Loop Closing for Visual Pose Tracking during Close-Range 3-D Modeling

Transcription

1 Loo Cosing for Visua Pose Tracking during Cose-Range 3-D Modeing Kaus H Strob Robotics and Mechatronics Center (RMC) German Aerosace Center (DLR) D Wessing, Germany Abstract This work deas with the assive tracking of the ose of a cose-range 3-D modeing device using its own high-rate images in reatime, concurrenty with customary 3-D modeing of the scene by aser trianguation Our former works in Refs [1,2] successfuy imemented visua ose tracking Accuracy being a centra requirement to 3-D modeing, however, here we note that accuracy can be further increased using a grah-based noninear otimization of the tracked ose by minimization of rerojection errors Loo cosures eg when having scanned a around the objects rovide the oortunity to increase ose tracking and 3-D modeing accuracy The sarse otimization is in the form of a hybrid, keyframe-based bunde adjustment agorithm on stereo keyframes, yieding raid otimization of the whoe trajectory and object mesh mode within a second The otimization is suorted by the use of aearance-based SURF descritors together with a bank of arae three-oint-ersective ose sovers 1 Introduction Cose-range 3-D modeing is a fied that, in our view, is going to raidy sread in nove areas ike human-comuter interaction and robotics due to the advent of cheaer and ighter range sensors It is beieved that it is through the exicit formation of 3-D modes that a considerabe number of the remaining chaenges of visua ercetion wi be eventuay soved This is, of course, subject to the erformance, cost, and fexibiity of aication of the 3-D modeing device It is often imossibe to acquire a comete 3-D mode in a singe measurement ste owing to eg object sef-occusion, object size, or imited fied of view; this is eseciay true in cose-range Mutie views (or mutie sensors) are reguary deoyed in order to fuse their range images into a registered 3-D mode The revaent aroach is to measure the ose of the sensors whie acquiring data, which aows for onine registration of data in absoute coordinates A range of ose tracking systems, robotic maniuators, turntabes, or eectromagnetic devices are commony deoyed for this urose These otions are inconvenient for three reasons: First, they imit the mobiity of the user; second, they require accurate caibration and synchronization wrt the range sensor; and third, they are (by far) the argest and most exensive art of the 3-D modeing system G Bebis et a (Eds): ISVC 2014, Part I, LNCS 8887, , 2014 c Sringer Internationa Pubishing Switzerand 2014

2 Loo Cosing for Visua Pose Tracking during Cose-Range 3-D Modeing 391 In Refs [1,2] we resented the first hand-hed 3-D modeing device for coserange aications that ocaizes itsef assivey from its own images in reatime, at a high data rate In Ref [1] ose tracking was otionay suorted by an on-board IMU for more efficient feature tracking In Ref [2] we resent an aternative tracking method that, insired by the Active Matching aradigm, achieves remarkabe tracking resiience without the need for inertia readings 3-D modeing by browsing an object is argey an exoratory act where oo cosing events are rare Hence rea-time ose tracking argey reies on dead reckoning, which is inconvenient as it invariaby accumuates drifts The utimate goa of 3-D modeing is, however, the comete reconstruction of objects eg by scanning a around the object This event invoves (at east) one oo cosure that rovides the oortunity to greaty increase resent and ast ose tracking accuracy so that the fina 3-D mode wi exce in accuracy irresective of rior motion drifts It is worth noting that visua odometry is sti erfecty usefu during the browsing eriod; first, in order to rovide ive image augmentation and ive meshing resuts; second, in order to suort raid, oca oo cosing In this work we use the DLR 3D-Modeer atform, which is a ow-cost, handhed device for geometric and radiometric reconstructionof cose-rangeobjects in reatime It exces in accuracy comared with eg deth sensors based on coded infrared ight [3] In detai, we extend our rior aroach resented in Ref [1], aiming at more accurate ose tracking by grah-based noninear otimization of the tracked ose by minimization of residua rerojection errors We ot for a hybrid, keyframe-based bunde adjustment (kba) agorithm on stereo keyframes, because kba is aegedy the most accurate and efficient otion to tacke this robem in the face of a higher number of features and keyframes [4] 2 State of the Art A straightforward otion to register range images is based on their geometry Deending on the acquired scene, however, this otion may be recuded if the surfaces do not show saient 3-D regions, or in the case of 1-D range data eg when using sit scanners A widesread aternative for deth image registration in reatime is to externay track the ose of the modeing device so that range data can be directy reresented in a common reference frame, in reatime and irresective of the range data quaity In Ref [1] the authors isted the dominant commercia 3-D modeing systems, which either use inconvenient externa reference systems, or ot for visua ose tracking reying on active iumination and adhesive markers on the scene They aso isted research work on assive visua tracking, which did not, however, run in reatime Dense methods (either based on GPGPU or on RGB-D hardware) are resenty the referred choice for inexensive 3-D modeing We beieve, however, that it is sti convenient to foow the method resented in Ref [1] because first, sit scanners sti rovide higher accuracy [3], second, its ower hardware and energy requirements (a GPU is not needed),and third, feature-based ose tracking methods rovide a higher degree of viewoint invariance than dense methods

