A robust model-based tracker combining geometrical and color edge information

Transcription

1 213 IEEE/RSJ Internatonal Conference on Intellgent Robots and Systems (IROS) November 3-7, 213. Tokyo, Japan A robust model-based tracker combnng geometrcal and color edge nformaton Antone Pett, Erc Marchand, Keyvan Kanan Abstract Ths paper focuses on the ssue of estmatng the complete 3D pose of the camera wth respect to a potentally textureless object, through model-based trackng. We propose to robustly combne complementary geometrcal and color edgebased features n the mnmzaton process, and to ntegrate a multple-hypotheses framework n the geometrcal edge-based regstraton phase. In order to deal wth complex 3D models, our method takes advantage of GPU acceleraton. Promsng results, outperformng classcal state-of-art approaches, have been obtaned for space robotcs applcatons on varous real and synthetc mage sequences and usng satellte mock-ups as targets. I. INTRODUCTION Determnng the complete 3D pose of the camera wth respect to the object s a key requrement n many robotc applcatons nvolvng 3D objects, especally n the case of autonomous, vson-based and uncooperatve space rendezvous wth space targets or debrs [3], [15]. Based on the knowledge of the 3D model of the target, common approaches address ths problem by usng ether texture [2] or edge features [5], [6], [1], [15]. Edge features offer a good nvarance to llumnaton changes or mage nose, condtons whch can be encountered n space envronments and are partcularly sutable for poorly textured objects such as space objects. For such class of approaches, the pose computaton s acheved by mnmzng the dstance between the projected edges of the 3D model and the correspondng edge features n the mage, usng weghted numercal nonlnear optmzaton technques lke Newton-Raphson or Levenberg-Marquardt. But though they have proven ther effcency, ths technque requres an mage extracton process whch can nvolve outlers and, contrary to feature ponts whch can be specfcally descrbed, suffer from havng smlar appearances. It can result n ambgutes between dfferent edges, leadng to trackng falures, partcularly n the case of complex objects lke satelltes or space debrs. Thus we propose a method to mprove the accuracy and the robustness of 3D model-based trackng, whle preservng reasonable computatonal costs. A. Related works In the recent lterature could be dstngushed three dfferent knds of approaches tacklng ths problem: One soluton s to combne the nformaton provded by edges wth nformaton provded by other features, A. Pett s wth INRIA Rennes - Bretagne Atlantque, Lagadc Team, France, Antone.Gullaume.Pett@nra.fr E. Marchand s wth Unversté de Rennes 1, IRISA, Lagadc Team, France, Erc.Marchand@rsa.fr K. Kanan s wth Astrum, Toulouse, France such as nterest ponts [16], [17], [19], color [13], or by addtonal sensors [8]. Some researches have focused on the low-level robustness. To reject outlers n the edge matchng process, methods lke RANSAC [2], [4] or the use of M-Estmators such as the Tukey estmator [5], [19] are common trends to make the algorthm robust to occlusons and llumnaton varatons. Also, nstead of handlng a sngle hypothess for a potental edge n the mage, multple hypotheses are extracted and regstered n the pose estmaton [18], [19]. Other studes have consdered Bayesan flters such as Kalman flter [21] and more recently partcle flters [4], [9], [18]. For such methods, a set of hypotheses on the camera pose s propagated wth respect to a dynamc model. The pose s then estmated by evaluatng the lkelhood of the hypotheses n the mage. In [18] the partcle set s effcently guded from edge low-level hypotheses. A lmtaton of these methods often les n ther executon tme. We propose, n the sprt of [13], to ntegrate geometrcal and color features along edges n the pose estmaton phase. The general dea s to combne n the crteron to be optmzed a geometrcal nformaton provded by the dstances between model and mage edges wth a denser color nformaton through object/background color separaton statstcs along the model