Efficient Multi-View Object Recognition and Full Pose Estimation

Transcription

1 Effcent Mult-Vew Object Recognton and Full Pose Estmaton Alvaro Collet Sddhartha S. Srnvasa Abstract We present an approach for effcently recognzng all objects n a scene and estmatng ther full pose from multple vews. Our approach bulds upon a state of the art sngle-vew algorthm whch recognzes and regsters learned metrc 3D models usng local descrptors. We extend to multple vews usng a novel mult-step optmzaton that processes each vew ndvdually and feeds consstent hypotheses back to the algorthm for global refnement. We demonstrate that our method produces results comparable to the theoretcal optmum, a full mult-vew generalzed camera approach, whle avodng ts combnatoral tme complexty. We provde expermental results demonstratng pose accuracy, speed, and robustness to model error usng a three-camera rg, as well as a physcal mplementaton of the pose output beng used by an autonomous robot executng grasps n hghly cluttered scenes. I. INTRODUCTION There has been recent renewed nterest ([1 4] to name a few) n enablng moble manpulators to perform useful tasks n unstructured human envronments, lke homes and offces. Such envronments are partcularly challengng due to ther dynamc nature and due to hgh clutter. These characterstcs demand speed and accuracy from all components: plannng, control, and percepton. Motvated by these practcal requrements, we demonstrated a sngle-vew object recognton and pose estmaton algorthm n [5] that s fast, accurate, and robust to clutter. Wth cameras gettng better, cheaper, and smaller, multple vews of a scene are often easly avalable. For example, our robot HERB (Fg. 1) has, at varous tmes, been outftted wth cameras on ts shoulder, n the palm, on ts ankle-hgh laser, as well as wth a stereo par. Multple vews of a scene are often desrable, because they provde depth estmaton, robustness aganst lne-of-sght occlusons, and an ncreased effectve feld of vew. Two standard approaches are popular for convertng a sngle-vew vson algorthm to multple vews. The frst, whch we term sngle-vew averagng, executes the sngle-vew algorthm on each of the mages and combnes the resultng output, often usng machne learnng technques [6] (Fg. 2(a)). Ths approach scales lnearly wth the number of mages and has the ablty to combne many sngle-vew algorthms at the same tme. However, t treats the sngle-vew algorthm as a black box: fused nformaton s not fed back to the algorthm for further refnement. The second, whch we term full mult-vew, combnes multple mages by consderng a network of cameras as one generalzed camera [7, 8] whch produces a sngle large aggregate mage (Fg. 2(b)). The sngle-vew algorthm s then appled to ths generalzed mage. Ths approach s A. Collet s wth The Robotcs Insttute, Carnege Mellon Unversty, 5000 Forbes Ave., Pttsburgh, PA , USA. acollet@cs.cmu.edu S. Srnvasa s wth Intel Labs Pttsburgh, 4720 Forbes Ave., Sute 410, Pttsburgh, PA , USA sddhartha.srnvasa@ntel.com Fg. 1. Object graspng n a cluttered scene usng our algorthm. (Top) Scene observed by each camera. Our ntrospectve mult-vew algorthm recognzes objects and computes consstent poses across multple vews. Each recognzed object s projected back nto the mages as a coordnate frame plus a convex hull of ts projected 3D model. (Bottom) Our robot platform HERB n the process of graspng an object, usng only the pose nformaton from ths algorthm. optmal: there s no loss of nformaton. However, the large search space created by the generalzed mage makes teratve algorthms such as RANSAC struggle n the presence of thousands of correspondences, due to the exponental ncrease n computaton tme when lnearly ncreasng the number of ponts to be tested. We propose a thrd approach, whch we term ntrospectve mult-vew, whch combnes the speed of sngle-vew averagng wth the accuracy of the full mult-vew approach (Fg. 2(c)). Each ndvdual vew s processed frst usng the sngle-vew algorthm [5], obtanng an ntal estmate of objects and ther poses. Then, a second stage clusters the output of multple vews, flterng out nconsstent data. Fnally, the object pose s re-optmzed usng a reduced generalzed mage comprsng only of ponts consstent across all mages. Our mult-step optmzaton ncurs only a slght computatonal overhead over sngle-vew averagng as a result of ts fnal stage, and only a slght reducton n accuracy over full mult-vew as a result of ts flterng (Fg. 2(d)). In the general case of complex scenes wth clutter, the ntrospectve multvew algorthm proves to be far superor than sngle-vew and generalzed mage algorthms, combnng the effcency of the former and the accuracy of the latter.