3 392 KH Strob 3 The DLR 3D-Modeer The DLR 3D-Modeer is a mutiurose atform for geometric and visua ercetion It combines comementary sensors in a comact, generic way It is ow weight and features onboard comutation, a FireWire connector, generic mechanica interfaces, and an extensive software suite Current aications comrise 3-D modeing, visua tracking and servoing, exoration, ath anning, and object recognition eg as the ercetion head of the humanoid robot Justin Stereo camera Laser Strie Profier IMU FireWire connection Laser-Range Scanner Fig 1 The DLR 3D-Modeer 4 Visua Pose Tracking at the DLR 3D-Modeer In the origina work in Ref [1] we rovide ose tracking estimations in reatime out of monocuar tracking of saient features in the context of an extended KLT feature tracker; the features have been accuratey reconstructed in 3-D by onetime stereo vision The major chaenge in this context is tracking features in cose-range; unike in the case of far-range tracking, cose-range feature tracking is affected by transation to a simiar extent as by rotation eseciay in the case of a hand-guided device rone to jerky motion A nove method was roosed that everages the rotationa readings of an IMU for imroved estimation of the disacement of features in between frames After that in Ref [2] we resented an aternative method that did without IMU readings by casting the KLT feature tracker unto the Active Matching (AM) aradigm, achieving robust feature tracking at an even higher motion bandwidth Reative ose estimation is based on an efficient, robustified V-GPS agorithm [5] In this work we contribute a nove grah-based otimization rocedure as we as aearance-based reocaization and oo-cosing to eventuay boost accuracy 41 Loca, Keyframe-Based Bunde Adjustment It is a ecuiarity of 3-D modeing that new areas are continuousy being exored and oo-cosing events are rare In this section we focus on otima motion estimation without cosing arge oos, ie, by dead reckoning; in Sect 43 we sha resent a more comete otimization in the event of a fina oo cosure eg after scanning a around an object Whie robust V-GPS rovides a robust, fast motion estimation from monocuar footage by dead reckoning in reatime, it is sti advisabe to erform otima motion and structure estimation by minimization of rerojection errors at handover stereo keyframes to further increase accuracy Foowing eg Refs [6,4]

