Robust 3D Visual Tracking Using Particle Filtering on the SE(3) Group

Transcription

1 Robus 3D Visual Tracking Using Paricle Filering on he SE(3) Group Changhyun Choi and Henrik I. Chrisensen Roboics & Inelligen Machines, College of Compuing Georgia Insiue of Technology Alana, GA 3332, USA Absrac In his paper, we presen a 3D model-based objec racking approach using edge and keypoin feaures in a paricle filering framework. Edge poins provide 1D informaion for pose esimaion and i is naural o consider muliple hypoheses. Recenly, paricle filering based approaches have been proposed o inegrae muliple hypoheses and have shown good performance, bu mos of he work has made an assumpion ha an iniial pose is given. To remove his assumpion, we employ keypoin feaures for iniializaion of he filer. Given 2D-3D keypoin correspondences, we choose a se of minimum correspondences o calculae a se of possible pose hypoheses. Based on he inlier raio of correspondences, he se of poses are drawn o iniialize paricles. For beer performance, we employ an auoregressive sae dynamics and apply i o a coordinae-invarian paricle filer on he SE(3) group. Based on he number of effecive paricles calculaed during racking, he proposed sysem re-iniializes paricles when he racked objec goes ou of sigh or is occluded. The robusness and accuracy of our approach is demonsraed via comparaive experimens. I. INTRODUCTION From roboic manipulaion o augmened realiy, esimaing poses of objecs is a key ask. Since Harris [1] proposed his early sysem which racks an objec by projecing a 3D CAD model ino a 2D image and aligning he projeced model edges o image edges, here have been acive effors o enhance he early edge-based racking sysem [2], [3]. Edges are employed because hey are easy o compue and invarian o illuminaion and pose changes. However, a criical disadvanage of using edges in visual racking is ha hey look similar o each oher. In general, edge correspondences are deermined by local search based on a prior pose esimae. So he racking performance of an edge-based racker direcly depends on correc pose priors. To improve pose priors, here have been aemps o enhance he pose accuracy beween frames by incorporaing ineres poins [4], [5], [6] or employing addiional sensors [7]. Since ineres poins and heir rich descripors [8], [9] can be exraced and mached well under illuminaion, scale, roaion changes, and reasonable projecion ransformaion, keypoin feaures complemen edges well. Considering muliple edge correspondences was anoher ineres in edge-based racking. Since edges are ambiguous and false edge correspondences direcly lead he racker o false pose esimaes, some approaches have considered muliple edge correspondences [5], [1]. However, heir work was sill limied because only one or wo hypoheses were mainained from he muliple correspondences during racking. Muliple hypoheses racking has been implemened using a paricle filering framework. Isard and Blake [11] applied a paricle filer o 2D visual edge racking and have shown grea poenial. Affine 2D visual rackers have also been proposed in a paricle filer framework wih incremenal measuremen learning [12], [13]. Among hem, Kwon e al. [13] proposed a paricle filer on a 2D affine Lie group, Aff(2), in a coordinae-invarian way. For 3D visual racking, Pupilli and Calway [14] have shown he possibiliy of applying a paricle filer o 3D edge racking. While [14] demonsraed he racking of simple 3D objecs, Klein and Murray [15] implemened a paricle filering approach which racks complex full 3D objecs in real-ime by exploiing he GPU. Mörwald e al. [16] also exploied he parallel power of GPU o implemen a fas model-based 3D visual racker. Wih edges from 3D CAD, hey also employed edges from exure which possibly conribues o avoid false edge correspondences as well as o enhance he accuracy of pose esimaes. Teulière e al. [17] recenly addressed a similar problem by mainaining muliple hypoheses from low-level edge correspondences. Wih a few excepions [18], mos of he work has made an assumpion in which rackers sar from a given pose. Several effors [15], [14] used annealed paricle filers o find he rue pose from scrach wihou performing an appropriae