2 Fg. 2. Mult-vew mergng alternatves. (a) Sngle-vew averagng: Process each vew ndvdually usng a sngle-vew algorthm and combne ther output (e.g. weghted votng, mxture of experts). (b) Full mult-vew: Embed all vews nsde a sngle generalzed camera model and use all nformaton to recognze objects and estmate pose. (c) Our method: Introspectve mult-vew: Process each vew ndvdually, and feed back consstent hypotheses to the pose estmaton algorthm for global refnement. (d) Our method has accuracy comparable to (b) and speed comparable to (a). (Rght) HERB graspng n clutter usng the mult-vew algorthm. II. SINGLE-VIEW RECOGNITION AND POSE ESTIMATION We buld upon the sngle-vew algorthm ntroduced n [5], whch ths secton detals. A. Modelng 3D objects Objects to be recognzed are modeled through an offlne learnng phase and stored n an object database O. For each object o O, a set of mages s frst taken wth the object n varous postons and orentatons. Relable local descrptors are extracted from natural features usng SIFT features[9]. Usng structure from moton [10] on matched SIFT features, nformaton from each tranng mage s merged to produce a sparse 3D model comprsng of a set of 3D ponts P o where each pont n the set s assocated wth a local descrptor. Fnally, algnment and scale for each model are computed to match the real object dmensons. B. Recognzng all objects n an mage From a sngle mage, the sngle-vew algorthm fnds all known objects n a scene and recovers ther accurate 6D pose, even under heavy occluson and the presence of multple confusng nstances of the same object class. Our goal s to obtan an object hypothess h comprsed of ts dentty o O and ts transformaton T o SE(3) wth respect to the camera frame, for each object present n the mage. We accomplsh ths by mnmzng the sum of reprojecton errors between ponts n the mage and projected ponts n the model. A novel combnaton of RANSAC and Mean Shft clusterng[11] allows for a real-tme soluton of the correspondence problem, even wth many nstances of the same object present. We repeat the followng procedure for each object o n the object database. An example of the robustness to clutter and multple nstances of o s seen n Fg. 3. 1) Extract SIFT features p from mage and match them aganst o, obtanng set of correspondences P o p o. 2) Cluster the 2D mage locatons of p o usng Mean Shft. 3) For each cluster c, choose a subset of ponts and estmate a hypothess wth the best pose accordng to those ponts. If the amount of ponts consstent wth the hypothess s hgher than a threshold ɛ, create a new object nstance and refne the estmated pose usng all consstent ponts n the optmzaton. Repeat ths procedure untl the amount of unallocated ponts s lower than a threshold, or the maxmum number of teratons has been exceeded. Ths produces a set of hypotheses h c for each cluster c. 4) Merge hypotheses from dfferent clusters whose estmates of T o are smlar. 5) Output a reduced set of hypotheses h for object o. III. MULTI-VIEW RECOGNITION AND POSE ESTIMATION Some mult-vew technques for pose estmaton parameterze a network of cameras as a sngle Generalzed Camera[7] and optmze the camera pose over ths generalzed space by solvng the resultng non-perspectve PnP (npnp) problem[12]. Whle such an approach s perfectly vald, t mght not be entrely feasble n real-tme f the correspondence problem needs to be taken nto account. Another alternatve s to combne multple sngle-vew algorthms va pose verfcaton[13], robust averagng, or weghted votng [14]. These methods avod the combnatoral exploson that plagues generalzed mages, but they fal to feedback useful fused nformaton to the underlyng algorthm for further refnement. The sngle-vew object recognton system descrbed n II analyzes an mage and returns several object hypotheses contanng nformaton about ts dentty, ts full pose relatve to the camera and the set of 3D-2D correspondences consstent wth each hypothess. We now descrbe our approach to use a sngle-vew object recognton system for a set of mages and effcently fuse the local nformaton to obtan a set of object detectons globally consstent wth all vews.