4 Loo Cosing for Visua Pose Tracking during Cose-Range 3-D Modeing 393 Rerojection residuas x 1 x 2 x 4 x 3 Features being otimized Origina stereo keyframe L i r T R r i i T fi L f i Fina monocuar frame Fig 2 Data concerned in oca, hybrid BA on feature set #i we ot for an efficient BA otimization disregarding image frames in between seected keyframes (ie, kba) Since in our aroach a 3-D features are being measured ocay, ie, on a unique static reference frame defined at keyframes, the goba otimization of the covered dead reckoning motion can be decomosed into indeendent sub-otimizations excusivey concerning one reference frame aong with its feature set In detai, the information required for every sub-otimization is confined to the stereo (eft and right) keyframe I i r I i that initiaized the ith feature set by stereo trianguation, aong with the fina, eft monocuar image f I i that both, tracks the ith feature set ast, and coincides with the eft frame I i+1 of the next keyframe (from which the foowing feature set #i+1 wi be initiaized), cf Fig 2 This fruga, hybrid keyframe seection oicy does deiver high accuracy as both, initia and ast tracking vantage oints, are being considered for every feature, maximizing their rojected araax In addition, the incusion of stereo images serves to anchor goba scae The nove formuation minimizes the sum of squared rerojection residuas as foows: M i Ω i =argmin ( m i ˆm i ( ˆx i ) 2 + r m i r ˆm i ( T r, ˆx i ) 2 =1 + f m i f ˆm i ( i T f i, ˆx i ) 2) (1) where the otimized ( ) arameters Ω i incude the 3-D coordinates x i =[ x i, y, i z] i T, N 1,i M i of the ith set of M i features wrt the eft camera at keyframe i, and the inter-keyframe transformation i T fi of the eft camera frame between keyframes #i and #i+1 The residua is comosed of estimated (ˆ) rerojections ˆm i =[ û i ˆv i ] T =roj( ˆx i )and r ˆm i =[ r û i rˆv i ] T =roj( r T ˆx i ) onto the eft and the right frames at the initia keyframe of feature set #i, resectivey, as we as their ast, fina feature rojections f ˆm i =[ fû i fˆv i ]T = roj( fi T i ˆx i ) at the eft frame (remember that fi i I i+1 ) These estimations are being subtracted from the actua measurements m i, r m i and f m i to form the residua rerojection errors The transformation r T stems from the eioar geometry of the stereo camera by camera caibration Note that the rojection function roj() does not incude ens distortion; for efficiency reasons, we ot for minimizing undistorted rerojection errors, undistorting actua rojections beforehand

5 394 KH Strob Note that goba scae coud aso be anchored even if the rojections r ˆm i had not been incuded in the residua function, but considered ground truth instead However, we stress that the nature of the 3-D features x i does not stem from seected, ground truth rojections into an image (eg r m i ) in the context of stereo vision, but from their rigid body geometry aone In this way, by reeasing a three key rojections the otima 3-D soution wi be soey constrained by the rigid body assumtion together with ersective geometry In addition, it is we known that fu BA turns out to be faster than any attemts to eiminate eg the structure arameters [7] The hybrid otimization utiizes the noninear east squares otimization function devmar der() [8], which imements the Levenberg-Marquardt method We are roviding anaytic Jacobians for imroved erformance Even though they are aways sarse, the sma size of the system of equations renders sarse methods unnecessary It is worth noting that minima reresentations are used for unknown rotations, secificay differentia erturbations of Euer anges In addition, the residua function has been robustified in case of outiers Δ m i ( m i ˆm i ) Ω i Δm Ω i = i = Δ rm i Ω i Ω i = Δ f m i 6M i (6+3M i) Ω i ΔT i+1 x i 1 {}}{ xi 1 x i {}}{{}}{ xi +1 xi M i {}}{ m i 0 Δ m i 2 3( 1) 0 x = i 2 3(Mi ) rm i Δ rm i = 2 3( 1) 0 2 3(Mi ) = fm i Δ fm i T x i 0 2 3( 1) Δ f m i x i 0 2 3(Mi ) ( 1) 0 2 3(Mi ) ( 1) 0 2 3(Mi ) 0 2 3( 1) 0 2 3(Mi ) White boxes corresond to zero eements; gray or back boxes to non-zero ones (2)