iniializaion, bu he search space migh be oo large o converge o he rue pose in reasonable ime, and even i migh no converge o he pose afer enough ime elapses. I is hus more desirable o employ oher informaion for iniializaion. The BLORT [18] employed SIFT keypoins [8] o recognize objecs and used hem for paricle iniializaion. In his paper we uilize a paricle filering echnique on he SE(3) group ha is based on [19]. For robus 3D visual racking, we employ keypoin feaures in iniializaion and edges in he calculaion of measuremen likelihoods. Like [15], our sysem can rack complex objecs by performing a self-occlusion es. By mainaining muliple hypoheses, our algorihm can reliably rack an objec on challenging image sequences ha have complex background and heavy cluer. Our key conribuions are as follows: We employ keypoin feaures as addiional visual informaion. While [15], [14] have used annealing paricle filer o find he iniial pose, we iniialize paricles o

2 highly probable saes based on pose esimaes calculaed from keypoin correspondences. The iniialized paricles end o converge faser han he usual annealed paricle filering. While previous edge-based rackers [15], [17] have employed random walk models as a moion model, we apply a firs-order auoregressive (AR) sae dynamics on he SE(3) group o be more effecive. To be fully auomaic and reliable in pracical seings, our approach moniors he number of effecive paricles and use he value o decide when he racker requires re-iniializaion. This paper is organized as follows. In Secion II, we inroduce a paricle filering framework wih sae and measuremen equaions. The AR sae dynamics is hen represened in Secion II-B. Afer explaining how paricles are iniialized and heir likelihoods are evaluaed in Secion II-C and II- D, respecively, he re-iniializaion scheme is represened in II-E. Experimenal resuls on various image sequences are shown in Secion III. II. PARTICLE FILTER ON THE SE(3) GROUP In 3D visual racking, a sae represens a 6-DOF pose of a racked objec, and racking esimaes ime-varying change of coordinaes. I is well known ha he rajecory is no on general vecor space, raher i is on Lie groups in general, he Special Euclidean group SE(3) and he affine group Aff(2) in 3D and 2D visual racking, respecively. Since he rajecory we wan o esimae is on a Lie group, he paricle filer should be applied on Lie groups. Mone Carlo filering on Lie groups is explicily addressed in [2], [19], [13]. As argued in [19] and [13], filering performance and noise disribuion of local coordinae-based paricle filering approaches are dependen on he choice of he local coordinaes, while paricle filering on Lie groups is coordinaeinvarian. A. Sae and Measuremen Equaions From he coninuous general sae equaions on he SE(3) group, discree sysem equaions is acquired via he firsorder exponenial Euler discreizaion [19]: X = X 1 exp(a(x, ) + dw ), (1) 6 dw = ǫ,i E i, i=1 ǫ = (ǫ,1,...,ǫ,6 ) T N( 6 1,Σ w ) where X SE(3) is he sae a ime, A : SE(3) se(3) is a possibly nonlinear map, dw represens he Wiener process noise on se(3) wih a covariance Σ w R 6 6, E i are he i-h basis elemens of se(3). The corresponding measuremen equaion is hen: y = g(x ) + n, n N( Ny 1,Σ n ) (2) where g : X R Ny is a nonlinear measuremen funcion and n is a Gaussian noise wih a covariance Σ n R Ny Ny. B. AR Sae Dynamics The dynamic model for sae evoluion is an essenial par ha has a significan impac on racker performance. However, many paricle filer-based rackers have been based on a random walk model because of is simpliciy [15], [17]. AR sae dynamics is a good alernaive since i is flexible, ye simple o implemen. In (1), he erm A(X, ) deermines he sae dynamics. A rivial case, A(X, ) =, is a random walk model. [13] modeled his via he firs-order AR process on he Aff(2) as: X = X 1 exp(a 1 + dw ), (3) A 1 = alog(x 1 2 X 1) (4) where a is he AR process parameer. Since he SE(3) is a compac conneced Lie group, he AR process model also holds on he SE(3) group [21]. C. Paricle Iniializaion using keypoin Correspondences Mos of he paricle filer-based rackers assume ha iniial saes are given. In pracice, iniial paricles are crucial o ensure convergence o a rue