edges. A low-level multple hypotheses edge matchng process s also embedded n our framework. Lke n our prevous work [15], the model projecton and model edge generaton phase reles on the graphcs process unts (GPU) n order to handle complex 3D models, of any shape and to be reasonably tme-consumng. We choose to restrct to a sngle nonlnear mnmzaton n our pose estmaton technque due to computatonal lmts fxed by our applcaton, but ntegratng our method nto a partcle flterng framework, as n [4], [18] would also mprove performances. The remander of the paper s organzed as follows. Secton II presents the general pose estmaton framework. Secton III and IV respectvely descrbe how the geometrcal and color features are determned and combned. Fnally some expermental results are provded n Secton V. II. COMBINING GEOMETRICAL AND COLOR EDGE-BASED FEATURES IN 3D MODEL-BASED TRACKING Our problem s restrcted to model-based trackng, usng a 3D model of the target. The goal s to estmate the camera pose r by mnmzng, wth respect to r, the error between the observed data s and the current value s(r) of the same /13/$ IEEE 3719

2 features projected n the mage accordng to the current pose: (r) = ρ(s (r) s ) (1) where ρ s a robust estmator, whch reduces the senstvty to outlers. Ths s a non-lnear mnmzaton problem wth respect to the pose parameters r. We follow the Vrtual Vsual Servong framework [5], smlar to the Gauss-Newton approach. In ths sense, we consder a robust control law whch computes the vrtual camera velocty skew v n order to mnmze s(r) s : v = λ(dl s ) + D(s(r) s ) (2) where L s + s the pseudo nverse of L s, the nteracton (or Jacoban) matrx of the feature vector s, whch lnks v to the velocty of the features n the mage. λ s a proportonal gan and D s a weghtng matrx assocated to the Tukey robust estmator. Fnally, the new pose r k+1, represented by ts homogeneous matrx c k+1 M o, can be computed usng the exponental map [11]: c k+1 M o = c k+1 M ck c k M o = e vc k M o (3) Our challenge s to combne geometrcal edge-based features wth a complementary type of features n order to overcome the lmtatons of classcal edge-based approaches. Snce we deal wth potentally textureless 3D objects, combnng ths nformaton wth texture features would not be sutable. Besdes, our dea s to avod any mage extracton or segmentaton that would lead to outlers and msmatches and that would make some nformaton lost. We propose to rely on denser and more accurate features. In ths sense, we follow [13], for whch color features are ntegrated wth classcal geometrcal edge-based features. These features refer to the Contractng Curve Algorthm [7], whch s desgned to optmze the separaton of color statstcs collected on both sdes of the projected edges of the 3D model. can then be rewrtten as: = w g g + w c c (4) g refers to the geometrcal error functon and c stands for the color-based one. w g and w c are weghtng parameters. Both knds of features rely on the projecton of the 3D model, n the vcnty of the projected model edges. III. GEOMETRICAL EDGE FEATURES A. Model projecton and generaton of model edge ponts As n our prevous work [15], we propose to automatcally manage the projecton of the model and to determne the vsble and promnent edges from the rendered scene, by consderng the drect use of a complete model, whch can be textured or not. By usng the graphcs process unts (GPU) and a 3D renderng engne, we avod any manual pre-processng. For each acqured mage I k+1, the model s rendered wth respect to the prevous pose r k. The goal s to obtan a set of 3D ponts X that belong to target rms, edges and vsble textures from the rendered scene. By processng the depth buffer through a Laplacan flter, we can determne the dscontnutes whch sut the geometrcal appearance of the vsble scene, resultng n a bnary edge map. We have mplemented the flterng computatons on the GPU through shader programmng, reducng computatonal tme. In the case of a textured 3D model, we propose to combne the depth dscontnutes wth texture dscontnutes. The rendered textures are passed through a Canny edge algorthm and