3 Fg. 3. Recognton of multple object nstances n a (left) Scene observed by the robot s camera, used for object recognton/pose estmaton. Coordnate frames show the dscovered pose of each object. (rght) 3D reconstructon where each object s represented usng a smple geometry. A. Mult-step pose optmzaton n statc camera rgs We defne the mult-vew pose optmzaton algorthm as a mult-step optmzaton n the sub-mage (clusters of ponts), mage and mult-mage (clusters of objects) domans. The algorthm n II s executed for each ndvdual mage, obtanng an ntal hypothess of all objects n a scene. At the end of ths step, each object hypothess h s lnked to ts dentty and a pose To relatve to camera. In order to fuse all hypotheses, each object pose s transformed from a camera-centrc coordnate system nto a common reference frame usng the extrnsc parameters T = (R, t ) for each camera producng a global pose T o = T To. Wth all objects n the same reference frame, Mean Shft clusterng s performed on all poses T o belongng to the same object class. It s convenent to parameterze rotatons n terms of quaternons and project them n the same half of the quaternon hypersphere pror to clusterng. As n the sngle-vew case, ths produces a set of hypotheses h c for each cluster c, wth a total number of clusters C. Ths s often the fnal output that mult-vew ntegraton algorthms offer, a set of reduced set of hypotheses h obtaned by rejectng clusters wth less than a certan number of hypotheses to flter out spurous detectons or by cluster-mergng lke n the sngle-vew case. However, t s possble to mprove ths result further. The optmal sngle hypothess h c for a gven cluster c s one that mnmze the sum of reprojecton errors of correspondences across all mages. To accomplsh ths, we frst collect the correspondences for each pont P j P o n the model across all mages, markng 0 f the vew does not contan a correspondng pont. Ths produces a correspondence set that looks lke P j {p 1 j, p2 j, 0, 0,..., pm j }, where M s the total number of vews. The optmal sngle hypothess s then gven by h c = arg mn T M P j P o =1 δ j [ p j proj ( T T P j )] 2 (1) where δj = 0 f p j = 0 and 1 otherwse. Alternatvely, one can defne an analogous optmzaton n terms of the backprojecton error, by tracng the lne L j from the camera center to each 2D pont p j ts dstance to the correspondng 3D pont P j. We parametrze a lne as L = (c, v), where v s a unt vector ndcatng the lne drecton and c s an arbtrary pont on that lne, e.g. the camera center. Usng projectve geometry, we obtan v j = K 1 p j K 1 p j (2) where K s a 3 3 ntrnsc camera matrx for vew. Each lne L j n a common reference frame s then gven by v j = (R ) T v j c j = (R ) T t (3) The dstance between a pont P and L j s gven by ( ) d(p j, L j) = I 3 3 vjv j T ( ) P c j (4) The analogous equaton to Eq. 1 that mnmzes the sum of backprojecton errors s gven by M h c = arg mn δ [ ( j d T T P j, L )] 2 j (5) T P j P o =1 Addtonally, we found t useful to constran the objects to le n front of the cameras. Gven that vj are vectors from the camera center pontng towards the mage plane, vj T (P c j ) > 0 for all ponts P n front of the camera. We ncorporate ths constrant as a regularzer (wth weght ξ > 0) n the mnmzaton M h c = arg mn δj T P j P o =1 [ d ( ( T T P j, L ) j + ξ 1 vj T (P j c j ) )] 2 P j c j (6) Both the reprojecton (Eq. 1) and backprojecton (Eq. 6) error functons are numercally equvalent when estmatng object poses n Eucldean space, so one may choose ether one. The reprojecton error s usually preferred n the computer vson communty because t s nvarant to projectve transformatons, whle the backprojecton error s meanngless n projectve space[15]. In our