sae. Several rackers [15], [14] search for he rue sae from scrach, bu i is desirable o iniialize paricle saes by using oher informaion. Using keypoins allows for direc esimaion of 3D pose, bu due o he need for a significan number of correspondences i is eiher slow or inaccurae. As such, keypoin correspondences are well suied for he filer iniializaion. For iniializaion, we use so-called keyframes which are composed of 2D images and keypoins coordinaes (2D and 3D) ha have been saved offline. An inpu image coming from a monocular camera is mached wih he keyframes by exracing keypoins and comparing hem. To find keypoin correspondences efficienly, we employ he Bes-Bin-Firs (BBF) algorihm using kd-ree daa srucure [22] ha allows execuion of he search in O(n log n). As described in [8], he raio es is hen performed o find disincive feaure maches. While we used RANSAC [23] afer deermining puaive correspondences in our previous work [24], we skip his procedure because in he paricle filer framework we can iniialize paricles in an alernaive way in which he basic idea is similar o RANSAC. Insead of explicily performing RANSAC, we randomly selec a se of correspondences from he given puaive correspondences and esimae a possible se of poses calculaed from hem. Since we have 3D coordinaes of keypoins in keyframes, we ge 2D-3D correspondences from he maching process described above. So we can regard his problem as he Perspecive-n-Poin (PnP) problem, in which he pose of a calibraed monocular camera is esimaed from n 2D-3D poin correspondences, on each se of correspondences. To find a pose from he correspondences, we use he EPnP algorihm [25] ha provide a O(n) ime non-ieraive soluion for he PnP problem. Afer all paricle poses are iniialized from randomly seleced minimum correspondences, weighs of paricles are assigned from he number of remaining correspondences c r and he number of inlier correspondences c i which coincide wih

3 Algorihm 1 Overall algorihm Iniializaion 1) Se :=. 2) Se number of paricles as N 3) For i := 1,...,N, se X (i) via EPnP, and A (i) := ) For i := 1,...,N, normalize weighs π (i) via (5), by (6). 5) For i := 1,...,N, draw from X (i) according o π (i) o produce X (i). Imporance Sampling 1) Se := ) For i := 1,...,N, draw X (i) P(X X (i) 1,Σ w) by a) Generae he Gaussian ǫ N(,Σ w ), and propagae X (i) 1 b) Compue A (i) o X (i) wih A (i) 1 wih (4). 3) For i := 1,...,N, opimize X (i) via (3). wih IRLS via (9) and (1). 4) For i := 1,...,N, evaluae he imporance weighs o X (i) via (8) and (11). 5) For i := 1,...,N, normalize he imporance weighs π (i) by (12). 6) Evaluae N eff by (13) Resampling 1) If N eff < N hres a) Go o Iniializaion 3) and iniialize X (i), π (i), and A (i) for i := 1,...,N. 2) Oherwise a) For i := 1,...,N, resample from X (i) A (i) and o and A (i) wih probabiliy proporional o π (i) produce i.i.d. random samples X (i) b) For i := 1,...,N, se π (i) := π (i) c) Go o Imporance Sampling. := 1 N. he pose calculaed from he randomly seleced se. For i = 1,...,N where N is he number of paricles, he iniial weighs of paricles are assigned as: p(y X (i) ) e ( λc cr c i ) cr where λ c is a parameer. Then he weighs are normalized by: π (i) = N j=1 π (j) Afer weighs are normalized, paricles are randomly drawn wih probabiliy proporional o hese weighs. By doing so, we can generae probable iniial pose hypoheses. We iniialize paricles when he number of correspondences is bigger or equal o 9, and he number of randomly seleced minimum correspondences is 7.. D. Measuremen Likelihood and Opimizaion using IRLS Once each paricle is iniialized and propagaed according o AR process and Gaussian noise, i has o be evaluaed (5) (6) based on is measuremen likelihood. In edge-based racking, a 3D wireframe model is projeced o a 2D image according o a paricle sae X (i). Then a se of poins is sampled along edges in he wireframe model per a fixed disance. The sampled poins are mached o neares edge pixels from he image by 1D perpendicular search [2], [24]. Then he measuremen likelihood can be calculaed from he raio beween he number of mached sample poins p m and he number of visible sample poins p v which pass a selfocclusion es as: p(y X ) e (pv pm) ( λv ) pv where λ v is a parameer. This likelihood has been similarly used in [15]. Anoher choice is aking arihmeic average disances (error) ē beween he mached sample poins and he edge pixels [17]: p(y X ) e ( λeē) where λ e is also a parameer o be uned. We noiced ha boh likelihoods are valid, and we empirically found ha using boh erms shows beer resuls. Therefore, in our approach he measuremen likelihood is evaluaed as: p(y X ) e (pv pm) ( λv pv ) e ( λeē) One of he challenges in paricle filering for 3D visual racking is he large sae space, so a large number of paricles is usually required for reliable racking performance. To reduce he number of paricles, [15] has used an annealed paricle filer, and [26], [17] have selecively employed local opimizaions in a subse of paricles. For more accurae resuls, we opimize paricles as well, in which Ieraive Reweighed Leas Squares (IRLS) is employed [24], [2]. From IRLS, he opimized paricle X (i) is calculaed as follows: X (i) = X (i) exp( (7) (8) 6 µ i E i ) (9) i=1 µ = (J T WJ) 1 J T We (1) where µ R 6 is he moion velociy ha minimizes he error vecor e R Ny, J R Ny 6 is a Jacobian marix of e wih respec o µ obained by compuing parial derivaives a he curren pose, and W R Ny Ny is a weighed diagonal marix. The diagonal elemen in W is w i = 1 c+e i where c is a consan and e i is i-h elemen of e. (For more deail informaion abou J and IRLS, please refer o [24], [2]). Noe ha he measuremen likelihood in (8) is calculaed before he IRLS opimizaion. To assign weighs of paricles, we have o evaluae he likelihood again wih he opimized sae X (i). However, compuing he likelihood of every paricle again is compuaionally expensive. Since every paricle is opimized a he same ime, we can approximae p(y X (i) ) as: p(y X (i) ) p(y X (i) ) (11)

4 Fig. 1. Tracking resuls wih (yellow wireframe) and wihou (red wireframe) our paricle filer for he four argeed objecs. From op o boom, eabox, book, cup and car door. From lef o righ, < 1, = 1, = 2, = 3, = 4 and = 5 where is he frame number. The very lef images are resuls of he pose iniializaion. Noe ha yellow wireframes are well fied o he racking objecs, while red wireframes are frequenly mislocalized. 1 paricles are used for he paricle filer. (i.e. N = 1) Then he weigh is normalized o π (i) π (i) = N j=1 π (j) E. Re-iniializaion based on N eff by: (12) Ideally a racked objec should be visible during an enire racking session. In realiy, however, i is quie common ha he objec goes ou of frame or is occluded by oher objecs. In hese cases, he racker is required o re-iniialize he racking. In general sequenial Mone Carlo mehods, he effecive paricle size N eff has been inroduced as a suiable measure of degeneracy [27]. Since i is hard o evaluae N eff exacly, an alernaive esimae N eff is defined [27]: N eff = 1 N i=1 ( π(i) ) 2 (13) Ofen i has been used as a measure o execue he resampling procedure. Bu, in our racker we resample paricles every frame, and hence we use N eff as a measure o do reiniializaion. When he number of effecive paricles is below a fixed hreshold N hres, he re-iniializaion procedure is performed. The overall algorihm is shown in Algorihm 1. III. EXPERIMENTAL RESULTS In his secion, we validae our proposed paricle filerbased racker via various experimens. Firs, we compare he performance of our approach wih he previous single hypohesis racker [24] which was based on IRLS. For he comparison, we use new challenging image sequences Teabox Book Cup Car door TABLE I RMS ERRORS IN THE GENERAL TRACKING RMS Errors x y z roll pich yaw The error unis of ranslaion and roaion are meer and degree, respecively. The upper rows are he resuls of he previous approach [24]. The lower rows are he resuls of he proposed approach. In boh upper and lower rows, beer resuls are indicaed in bold numbers. as well as image sequences used in [24]. To verify he effeciveness of he AR sae dynamics, we show he resuls of our proposed racker wih and wihou he AR sae dynamics. A. Experimen 1: Image Sequences from Choi and Chrisensen [24] In [24], he sequences of images were capured from a monocular camera in saic objec and moving camera seing. A se of image sequences used in Secion III-A.1 are acquired o es racking performance in general seing, i.e. no occlusion, relaively simple background, reasonable cluer, and smooh movemens of he camera. To es reiniializaion capabiliy, a sequence of images is capured