the obtaned edges are added to the ones generated from the depth buffer. We can sample ths set of edge ponts along the x and y coordnates of the mage n order to keep a reasonable number ponts x. The 3D coordnates of the determned edge ponts n the scene are retreved usng the depth buffer and the pose used to project the model. Besdes, the computaton of both the edge and color based objectve functons requres the orentaton of the edge underlyng a pont x. For the texture edges, t s done wthn the Canny algorthm on the rendered textures. For the depth edges, we compute the Sobel gradents along x and y on a graylevel mage of the normal map of the scene, fltered usng a Gaussan kernel, snce the renderng phase can suffer from alasng. These basc mage processng steps are processed on the GPU, optmzng computatons. B. Feature computaton and nteracton matrx The edge-based functon g s computed n a smlar way to [15]. From the model edge ponts we perform a 1D search along the normal of the underlyng edge of each x (r k ). A common approach s to choose the pxel wth the maxmum gradent as the matchng edge pont x n the mage. Once correspondences are establshed, we consder the dstance between the projected 3D lne l (r) underlyng the projected model edge pont x (r) (projected from the 3D pont X ) and the selected matchng pont x n the mage. g can be wrtten as: g = ρ g (s g (r) sg ) = ρ g (d (l (r), x ))) (5) wth s g = d (l (r), x )), sg = and ρ g s a Tukey robust estmator. Ths functon mproves the approaches n [4], [13], [2], whch consder the dstance between x (r) and x along the 2D normal vector to the edge underlyng x (r k ), determned at the model projecton phase. A key requrement to our method s to compute the 3D equaton of the lne l n the world frame n order to perform ts projecton durng the mnmzaton process and to compute the nteracton matrx L d, related to the pont to lne dstance. Ths s addressed through the knowledge of the edge orentaton durng the renderng phase and the knowledge of the normal to the surface underlyng l, retreved wth the rendered normal map. For the complete computaton of L d, see [5]. C. Multple-hypotheses framework Regardng the geometrcal edge regstraton process, a novel multple-hypotheses soluton s proposed to mprove robustness. Ths approach extends the one presented n [15], [19] by takng advantage of some elements proposed by [18]. In [15], the dea was to consder and regster dfferent hypotheses correspondng to potental edges. They correspond to dfferent local extrema of the gradent along the scan lne. But the projected model edge ponts are treated 372

3 ndependently, regardless ther membershp to prmtves such as lnes or partcular curves. To overcome ths ssue, the dea s to cluster the model edge ponts nto dfferent prmtves and to regster dfferent hypotheses consstently wth these prmtves. Here, we restrct to lne prmtves, for computatonal reasons. a) Clusterng model edge ponts nto lnes: from the edge map provded by the projecton of the 3D model, a set of N l 2D lne segments {l } N l =1 s extracted usng a Hough lne detector. A model edge pont x k for whch the dstance to the closest lne s under a certan threshold s assocated to ths lne. We obtan a set of clusters {C } N l =1 of model edge ponts correspondng to the extracted lnes {l } N l =1. b) Multple-hypotheses regstraton: for each cluster C, we process n a smlar manner to [18]. For a pont x n C, we consder several edge hypotheses x,l (see Fgure 1). These canddates are then classfed nto k sets of ponts or classes {c m} k m=1 usng the k-mean algorthm, each c m beng represented by a mean lne lm, whch best fts the ponts of c m, and a correspondng weght wm. wm represents the lkelhood of class c m wth respect to the others n C. x',2 x',1 x', Class c 2 Lne l 2 x (r k ) Class c 1 Lne l 1 Class c Lne l Correspondng mage edge Model projected edge Extracted lne l Fg. 1: Multple hypotheses framework. Ponts x (blue dots) form the cluster C correspondng to the extracted lne l. For a pont x, several hypotheses x,l are regstered, and are used to buld classes c m ted to lnes l