partcular case, workng wth calbrated cameras n an Eucldean space, we have chosen the backprojecton error because t makes our framework more easly extensble to other types of multmodal data, such as LASER pont clouds, whch we plan to ncorporate n the near future. If we were consderng the general case of pose estmaton n multple vews from scratch, ntalzng the non-lnear mnmzaton from Eq. 6 nvolves solvng the npnp problem[12] for each teraton of RANSAC, whch s computatonally very expensve. In our case, we wll use the good estmate provded by each cluster centrod as the startng pose. Two further refnements are necessary to construct a multvew algorthm from the algorthm descrbed n II.B. Frst, the sngle-vew algorthm contans a cluster mergng step, desgned to fuse nformaton from dfferent clusters wthn the same mage. In the mult-vew algorthm, t s also necessary to cluster object poses across dfferent vews, and both actons can be ntegrated n a sngle clusterng step, to merge all clusters wthn multple mages at the same tme. A second ssue that requres careful consderaton s the clusterng radus,.e. the dstance between two object hypotheses to be merged together. Regardless of the choce, t s hghly unlkely that a sngle threshold dstance wll satsfy

4 Cam 3 Cam 1 Z Y X Cam 2 Fg. 4. Three-camera rg used for accuracy tests wth coordnate frame ndcated on bottom left corner. all possble cases. If ths radus s too small, hypotheses that belong to the same physcal object mght not be clustered together. If t s too large, a sngle cluster mght envelope several physcal objects that are close together (e.g. Fg. 3). The soluton s avalable n the sngle-vew algorthm: RANSAC and a mergng step handle well clusterng radus ssues. The fnal mult-vew algorthm s as follows: 1) Run sngle-vew algorthm on each mage wthout cluster mergng. 2) Collect all hypotheses n a common reference frame. 3) For each object class, cluster hypotheses wth Mean Shft to obtan sets of hypotheses h c for cluster c. 4) For each cluster c, mnmze Eq. 6 usng all 3D- 2D correspondences from all objects that belong to the cluster. Intalze the optmzaton at the cluster centrod. If number of ponts consstent wth h c s greater than a threshold ɛ 2, consder pose as correct and process next cluster. 5) If ɛ 2 s not met, choose a subset of n ponts and estmate a hypothess wth the best pose accordng to those ponts. If the amount of ponts consstent wth the hypothess s greater than a threshold ɛ 1 < ɛ 2, create a new object nstance and refne the estmated pose usng all consstent ponts n the optmzaton. Repeat ths procedure untl the number of unallocated ponts s lower than a predetermned amount, or untl the maxmum number of teratons are exceeded. 6) Merge smlar hypotheses usng the sngle-vew cluster mergng algorthm. Re-optmze usng all ponts. B. Implementaton detals The performance of ths mult-vew algorthm n real scenes depends largely on the chosen termnaton condtons for each procedure. Gven that each pass refnes the soluton n search of greater accuracy, t s safe to enforce more strngent constrants as the algorthm proceeds forward. When consderng ɛ 2, we are amng to dentfy those pose clusters wth a strong agreement to avod further processng. Therefore, choosng a hgh number of ponts (e.g. 75% of the total number of ponts wthn the cluster) s advsable. ɛ 1 s a fal-safe condton that operates on those clusters wth dsagreeng poses. We are n an equvalent poston to that n the sngle-vew RANSAC step, so a smlar value should be chosen. Fnally, the last mergng step only receves hghly refned poses (ths algorthm s average translaton error s 0.61%), so mergng hypotheses should only be performed Fg. 5. Examples scenes