITHM (PCL-KINFU), FEATURE-BASED NORMAL DISTRIBUTIONS TRANSFORM REGISTRATION (NDT-F) AND RGB-D SLAM Abs err. [m] Rel err. [m] Rel err. [deg] Dataset Algorthm RMS max RMS max RMS max Ours rgbd dataset freburg1 xyz PCL-KnFu (trajectory length: m) RGB-D SLAM NDT-F rgbd dataset freburg1 desk Ours PCL-KnFu (trajectory length: m) RGB-D SLAM NDT-F rgbd dataset freburg1 desk2 Ours PCL-KnFu (trajectory length: m) RGB-D SLAM NDT-F rgbd dataset freburg1 floor Ours PCL-KnFu (trajectory length: m) RGB-D SLAM NDT-F for the on-lne scenaro n the scope of ths work. Due to the dstance values beng unsgned, surface extracton also becomes less straghtforward. A sgned verson of the EDT s smlarly costly, but provdes addtonal challenges when faced wth partal observatons[13]. Both for sake of speed, and due to the ncomplete observatons of the envronment, we avod computng the Sgned EDT, and nstead proceed as detaled n Secton II. As an analogy, one can thnk of the presented method as pre-computng an approxmate closest-pont dstance throughout the entre volume, makng evaluatons as smple as accessng a look-up table, wthout the need for matchng correspondng ponts explctly. The Knect Fuson algorthm to whch we compare our results, solves the camera trackng problem by mantanng an updated TSDF from whch t can generate vrtual depth mages by means of ray-castng from a vrtual sensor. Usng the depth mages from the vrtual camera and the actual sensor, a mult-scale pont-to-plane ICP method s used to compute a transformaton between them. Due to the use of the pont-toplane error metrc, surface normals have to be estmated both from the raw nput data and for the vrtual data, requrng the use of a blateral flter to obtan smooth normals n the raw mage. The update of the TSDF s acheved n the same way as n ths work. Interestng to note, s that the Knect Fuson algorthm could be modfed to work just as well wth a dfferent model representaton (as long as a dense depth mage can be generated from t). Ths s qute dfferent from our method, n whch the model representaton and the cost functon are nseparable. IV. RESULTS To evaluate the accuracy of the proposed algorthm n an off-lne settng, we tested on a subset of the RGB-D datasets from the hand-held SLAM category, provded by the CVPR group at the Techncal Unversty of Munch [4]. The parameters and constants ntroduced n Secton III are lsted n Table II wth the values used throughout the benchmark. We evaluate the accuracy of our algorthm by computng the absolute trajectory error, relatve poston error TABLE II PARAMETERS USED DURING EVALUATION Parameter value Voxels Voxel sze [m] 0.03 truncaton (postve) [m] 0.1 truncaton (negatve) [m] 0.06 Huber constant k [m] Iteraton levels 3 Downsamplng / level 4, 2, 1 Iteratons / level 12, 6, 2 Regularzaton α teraton count Stoppng condton (nterrupts current level) < and relatve orentaton error as ndcated n [4]. We compare the results to those of Knect Fuson (as mplemented by the Pont-Cloud Lbrary 3 [14]) and to two algorthms that use depth nformaton n conjuncton wth vsual features, namely RGB-D SLAM 4 [15], and feature-based 3D Normal Dstrbutons Transform (NDT-F) [16]. As can be seen n Table I, our method acheves smlar performance to the tested vsual feature-based methods, n spte of trackng from depth alone and not performng any pose-graph optmzaton. Our method slghtly outperforms the reference mplementaton of Knect Fuson on the desk and xyz datasets but fares slghtly worse on the desk2 and floor sets. It s nterestng to note that RGB-D SLAM typcally has a larger nter-frame error but, due to global optmzaton and loop-closures, acheves a smaller absolute error. Compared to the results obtaned usng NDT-F around vsual features, we generally acheve better results. Ths s expected, snce NDT-F s a frame-to-frame method and can therefore not take advantage of a map wth reduced nose. A notable excepton to these statements s the rather poor performance of the proposed algorthm on the floor sequence. A closer 3 Open Source Knect Fuson mplementaton, PCL: accessed: Sept ROS packages of TUM/CVPR (cvpr-ros-pkg) benchmark/rgbd benchmark tools/data/rgbdslam accessed: Sept. 2012

6 (a) Relatve rotaton error (b) Relatve poston error Fg. 4. Relatve errors. A large spke s seen n both graphs at ca. 25s, caused by an nsuffcently constraned soluton for the depth-based algorthms Fg. 6. The tme requred to process each frame ncreases wth the number of voxels Fg. 5. Input n rgb and depth showng a largely planar scene, though rch n vsual features look at the relatve errors n pose estmaton for that data set, shown n Fg. 4 reveals large spkes both n the rotatonal and translatonal error, occurrng after ca. 25s. Lookng at the nput data (example n n Fg. 5) for whch ths error s produced (color mage provded only for reference), we note that t s ndeed a representatve example for one of the falure modes dscussed n Secton III-D (namely, H close to sngular). The Knect Fuson algorthm produces smlar behavour, for the same reasons. The run-tme of our algorthm, as measured on an Intel Core QM (2.70 GHz, 4 cores) CPU s dependent on the number of voxels used and s presented