m. The hypotheses n the class c 1 (red dots), whch matches l, wll have hgher weghts than the hypotheses of classes c and c 2 (green and lght blue dots), whch correspond to clutter. Thus model edge ponts x wll more lkely converge towards the hypotheses of class c 1. In [18], random weghted draws are then performed n order to get several hypotheses on the pose. Snce t s tme consumng, here, we smply use the weghts wm to determne the probablty π,l of a canddate x,l to belong to a lne. If c m l denotes the class ncludng x,l, we have: π,l = p(c m l x,l) = p(c m l )p(x,l c m l ) (6) wth p(c m l ) wm l and where the probablty p(x,l c m l ) s related to the dstance between x,l and the mean lne lm l assocated to c m l. The functon correspondng to the ponts x clustered nto the lne classes {C } N l =1 can be wrtten as: g = ρ g (mn π,l (d (l (r), x )))) (7) l j wth l the projected lne, for pose r, underlyng x. For the remanng ponts x whch have not been classfed nto lne clusters, we apply the multple hypotheses approach proposed n [15], gvng: g 1 = ρ g 1 (mn d (l (r), x )) (8) j g = g + g 1 (9) IV. COLOR FEATURES The color-based functon c s elaborated to characterze the separaton between both sdes of projected model edges, by relyng on color nformaton. In order to compute c, as n [13], we restrct ourself to slhouette edges, snce t makes more sense than for crease or texture edges and t lmts the computatonal burden. The prncple s to compute local color statstcs (means and covarances) along the normal to the projected model slhouette edges, on both sdes. Then for each pxel along the normal, we determne a resdual representng the consstency of the pxel wth these statstcs, accordng to a fuzzy membershp rule to each sde. A frst contrbuton we propose s to use a robust M-estmator n the computaton of c. Another contrbuton conssts n addng consstency wth respect to the color statstcs computed on the prevous frame. A. Computaton of color local statstcs Gven the set of projected slhouette model edge ponts x (r), determned from X (see Secton III), we compute color statstcs up to the 2 nd order, on both sde of the edge (object O and background B) usng 2D + 1 pxels along the edge normal n, up to a dstance L (see Fgure 2). For the object sde, we have: ν,o = D j= D µ O ν 1,O = ν 2,O = D j= D D j= D µ O I(y ) (1) µ O I(y )I(y ) T (11) y = x (r) + Ldn are the pxels located on both sdes. d = j D s the normalzed sgned dstance to x (r). I(y ) s the RGB color vector of pxel y and µ O are local weghts gvng a hgher confdence on the object sde, close to the edge (see [7]). As n [13] these statstcs are then blurred wth respect to the other slhouette ponts, and normalzed, to defne RGB means I O and covarances R O for x (r): ν k,o = e λ j ν k,o j, k =, 1, 2 j (12) I O = ν 1,O,O ν and RO = ν 2,O,O ν We proceed the same way for the background B. (13) B. Feature computaton and nteracton matrx The consstency of observed color components of pxels y accordng to the computed color statstcs are evaluated usng a functon a(d) as a fuzzy membershp rule to the object, wth: a(d) = 1 2 (erf( d + 1), d = 1..1 (14) 2σ 3721

4 Background Ī B, R B Ī O, R O Object n x (r) L y, j Model slhouette projected edge Fg. 2: Collecton of local color statstcs on both the background (B) and object (O) sdes. erf s the error functon [1]. σ s a standard devaton defnng the sharpness of the membershp rule. Both object and background statstcs can thus be mxed: Î (r) = a(d(r))i O + (1 a(d(r)))i B (15) ˆR (r) = a(d(r))r O + (1 a(d(r)))r B (16) and the error e c (r) = Î(r) I(y ) defne the color feature s c (r) as: s c (r) = s normalzed to e c 1 (r)t ˆR e c (r) (17) Î (r) represents a desred color value for the j th pxel y on the normal n, wether t s on the object O or background sde B, wth j = Dd(r). The dea s to optmze the poston d(r) of the membershp rule a along the normal, so that the desred value Î(r) best matches the actual value I(y ), mnmzng e c (r) and sc (r). The dependence of ˆR (r) on to the pose r s neglected to reduce computatons. In order to cope wth possble outlers and to mprove