captured by the rg wth Cam 1 (top), Cam 2 (mddle), and Cam 3 (bottom). (Col 1) Rce box at 50 cm. (Col 2) Notebook at 60 cm. (Col 3) Coke can at 80 cm. (Col 4) Juce bottle at 1m. (Col 5) Pasta box at 1.2m. when ther postons are closer than 1 2cm. apart. In addton, mult-vew constrants should be enforced to completely elmnate possble false postves n the sngle-vew algorthm, e.g. valdatng an object hypothess by requrng that consstent ponts exst n at least two cameras. IV. EXPERIMENTS Three sets of experments have been conducted to prove our pose estmaton algorthm s sutablty for robotc manpulaton. The frst set evaluates the accuracy of the proposed algorthm n estmatng the poston and orentaton of a gven object n a set of mages. The second set of experments evaluates our algorthm s robustness aganst modelng errors, whch greatly nfluence the accuracy of pose estmaton. Fnally, the thrd set uses the pose estmaton algorthm alongsde a state-of-the-art plannng algorthm to grasp objects wth a Barrett WAM robotc arm. In all experments estmate the full 6-DOF pose of objects, and no assumptons are made on ther orentaton or poston. In all cases, the sngle-vew algorthm clusters the scene wth a Mean Shft radus of 100 pxels, and chooses subsets of 5 correspondences to compute each RANSAC hypothess. The maxmum number of RANSAC teratons s set to The mult-vew algorthm requres that a pose s seen by at least two vews, and that at least 50% of the ponts from the dfferent hypotheses are consstent wth the fnal pose. The expermental setup s a statc three-camera rg wth approxmately 10cm baselne between each two cameras (see Fg. 4). Both ntrnsc and extrnsc parameters for each camera have been computed, consderng camera 1 as the coordnate orgn. A. Pose estmaton accuracy In ths set of experments, we evaluate our system s accuracy over the range most useful n robotc manpulaton. The three-camera rg was mounted and calbrated on a flat table(see Fg. 4). Our database s composed of fve common household objects of varous shapes and appearances. A set of 27 dfferent postons and orentatons for each object were gathered, wth depths (.e. dstances from the central camera) rangng from 0.4m to 1.2m n 10cm ncrements, lateral movements of up to 20cm and out-of-plane rotatons of up to 45 degrees. 10 mages were taken wth each camera at each poston to account for possble mage nose and artfacts, producng 810 mages per object and a total of 4050 mages.

5 Fg. 6. Examples of ntrospectve mult-vew n complex scenes. (Cols 1-3) depct the recognzed poses overlad on each mage. (Col 4) shows a reconstructon of the gven scenes n our vrtual envronment. TABLE I TABLE II AVERAGE ACCURACY TEST. (1) SINGLE-VIEW. (2) ROBUST POSE AVERAGE DISTANCE-NORMALIZED TRANSLATION ERROR WITH AVERAGING. (3) INTROSPECTIVE MULTI-VIEW. (4) FULL MULTI-VIEW. VARYING MODEL SCALE. (1) (2) (3) (4) TX error (cm) TX error/dst. 1.80% 1.71% 0.61% 0.60% Rot. error (deg) Correct det. rate 85.0% 88.3% 88.3% 71.9% False pos. rate 2.78% 0% 0% 0% False neg. rate 13.61% 11.67% 11.67% 28.15% Num ter./vew Table I compares the accuracy of Collet et al s snglevew algorthm, robust pose averagng of sngle vews, the proposed mult-vew algorthm and a Full Mult-vew (Generalzed Image) approach. Sngle-vew results show the average performance of [5] over each of the three cameras n our setup. Robust pose averagng computes a weghted mean pose based on the sngle-vew pose hypotheses, usng a metrc based on the number of consstent ponts and average reprojecton error as a weghtng factor. The dstancenormalzed translaton error refers to the absolute translaton error dvded by the dstance wth respect to the closest camera. Rotaton error s measured