6 Loo Cosing for Visua Pose Tracking during Cose-Range 3-D Modeing 395 By way of iustration, we go into detai about the cacuation of the back Jacobian eement above: where ( f ṽ i fˆv i ) ŷ i = fˆv i f ŷ i f ŷ i ŷ i fˆv i f ẑ i f ẑ i ŷ i fˆv i =(β ŷ i f fẑ i + v 0 ) fˆx i ˆx i fŷ i fẑ i = Δ T 1 i+1 f i T i ŷ i }{{} ẑ i 1 erturbation 1 (3) ; (4) β and v 0 are art of the intrinsic arameters of the eft camera, and Δ T i+1 reresents the estimated rigid body erturbation on the eft camera ose at keyframe i+1 This method yieds sub-miimetric corrections wrt V-GPS on 3-D feature ocations x i and the reative ose i T fi for every keyframe or feature set Miimetric differences may arise on eventua oo cosures after many keyframes, eg when scanning a around an object On baance, it turns out that this method does not substantiay imrove the aready accurate dead reckoning motion estimation by V-GPS On the other hand, its comutationa cost is sti ow (2 to 5 ms) roughy twice as ong as V-GPS 42 Aearance-Based Reocaization Whenever 1 saccadic motion recudes sequentia tracking, 2 the user browses outside a roximate scene, or 3 the cameras return to an area used before (oo cosing), ose tracking accuracy gets too ow for consistent KLT tracking to be warranted anymore even in its AM variant Due to the richness of visua data, cameras are ideay suited for recognizing simiarity; aearance-based reocaization can he to resume scanning on the origina reference frame There exist a number of oerators, caed descritors, that concern about the visua aearance of features in order to be distinctive and invariant to their viewoint ose We choose the erformant SURF features in its origina imementation, on stereo images By using stereo images, the 3-D osition of SURF features wrt the camera eft T SURF can be trianguated at the same frame during stereo initiaization of the KLT feature set, where we obtained eft T KLT By doing so, whenever 3 or more SURF features and consequenty now T SURF are KLT found again, now T can be roughy estimated as foows: now T KLT = now T SURF( eftt SURF) 1eftT KLT (5) This estimation is far ess accurate than sequentia ose tracking using V-GPS, comromising seamess transition to KLT tracking We ot for using intereaved,

7 396 KH Strob monocuar three oint ersective (P3P) ose estimation on KLT features for increased accuracy Finay, reguar KLT tracking takes on sequentia ose tracking on the origina reference frame not without rior scaing and affine distortion of the features temates according to the current reative ose 43 Goba, Hybrid Bunde Adjustment on Loo Cosures Loo cosure events occur whenever former scene features that have not been recenty tracked are being revisited These events resent the oortunity to greaty increase resent and ast ose tracking accuracy We distinguish between two tyes of oo cosures: oca oo cosures can sti take advantage of metric information for imroved erformance, whereas goba, arge-scae oo cosure ought to be indeendent of motion estimation recisey because its main objective is to correct inaccurate motion estimation in the first ace Goba, arge-scae oo cosing may instead concern itsef with the rojected aearance of features, which are sti discriminative in the face of unknown ocaization, see Sect 42 Whatever the nature of the oo cosure, it is indicated to subsequenty otimize structure and motion estimations in the ight of the discreancies between exected and actuay matched oo-cosing features In the absence of oo cosures, current measurements (rojections) ony deend on their initia stereo keyframe and on the current reative ose wrt that frame In the event of oo cosure, however, current rojections aso deend on the camera motion history, ie, on a reative transformations and stereo feature trianguations even since the creation of the newy regained features, see Fig 3 SURF features Loo cosure! f r L N R N T N+1 R N N+1 = N+1 r N L Object L 1 R KLT features r 1 1 T 2 R L R L Motion 2 r 2 Fig 3 Skeeton of stereo keyframes 1N when browsing around an object During monocuar tracking of feature set #N, feature set #1 can be retrieved at images,r I N+1 Deending on the distance traveed, oo cosing occurs either by monocuar tracking of KLT features or with the he of stereo SURF features 2 T 3 As a consequence, the otima soution by noninear otimization consisting in the minimization of squared rerojection residuas resents higher comexity than the oca otimization in Eq (1)