5 X Translaion 2 Y Translaion Z Translaion Roll Angle Pich Angle Yaw Angle Ground Truh Fig. 2. Pose plos of he eabox objec in he general racking es. The proposed approach (PF+IRLS) shows superior accuracy han he previous approach (IRLS). Especially, using our paricle filer significanly enhances roaional accuracy. IRLS PF+IRLS 3 Normalized Translaional Residual: T 15 Normalized Roaional Residual: R IRLS PF+IRLS Fig. 3. Normalized residual plos of he eabox objec in he general racking es. In general, he proposed approach (PF+IRLS) shows lower residual and more consisen resuls han he previous one (IRLS). wih fas camera moion and occlusions. This sequence is esed in Secion III-A.2. 1) General Tracking: The single hypohesis racker in [24] has shown reasonable racking resuls on he general racking sequences. To show quaniaive resuls, AR markers are employed o gaher ground ruh pose esimaes. To compare our proposed approach wih he previous one, we execued our new approach on he same image sequences. The racking resuls are shown in Fig. 1. In he proposed approach, 1 paricles are mainained, and he mean of paricles is depiced in he figures. To calculae he mean of paricles, we follow he mean roaion evaluaion of he special orhogonal group SO(3) by Moakher [28] ha is also considered in [19], [17]. To clearly show he difference of he wo approaches, boh of he pose resuls are depiced in he same image sequences. The yellow and red wireframes are projeced o images wih respec o he pose resuls esimaed by he proposed approach and previous approach, respecively. We can easily verify ha he proposed approach shows more accurae resuls. To decompose pose resuls, 6-DOF pose and residual plos of he eabox objec are represened in Fig. 2 and 3, respecively. Based on he plos, we can easily see he difference where he proposed approach (PF+IRLS) shows much beer resuls han he previous approach (IRLS). Noe ha he considerable differences in orienaion esimaes. This is due o some false edge correspondences ha lead o errors in pose, mainly in orienaion. Since our paricle filer considers muliple hypoheses and resamples based on measuremen likelihood, i is quie robus o false edge correspondences from which he single hypohesis racker is ofen suffered. A quaniaive analysis of hese ess is represened in Table I which shows he roo mean square (RMS) errors. For each objec, he upper rows are he resuls of he previous approach and he lower rows are he resuls of he proposed approach. Wih a few excepions, he proposed approach ouperforms he previous one in erms of accuracy. As menioned earlier, he proposed approach shows beer orienaion esimaes. Alhough here are a few excepions, he difference is abou 1 mm in ranslaion and.16 deg in roaion. Since he ground ruh was measured via he AR marker and he displacemen beween he objec and he AR marker was measured manually, ha errors migh come from hese measures. 2) Re-iniializaion: In our previous sysem, we used a simple heurisic in which he difference in posiion of he objec beween frames and he number of valid sample poins are moniored o rigger re-iniializaion [24]. While ha heurisic works well when he pose hypohesis drifs fas, i migh no always be he case when he hypohesis suck in local minima. Here we propose anoher way for reiniializaion by aking advanage of muliple hypoheses. As in Algorihm 1, our sysem re-iniializes when he number of effecive paricles N eff is below a hreshold. To verify his mehod, we run he proposed racker on he re-iniializaion sequence. The racking resuls are shown in Fig. 4 and he number of effecive paricles is ploed over he frame numbers in Fig. 5. The gray line represens he hreshold value N hres. When he racked objec goes ou of frames, images are blurred because of camera shaking, or he objec is occluded wih a paper, he N eff decreases significanly, and ha riggers he re-iniializaion. During re-iniializaion, he racker maches keypoins unil i has a leas he minimum