as the quaternon angle α = 2cos 1 (q T q gt ). The correct detecton rate counts all pose hypotheses that le wthn 5 cm of the true pose. It s mportant to note that the correct detecton, false postve and false negatve rates do not necessarly need to add up to 100%, because an algorthm mght output a correct and an ncorrect pose n the same mage. As we can see n Table I, accuracy s ncreased threefold usng the ntrospectve mult-vew scheme wth respect to pose averagng, whle requrng smlar processng tme. It s noteworthy that the ntrospectve mult-vew and full multvew, consdered a theoretcal lmt, perform very smlarly n terms of accuracy. The low detecton rate of the full multvew algorthm s due to ts enormous computatonal cost, as t often exceeds the maxmum number of teratons wth no correct detecton. The average number of teratons requred to detect a sngle object wth a full mult-vew approach s Model scale (1) (2) (3) (4) % 4.20% 0.81% 0.81% % 2.65% 0.68% 0.62% % 1.76% 0.61% 0.54% % 1.95% 0.74% 0.69% % 2.90% 0.98% 0.94% % 4.43% 1.29% 1.18% three tmes greater than wth any other technque, and ts computatonal complexty grows exponentally wth respect to the number of objects n a scene. B. Robustness aganst modelng nose Ths set of experments evaluates our proposed algorthm s robustness aganst modelng naccuraces. Successful pose estmaton n our sngle-vew algorthm s heavly dependent on a good model calbraton, specally n terms of scalng, because depth s estmated entrely based on an object s scale. Therefore, extreme care needs to be taken when creatng models to set a proper scale, and several tests need to be conducted before a new object model can be ncorporated nto the robot s knowledge database. For example, a modelng error of 1mm n a coke can (.e. 1mm larger than ts real sze), translates nto a depth estmaton error of up to 3cm at a dstance of 1m, large enough to cause problems to the robotc manpulator. On the other hand, havng multple vews of the same object enables the use of further constrants n ts pose. In partcular, f the cameras have been fully calbrated, an mplct trangulaton takes place durng the optmzaton, wth the object drftng to ts true poston to mnmze the global backprojecton error, despte the larger error when each vew s processed ndvdually. Table II and Table III showcase the effect of scale errors durng the object modelng stage. The proposed mult-vew algorthm outperforms every other approach n the presence of modelng nose. It s remarkable that ts worst result (wth models ncreasng 5% n scale) outperforms every other approach s best result (wth no modelng error, Table I).

6 TABLE III AVERAGE CORRECT DETECTION RATE WITH VARYING MODEL SCALE. Model scale (1) (2) (3) (4) % 71.7% 80.8% 59.3% % 85.0% 85.8% 66.7% % 86.7% 86.7% 71.1% % 88.3% 88.3% 70.4% % 77.5% 87.5% 65.2% % 58.3% 85.0% 54.1% TABLE IV GRASPING IN CLUTTERED SCENES Can Juce Rce Pasta Notebook Total Attempts Successful grasps hold objects whch proves to ncrease both accuracy and computaton tme by a factor of three aganst other multvew approaches. We have demonstrated that the results are accurate enough for a robot to reach nto a cluttered scene and pck up all objects, wth a graspng success rate of 98%. We beleve that our system provdes a crucal capablty that wll enable moble manpulators to functon and nteract n crowded ndoor envronments wth speed and accuracy. VI. ACKNOWLEDGMENTS Ths materal s based upon work partally supported by the Natonal Scence Foundaton under Grant No. EEC Alvaro Collet s partally supported by Caja Madrd fellowshp. Specal thanks to Chrs Atkeson and members of the Personal Robotcs project at Intel Labs Pttsburgh for nsghtful comments and