8 Loo Cosing for Visua Pose Tracking during Cose-Range 3-D Modeing 397 Now: ( N Mi ( Ω =arg min m i ˆm i ( ˆx i ) 2 + r m i r ˆm i ( T r, ˆx i ) 2 (6) i=j =1 ) + f m i f ˆm i f ( i T i, ˆx i ) 2 + ) r j ˆr j f ( j T j f,, N T N, ˆx j ) 2 R where the arameters to be otimized Ω =[Ω j Ω N ] incude a history of 3-D features between the oder feature set #j being found again, and the ast tracked feature set #N (ie, N j +1 feature sets in tota), as we as the N j reative, inter-keyframe transformations between their resectives keyframes and the f fina oca ose N T N where the oo was cosed (incuded in Ω N ) In tota, this amounts to N i=j (3 M i+6) arameters, comared to 3 M i +6 in Eq (1) Note that, due to the non-convexity of the reguar BA robem, we are otimizing over (differentia erturbations of) non-rivieged, reative transformations in order to avoid oca minima [9] Consequenty, feature ocations and camera motions are both ocay Eucidean, but gobay tooogica The goba Eucidean reresentation remains as a searate task, eft aside eg for the reatime meshing aication to consistenty visuaize it in reatime, erhas augmenting it with the ive image stream The residua in Eq (6) is comosed of the accumuation of residuas Δm i in Eq (1), now for every feature set i within the oo, as we as for the subset R of features contained in feature set j that have been found again in rojections r j =[ N+1 ũ j N+1 ṽ j ]T, see Fig 3 In matricia form, the number of equations amounts to N i=j (2 3 M i)+2 size(r) comaredto2 3 M i in the case of oca BA for dead reckoning in Eq (1) Otimization rocesses with system equations of this magnitude ceary benefit from sarse otimization methods if their Jacobians are sarse Indeed, zero eements are ervasive in the Jacobian of this system of equations wrt the abovementioned arameters due to the reative nature of the formuation used: where Δr j Ω = Δr j [ Ω j = ( m ˆm) Ω Δr j Ω j Ω j {}}{ { ΩN }}{ Δm j 0 m Ω j j = 0 Δm N Ω N m N Δr j r Ω j Δrj Δr j Ω k Ω N 0 2 3( 1) 0 2 3(Mi ) ] (7)

9 398 KH Strob Δr j [ ] Ω k = 0 2 3Mi Δr j [ ] Ω N = 0 2 3Mi (8) White boxes corresond to zero eements; gray or back boxes to non-zero ones We now go into detai about the cacuation of the back Jacobian eement highighted above concerning features within R that have been tracked again The estimated rerojection ˆr j of these features from feature set #j onto the eft camera frame at keyframe #N+1 is a function of both, the 3-D structure ˆx j f of the origina set #j and the current eft camera ose j T N that, in turn, is a function of a oca transformations by dead reckoning ying between keyframes #j and #N + 1 Here the cacuation of its artia derivative wrt the first Euer ange α k of the differentia erturbation Δ T 1 k at the eft camera frame of keyframe #k is detaied: where ( N+1 ṽ j N+1ˆv j ) α k N+1 ẑj 1 = N+1ˆvj N+1 ŷ j N+1 ŷ j α k N+1ˆvj N+1 ẑ j N+1ˆv j ŷ j =(β N+1 + v 0 ) N+1 ẑj N+1 ˆx j N+1 ŷj = f N T k+1 Δ T 1 j }{{ k+1 f k T } erturbation jˆx j j ŷ j j ẑ j 1 N+1 ẑ j α k (9) (10) These few features are of extreme imortance, as they roduce the ony residuas bringing about oo-cosing information ese goba otimization equas reeated oca otimization by dead reckoning in Eq (1) In reaity, the formuation exained above corresonds to the idea case where a features tracked at oo cosure have aso been tracked at their trianguation frame, ie, f m j exists and is incuded in both Eqs (6) and (7); however, features that were not succesfuy tracked unti keyframe #j+1 can readiy be found again when cosing the oo In that case (arox 15% of the detected features), the residua Eq (6), the otimization arameters Ω, as we as the Jacobian in Eq (7) have to be extended to incude their initia rojections m j and rm j as we as their 3-D ocations Our hybrid otimization utiizes the noninear, east squares sarse otimization function sarsem dercrs() detaied in Ref [10], as we as suernoda sarse Choesky factorization by CHOLMOD and grah artitioning by METIS to observe both rimary and secondary sarsity structures of the Jacobian in Eq (7) [11] We rovide the abovementioned, fu anaytic Jacobian in CRS format for imroved erformance Of course, common derivative terms are being stored