6 Fig. 4. Tracking resuls on he re-iniializaion sequence. From op-lef o boom-righ, he frame numbers are =, 1, 2, 275, 3, 328, 4, 5, 589, 6, 627, 7, 8, 9, 984, 1, 136, and 11. The green wireframes represen paricles and he yellow hick wireframe shows he mean of paricles on each image. When he racked objec goes ou of frames, images are blurred because of camera shaking, and he objec is occluded wih a paper, our racker re-iniialize. (N = 1) N eff Fig. 5. The N eff plo for he re-iniializaion sequence. (N = 1) number of keypoin correspondences. Once enough poin correspondences are acquired, he proposed sysem iniializes paricles. B. Experimen 2: More Challenging Image Sequences Since he aforemenioned image sequences were prepared for he previous approach, i is relaively easy o rack objecs in hese sequences. Therefore, we need oher daases o compare our new approach. So we prepared more challenging image sequences in which a complex background is considered. 1) Effeciveness of Paricle Filer: When he background is relaively simple, single hypohesis edge-based racking works reasonably. Bu i is quie challenging o reliably rack an objec when he background is complex or here is an amoun of cluer. These challenging siuaions ofen make erraic edge correspondences, hence single hypohesis racking can be a fragile soluion in hese cases. To validae his argumen, we compare our proposed racker wih he single hypohesis racker. We capured wo image sequences for he book and cup objecs. To make he background complex, we pu hese objecs on a camera calibraion plae in which he grid paern is likely o generae false edge correspondences. The comparaive racking resuls are shown in Fig. 6. The grid paern and he background exure play a role as srong cluer, hence he previous approach suffers from he local minima. However, our approach dependably racks objecs in spie of he cluer. 2) Effeciveness of AR Sae Dynamics: To verify he effec of he AR sae dynamics, we execue he proposed approach wih and wihou he AR sae dynamics. To disable he dynamics, we se he parameer a in (4) as which is equivalen o a random walk model. For fair comparison, we use he same parameers excep he AR parameer. We es on a sequence of he book objec used in he previous experimen. The racking resuls are represened in Fig. 7. Alhough boh use he same number of paricles, Gaussian noise, and measuremen likelihood, he racking performances are quie disincive. This difference is mainly due o he AR sae dynamics which propagaes paricles according o he camera moion. IV. CONCLUSIONS We have presened an approach o 3D visual objec racking based on a paricle filering algorihm on he SE(3) group. For fas paricle convergence, we employed keypoin feaures and iniialized paricles by using a linear ime non-ieraive soluion for he PnP problem. Paricles are propagaed by he sae dynamics which is given by an AR process on he SE(3), and he sae dynamics disribued paricles more effecively. Measuremen likelihood was calculaed from boh he residual and he number of valid sample poins of he edge correspondences. During he racking, he proposed sysem appropriaely re-iniialized by iself when he number of effecive paricles is below a hreshold. Our approach has been esed via various experimens in which our muliple hypoheses racker has shown noable performance on challenging background and cluer. One of he possibiliies for fuure work is exploiing he parallel power of GPU for real-ime performance [15], [16]. Anoher ineres is in muliple objec recogniion and racking [29] which is necessary for a realisic scenario.