robustness, we propose to ntegrate a M-estmator n c, whch becomes: c = ρ c (s c (r) s c ) (18) j = ρ c ( e c 1 (r)t ˆR e c (r)) j wth s c =. As for g, we choose a Tukey estmator. The nteracton matrx L s c can be computed as follows: L s c = sc (r) = 1 s c and the nteracton matrx L e c L e c = Î(r) ( ec (r) T ) ˆR 1 e c (r) (19) = ec (r) = (I O I B ) a(d(r)) d d s computed as: (2) C. Temporal consstency For more accuracy, we ntroduce a temporal constrant to the objectve functon by consderng the nformaton of past frames. The dea s to ntegrate the color statstcs computed on the prevous frame P I for the slhouette edge ponts x (r k ) at the frst teraton of the mnmzaton process. e c (r) becomes: e c (r) = αî(r) + β( P Î (r)) I(y ) (23) wth α + β = 1, and we have: L e c = α Î,d(r) + β P Î (r) = (α(i O I B ) + β( P I O P I B )) a(d(r)) D. Combnaton wth geometrcal features As n [4], [13], d = 1 L nt L x wth L x = x(r) beng the nteracton matrx of a pont, whch s gven by: 2.8GHz Intel Core 7 CPU. For all the followng tests, our [ ] 1/Z x/z xy (1 + x L x = K 2 ) y algorthm has been ntalzed manually. Besdes, snce t s 1/Z y/z (1 + y 2 ) xy x not avalable onlne, we have not mplemented the algorthm [ ] (21) of [13] exactly the same way as n the paper. Instead we wth fx K = (22) have equvalently tested our new soluton wthout the M- f y Estmators for both edge-based and color-based objectve the focal rato parameters of the camera. (x, y) denotes the functons, wthout the multple-hypotheses framework and meter coordnates of the mage pont x, and Z the depth of wthout the temporal consstency for the color-based functon. the correspondng 3D pont (24) The combnaton of the geometrcal features and color features s g (r) and sc (r) n the Vrtual Vsual Servong framework s acheved by stackng these features nto a global feature vector s and ther correspondng nteracton matrx nto a global nteracton matrx: s = [ w g s g 1 w g s g N g w c s c 1,1 w c s c N s,2d L s = [ w g L g 1 w g L g N g w c L c 1,1 w c L c N s,2d ] T (25) wth N g the number of geometrcal features. N s refers to the number of model edge ponts belongng to the slhouette of the projected model, so that N c = 2DN s accounts for the number of color features, wth D the range along the normals to the edge ponts. s s a N g + N c vector and L s s a (N g + N c ) 6 matrx. Regardng the weghtng matrx D, t s wrtten as D = blockdag(d g, D c ), where D g and D c are the weghtng matrces assocated to the robust estmators ρ g and ρ c. V. EXPERIMENTAL RESULTS In ths secton we valdate the proposed method, both qualtatvely on real mages and qualtatvely on synthetc mages and the advantages of our contrbutons are verfed. A. Implementaton The renderng process of the 3D polygonal and textured model reles on OpenSceneGraph, whch s flexble 3D renderng engne. As presented n Secton II.B, we have consdered shader programmng for some mage processng steps durng the renderng and edge generaton phases. Ths s done usng OpenGL Shadng Language (GLSL). The remander of the algorthm has been mplemented thanks to the C++ VSP lbrary [12]. Regardng hardware, an NVIDIA NVS 31M graphc card has been used, along wth a ] T

5 B. Results on synthetc mages Poston / z Rotaton / z (Roll) Error (rad.) Error (m) Rotaton / y (Yaw) Error (rad.) Error (m) Poston / y Poston / x Rotaton / x (Ptch).3.2 Error (rad.) Error (m) We have acheved a quanttatve evaluaton of our algorthm on synthetc mages, usng a realstc ray-tracng smulator developed by Astrum for space envronments. We present the same sequence as n [15], whch features a Spot satellte and whch s provded wth ground truth. For space debrs removal concerns, we consder an arbtrary rotaton for the target atttude and a chaser spacecraft s supposed to be located on a smlar orbt, wth a slghtly dfferent eccentrcty n order to make the chaser fly around the target. We have nvestgated the performances of our algorthm comparatvely to our former soluton [15], whch we denote as the Nomnal Mode () and to our mplementaton of the method presented n [13], denoted by (see provded vdeo). The results