dscussons. Fg. 7. Dstrbuton of dstance-normalzed translaton errors for dfferent mult-vew approaches. Introspectve mult-vew obtans the most amount of pose hypotheses under 1% error, and global average error of 0.61% C. Graspng objects We ntegrated the mult-vew algorthm wth a plannng algorthm on HERB. The plannng algorthm, called the Inverse-Knematcs BDrectonal Rapdly-explorng Random Tree algorthm (IKBRRT) [16], plans a trajectory for the arm startng from ts current confguraton and endng at a confguraton that places the wrst of the robot at an acceptable locaton for graspng. Each object that was localzed has an assocated set of wrst locatons that are sutable for graspng. Once the transform of the object s found, the assocated wrst locatons are nput as goal regons for the planner, whch then samples from these goal regons as t plans. Note that, for scenes where multple graspable objects are present, we nput all the assocated wrst locatons for all objects nto the planner, whch fnds a trajectory to reach any one of them. Once the robot completes the trajectory, the fngers are closed and the object s lfted. In the graspng experments, one object of each class was placed on a table wthn the robot s reachable workspace. Before each test, objects were placed n a new arbtrary poston and orentaton wthn 10 cm of each other on the table. The robot then planned a trajectory to retreve each object from the table avodng the rest and throw t to a trash can. Durng 20 such scenaros, the robot successfully grasped 98 of the 100 objects (see Table IV), valdatng the accuracy of the proposed mult-vew pose estmaton algorthm for robotc manpulaton of objects n cluttered scenes. V. CONCLUSIONS We have presented and valdated an effcent mult-vew system for the recognton and regstraton of common house- REFERENCES [1] S. Srnvasa, D. Ferguson, C. Helfrch, D. Berenson, A. C. Romea, R. Dankov, G. Gallagher, G. Hollnger, J. Kuffner, and J. M. Vandeweghe, HERB: a home explorng robotc butler, Auton. Robots, vol. 28, no. 1, pp. 5 20, Jan [2] The PR platform, [3] A. Saxena, J. Dremeyer, and A. Ng, Robotc Graspng of Novel Objects usng Vson, IJRR, vol. 27, no. 2, pp , [4] H. Nguyen, C. Anderson, A. Trevor, A. Jan, Z. Xu, and C. Kemp, El-e: An Asstve Robot that Fetches Objects from Flat Surfaces, n HRI, The Robotcs Helpers Workshop, [5] A. Collet, D. Berenson, S. S. Srnvasa, and D. Ferguson, Object recognton and full pose regstraton from a sngle mage for robotc manpulaton, n IEEE ICRA, Kobe, May 2009, pp [6] T. Haste, R. Tbshran, and J. H. Fredman, The Elements of Statstcal Learnng, 1st ed. Sprnger, July [7] M. D. Grossberg and S. K. Nayar, A general magng model and a method for fndng ts parameters, n ICCV, 2001, pp [8] R. Pless, Usng many cameras as one, IEEE CVPR, vol. 2, p. 587, [9] D. G. Lowe, Dstnctve mage features from scale-nvarant keyponts, IJCV, vol. 60, pp , [10] R. Szelsk and S. B. Kang, Recoverng 3d shape and moton from mage streams usng non-lnear least squares, Robotcs Insttute, CMU, Pttsburgh, PA, Tech. Rep., March [11] Y. Cheng, Mean shft, mode seekng, and clusterng, IEEE PAMI, vol. 17, no. 8, pp , [12] C.-S. Chen and W.-Y. Chang, On pose recovery for generalzed vsual sensors, IEEE PAMI, vol. 26, no. 7, pp , July [13] A. Selnger and R. C. Nelson, Appearance-based object recognton usng multple vews, CVPR, vol. 1, p. 905, [14] F. Vkstén, R. Söderberg, K. Nordberg, and C. Perwass, Increasng pose estmaton performance usng mult-cue ntegraton, n IEEE ICRA, Orlando, Florda, USA, May [15] R. Hartley and P. Sturm, Trangulaton, [16] D. Berenson, S. Srnvasa, D. Ferguson, A. Collet, and J. Kuffner, Manpulaton plannng wth workspace goal regons, n IEEE ICRA, 2009.