7 Fig. 6. Tracking resuls on more challenging image sequences. Top and boom rows represen seleced frames from book and cup sequences, respecively. For comparison, he poses esimaed by he proposed (PF+IRLS) and he previous (IRLS) approaches are depiced in yellow and red wireframes, respecively. Because of background exure, he previous approach is ofen misled o local minima, while he proposed approach robusly esimaes poses of objecs under ambiguous background exure and fas camera moions. (N = 1) Fig. 7. Tracking resuls for he proposed approach wih (yellow wireframe) and wihou (red wireframe) he AR sae dynamics. I shows ha he AR sae dynamics conribues o propagae paricles more effecively. (N = 1) V. ACKNOWLEDGMENTS This work was parially funded and developed under a Collaboraive Research Projec beween Georgia Tech and he General Moors R&D, Manufacuring Sysems Research Laboraory. The suppor from General Moors is graefully acknowledged. REFERENCES [1] C. Harris, Tracking wih Rigid Objecs. MIT Press, [2] T. Drummond and R. Cipolla, Real-ime visual racking of complex srucures, PAMI, vol. 24, no. 7, pp , 22. [3] A. I. Compor, E. Marchand, and F. Chaumee, Robus model-based racking for robo vision, in IROS, vol. 1, 24. [4] E. Rosen and T. Drummond, Fusing poins and lines for high performance racking, in ICCV, vol. 2, 25. [5] L. Vacchei, V. Lepei, and P. Fua, Combining edge and exure informaion for real-ime accurae 3d camera racking, in ISMAR, 24, pp [6] M. Pressigou and E. Marchand, Real-ime 3d model-based racking: Combining edge and exure informaion, in ICRA, 26, pp [7] G. Klein and T. Drummond, Tighly inegraed sensor fusion for robus visual racking, Image and Vision Compuing, vol. 22, no. 1, pp , 24. [8] D. G. Lowe, Disincive image feaures from scale-invarian keypoins, IJCV, vol. 6, no. 2, pp , 24. [9] H. Bay, A. Ess, T. Tuyelaars, and L. V. Gool, Speeded-up robus feaures (SURF), Compuer Vision and Image Undersanding, vol. 11, no. 3, pp , 28. [1] C. Kemp and T. Drummond, Dynamic measuremen clusering o aid real ime racking, in ICCV, 25, pp [11] M. Isard and A. Blake, Condensaion condiional densiy propagaion for visual racking, IJCV, vol. 29, no. 1, pp. 5 28, [12] D. A. Ross, J. Lim, R. S. Lin, and M. H. Yang, Incremenal learning for robus visual racking, IJCV, vol. 77, no. 1, pp , 28. [13] J. Kwon and F. C. Park, Visual racking via paricle filering on he affine group, IJRR, vol. 29, no. 2-3, p. 198, 21. [14] M. Pupilli and A. Calway, Real-ime camera racking using known 3D models and a paricle filer, in ICPR, vol. 1, 26. [15] G. Klein and D. Murray, Full-3d edge racking wih a paricle filer, BMVC, 26. [16] T. Mörwald, M. Zillich, and M. Vincze, Edge racking of exured objecs wih a recursive paricle filer, in 19h Inernaional Conference on Compuer Graphics and Vision (Graphicon), Moscow, 29, pp [17] C. Teulière, E. Marchand, and L. Eck, Using muliple hypohesis in model-based racking, in ICRA, 21. [18] T. Mörwald, J. Prankl, A. Richsfeld, M. Zillich, and M. Vincze, BLORT - he blocks world roboic vision oolbox, in In Bes Pracice in 3D Percepion and Modeling for Mobile Manipulaion (in conjuncion wih ICRA 21), 21. [19] J. Kwon, M. Choi, F. C. Park, and C. Chun, Paricle filering on he Euclidean group: framework and applicaions, Roboica, vol. 25, no. 6, pp , 27. [2] A. Chiuso and S. Soao, Mone Carlo filering on Lie groups, in IEEE Conference on Decision and Conrol, vol. 1, 2, pp [21] J. Xavier and J. H. Manon, On he generalizaion of AR processes o Riemannian manifolds, Proceedings of IEEE Inernaional Conference on Acousics, Speech, and Signal Processing., 26. [22] J. Beis and D. Lowe, Shape indexing using approximae nearesneighbour search in high-dimensional spaces, in CVPR, 1997, pp [23] M. A. Fischler and R. C. Bolles, Random sample consensus: a paradigm for model fiing wih applicaions o image analysis and auomaed carography, Commun. ACM, vol. 24, no. 6, pp , [24] C. Choi and H. I. Chrisensen, Real-ime 3D model-based racking using edge and keypoin feaures for roboic manipulaion, in ICRA, 21, pp [25] V. Lepei, F. Moreno-Noguer, and P. Fua, EPnP: An accurae O(n) soluion o he PnP problem, IJCV, vol. 81, no. 2, pp , 29. [26] M. Bray, E. Koller-Meier, and L. V. Gool, Smar paricle filering for 3D hand racking, in Sixh IEEE Inernaional Conference on Auomaic Face and Gesure Recogniion, 24. Proceedings, 24, pp [27] A. Douce, S. Godsill, and C. Andrieu, On sequenial Mone Carlo sampling mehods for Bayesian filering, Saisics and compuing, vol. 1, no. 3, pp , 2. [28] M. Moakher, Means and averaging in he group of roaions, SIAM Journal on Marix Analysis and Applicaions, vol. 24, no. 1, p. 116, 23. [29] A. Colle, D. Berenson, S. S. Srinivasa, and D. Ferguson, Objec recogniion and full pose regisraion from a single image for roboic manipulaion, in ICRA, 29, pp