10 Loo Cosing for Visua Pose Tracking during Cose-Range 3-D Modeing 399 instead of recacuated By way of exame, timekeeing imroves from 94 sec (standard BA with fu anaytic Jacobian) to between 750ms and 14sec using the sarse variant Not roviding anaytic Jacobians roves sower by a factor of 2 or 3 Goba BA is erformed in a searate comuting thread in order not to disrut concurrent rea-time ose tracking and 3-D modeing In Sect 6 we show extended oo cosure exeriments, where goba BA comensates for substantia dead reckoning errors of severa cm in the course of obtaining consistent tooogy of the ma Aart from the nove, hybrid nature of our aroach to anchor goba scae by stereo vision in seected frames (which incidentay deskis oca ose tracking), our work differs from simiar reative imementations in the SLAM iterature ([12,13,14,9,15,16,17]) since accurate motion tracking is here required gobay, for the whoe motion history, whereas in SLAM metric accuracy is encouraged ony ocay, as goba tooogica integrity suffices [13] 5 Exerimenta Vaidation We suggest the interested reader to retrieve the videos of the origina visua ose tracking in Refs [1,2] at htt://goog/8zaj52 and htt://goog/pjdeox In this section we describe the image sequence attached as suementary materia to this aer, see htt://goog/tqf4vb It shows an extended scan around a 50 cm ta scuture A natura browsing rocedure asks for roonged swees and is characterized by the absence of oo cosure events (neither oca nor goba), ie, ony dead reckoning estimation is ossibe Tracking starts in frame #23033, featuring 4 swees in 90 reative yaw anges, rior to oo cosing in frame #24521 for a tota motion ength of 320 cm During the whoe trayectory 44 feature sets are initiaized by feature-based stereo vision As can be seen by the drift of the white circes corresonding to the features of the two first datasets, dead reckoning errors accumuate to an extent that recudes seamess KLT tracking when trying to retrieve these sets based on their exected reative ose to the camera even in its AM imementation Aearance-based reocaization on stereo images (triggered on a sensibe basis based on the rough ose of the camera) may detect oder SURF features, but their ositioning accuracy by stereo vision is sti insufficient It is ony by the incusion of the intermediate stage concerning P3P ose estimation on KLT features with arger search regions that we achieve the required ose accuracy for seamess KLT tracking of 55 features ertaining to the feature set #1 After that, ose refinement by goba, hybrid BA as exained in Sect 43 takes ace Of course, reocaization on SURF features and subsequent P3P ose estimation haened at an oder image frame because these rior stages run in a searate comuting thread After successfu ose refinement by P3P ose estimation, the AM imementation of the extended KLT tracker takes over [2], tracking as many features of the origina feature set #1 as ossibe These 55 features in turn trigger the goba, hybrid BA rocess exained in Sect 43 in a searate comuting thread It is ony by image frame #24535 that ose refinement on the

11 400 KH Strob whoe ose grah is comete, udating a 43 reative transformations i T f i, i N 1,i 44 aong with the 3-D ose of a 1816 features x i, N 1, M i Using a dated notebook equied with an Inte R Core TM 2 Duo P8700 rocessor, the robustified noninear otimization takes 870 ms The arameters vector contains a features and reative oses invoved in the oo cosure (size 5769) The size of the residuas vector is incuding ast and current hybrid residuas on stereo and monocuar images The fina ose correction after 320 cm of dead reckoning estimation amounts to 25 cmand65 The aearance-based stage in Sect 42 misses the oint by 75 mmand15, which is sti adequate for successfu tracking by the AM imementation of the KLT tracking in Ref [2] Fig 4 shows a tyica correction of the resuting fu mesh after successfu cosure of the oo Fig 4 Fu mesh before and after oo cosure correction 6 Concusions In this contribution we extend the rea-time visua ose tracking agorithm originay resented in Refs [1] and [2] into ose-grah otimization in the form of a hybrid, sarse bunde adjustment (BA) on a set of stereo keyframes and monocuar views This extension is necessary as 3-D modeing by scanning techniques is argey an exoratory act, ie, dead reckoning motion estimation ays a centra roe It is we known that dead reckoning is subject to drifts, which wi recude arger 3-D modeing tasks eg scanning around objects We earned that BA for dead reckoning estimation hardy imroves accuracy comared with V-GPS In the case of oo cosures, however, the use of BA makes arge ose corrections ossibe This is on the assumtion that oder features are tracked at oo cosures, which is not ossibe in the resence of motion drifts without further ado It is by aearance-based reocaization methods, together with a bank of arae three-oint-ersective ose sovers, that seamess feature tracking foowing Ref [2] is ossibe irresective of the accumuated motion drift In addition, we confirm that it is crucia to consider the sarsity of the ose-grah otimization robem for BA to erform in a timey manner These tyes of ow-cost systems have the otentia to romote 3-D modeing and conquer new markets owing to their assivity and fexibiity of use

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