graphcally n Fg. 6. Performance scales up wth the number of cores avalable on the system and ther speed. The algorthm spends the majorty of ts tme evaluatng the TSDF whch requres fetchng eght floatng-pont values from memory, performng a tr-lnear nterpolaton between them and castng the result to a double-precson value. Ths operaton s needed to compute the error assocated wth a surface pont, but also to compute the dervatve of the error relatve to poston. V. C ONCLUSIONS We have presented a camera-trackng method that uses the 3D scene representaton drectly as a cost functon to perform 6 DoF algnment of 3D surface ponts. The trajectores estmated by our method, on a well-known dataset, are comparable to those of current state of the art methods, ncludng algorthms whch, n addton to depth also employ vsual features. Our man contrbuton les n a drect model-based approach to on-lne regstraton, as opposed to generatng vrtual sensor data from a model and performng regstraton n a sensor-centrc frame of reference. Ths allows hgh qualty surface reconstructon (e.g. Fg. 7) and accurate pose Fg. 7. Example reconstructon from the fb1 xyz dataset, usng 4003 voxels of sze 0.006m estmaton to be done on systems wthout a GPU. However, n lack of standardzed mplementatons for both CPU and GPU archtectures, practcal comparsons to other algorthms n terms of computatonal complexty are dffcult make. In addton, we make our mplementaton freely avalable to the beneft of the robotcs communty for use and verfcaton of our results. As a future work, alternatve objectve functons, based on the pont-to-plane [17] metrc could be used for better convergence, at a modest ncrease n computatonal cost. Embeddng nformaton about local texture nto the TSDF may provde addtonal mprovements for stuatons where depth alone s nsuffcent to successfully estmate the sensor moton. ACKNOWLEDGMENT D.R.C. thanks R. A. Newcombe, S. Lovegrove and J. Sturm for explanatons, nspraton and support n the course of ths work. Ths work was partly funded by the 7th European Framework Project, RobLog. R EFERENCES [1] R. Newcombe, S. Lovegrove, and A. Davson, Dtam: Dense trackng and mappng n real-tme, n Computer Vson (ICCV), 2011 IEEE Internatonal Conference on. IEEE, 2011, pp

7 [2] A. Fuhrmann, G. Sobottka, and C. Gross, Abstract dstance felds for rapd collson detecton n physcally based modelng, n Internatonal Conference on Computer Graphcs and Vson (Graphcon), 2003, pp [3] M. Qugley, K. Conley, B. P. Gerkey, J. Faust, T. Foote, J. Lebs, R. Wheeler, and A. Y. Ng, Ros: an open-source robot operatng system, n ICRA Workshop on Open Source Software, [4] J. Sturm, N. Engelhard, F. Endres, W. Burgard, and D. Cremers, A benchmark for the evaluaton of rgb-d slam systems, n Proc. of the IEEE Internatonal Conference on Intellgent Robot Systems (IROS), [5] R. Newcombe, A. Davson, S. Izad, P. Kohl, O. Hllges, J. Shotton, D. Molyneaux, S. Hodges, D. Km, and A. Ftzgbbon, Knectfuson: Real-tme dense surface mappng and trackng, n Mxed and Augmented Realty (ISMAR), th IEEE Internatonal Symposum on. IEEE, 2011, pp [6] B. Curless and M. Levoy, A volumetrc method for buldng complex models from range mages, n Proceedngs of the 23rd annual conference on Computer graphcs and nteractve technques. ACM, 1996, pp [7] D. RICAO CANELHAS, Scene representaton, regstraton and objectdetecton n a truncated sgned dstance functonrepresentaton of 3d space, Master s thess, Örebro Unversty, [8] Z. Zhang, Parameter estmaton technques: A tutoral wth applcaton to conc fttng, Image and vson Computng, vol. 15, no. 1, pp , [9] A. Ftzgbbon, Robust regstraton of 2d and 3d pont sets, Image and Vson Computng, vol. 21, no. 13, pp , [10] T. Whelan, M. Kaess, M. Fallon, H. Johannsson, J. Leonard, and J. McDonald, Kntnuous: Spatally extended knectfuson, n Proc. of RSS workshop on RGB-D: Advanced Reasonng wth Depth Cameras, [11] H. Roth and M. Vona, Movng volume knectfuson, n Brtsh Machne Vson Conf.(BMVC),(Surrey, UK), [12] S. Frsken, R. Perry, A. Rockwood, and T. Jones, Adaptvely sampled dstance felds: A general representaton of shape for computer graphcs, n Proceedngs of the 27th annual conference on Computer graphcs and nteractve technques. ACM Press/Addson-Wesley Publshng Co., 2000, pp [13] P. Mullen, F. De Goes, M. Desbrun, D. Cohen-Stener, and P. Allez, Sgnng the unsgned: Robust surface reconstructon from raw pontsets, vol. 29, 2010, pp [14] R. Rusu and S. Cousns, 3d s here: Pont cloud lbrary (pcl), n Robotcs and Automaton (ICRA), 2011 IEEE Internatonal Conference on. IEEE, 2011, pp [15] N. Engelhard, F. Endres, J. Hess, J. Sturm, and W. Burgard, Real-tme 3d vsual slam wth a hand-held rgb-d camera, n Proc. of the RGB- D Workshop on 3D Percepton n Robotcs at the European Robotcs Forum, Vasteras, Sweden, [16] H. Andreasson and T. Stoyanov, Real tme regstraton of rgb-d data usng local vsual features and 3d-ndt regstraton, n Proc. of Internatonal Conference on Robotcs and Automaton (ICRA) Workshop on Semantc Percepton, Mappng and Exploraton (SPME), [17] C. Yang and G. Medon, Object modellng by regstraton of multple range mages, Image and vson computng, vol. 10, no. 3, pp , 1992.