can be seen on Fgure 4 where the accuracy of rotaton and translaton components of an estmated camera pose r wth respects to the true pose r s determned throughout the sequence, through error plots on the pose parameters. For our new soluton and for, the trackng s properly performed, as depcted on the mage sequence on Fgure 3. In terms of pose errors, the approach presented n ths paper shows better performances, especally when the satellte s far, wth low lumnosty (between frame 12 and 15). Wth, the trackng fals, manly due to the absence of a multple hypothess framework and to the absence of Mestmators for both edge-based and color-based functons Fg. 4: Estmated camera pose parameters of the target over all the sequence, along wth the ground truth, for the nomnal mode (), the soluton mplemented from [13] (), and the proposed soluton. TABLE I: RMS errors for the Nomnal Mode (), along wth the dfferent contrbutons (C1, C2, C3), for frames tx, ty, tz (n meters) and Rx, Ry, Rz (n radans) respectvely refer to translaton and rotaton (Euler angles) parameters. Mode, C1, C2, C2, C3, C1, C2, C3 tx ty tz Rx Ry Rz advantages of the proposed methods. Executon tmes are also gven (Table II). C. Results on real mages Fg. 3: Trackng for the Spot sequence wth the proposed method. We have also examned and verfed the effectveness and beneft of some of our contrbutons whch are: Incorporatng lne prmtves nto our multplehypotheses framework for the edge-based regstraton process, what s descrbed n Secton III.B. Ths contrbuton s denoted by C1. Integratng the color-based objectve functon to the global functon, denoted by C2. Temporal consstency for the color-based functon (C3), presented n Secton IV.C. The results are represented on Table I by root mean square errors on the pose parameters between frame 12 and 15, whch s the most challengng phase, to better enhance the Soyuz sequence: ths sequence shows the Soyuz TMA3M undockng from the Internatonal Space Staton (ISS). We also run on ths sequence the Nomnal Mode () [15], the algorthm presented n [13] () and the one descrbed n ths paper. As seen on Fgures 5, the trackng s successfully acheved, whereas t tends to fal for both (Fgure 6a) and (Fgure 6b) modes. Fg. 5: Trackng for the Soyuz sequence wth the new proposed soluton 3723

6 TABLE II: Mean executon tmes for frames Mode Tme (s).85, C1.111, C2.31, C2, C3.36, C1, C2, C3.344 a b Fg. 6: Trackng for the Soyuz sequence wth (a) and (b). Mock-ups vdeo sequences: two sequences are processed. In a smlar way to our former work [14], the frst one has been taken on the Lagadc robotc platform and Astrum provded a 1/5 mock-up of Amazonas-2, a telecom satellte. A sx degrees of freedom robot has been used to smulate a space rendezvous, wth a camera mounted on the endeffector of the robot, and enables to have regular and qute realstc movements. Let us however note that the specfc dynamc of the chaser spacecraft s not consdered n ths paper. Sun llumnaton s also smulated by a spot lght located around the scene. As the complete 3D model of the satellte shows dfferences wth respect to the mock-up, t has been redesgned manually. Trackng results can be observed on Fgure 7(a-c). The second sequences has been provded by Astrum and concerns a fly-around a mock-up of Envsat, an observaton satellte whch can be now consdered as a space debrs (Fgure 7(d-f)). a b c d e f Fg. 7: Trackng results for the sequences nvolvng Amazonas (a-c) and Envsat (d-f) mock-ups. VI. CONCLUSION In ths paper we have presented a robust and hybrd approach of 3D vsual model-based object trackng. The general dea was to combne n the global crteron to be mnmzed two complementary cues: a geometrcal one, relyng on dstances between edge features, and a ntensty-based one, relyng on color features computed around slhouette edges. For robustness purposes, we employed a new multple hypotheses framework takng advantage of lne prmtves, along wth M-estmators for both objectve functons, and we added temporal consstency for the color-based features. 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