Robot Navigation Using 1D Panoramic Images

Transcription

1 In 26 IEEE Intl. Conference on Robotcs and Automaton (ICRA 26), Orlando, FL, May 26 Robot Navgaton Usng 1D Panoramc Images Amy Brggs Yunpeng L Danel Scharsten Matt Wlder Dept. of Computer Scence, Mddlebury College, Mddlebury, VT 5753, [brggs,schar]@mddlebury.edu Dept. of Computer Scence, Cornell Unversty, Ithaca, NY 14853, yul@cs.cornell.edu Abstract Ths paper presents a new method for navgaton and localzaton of a moble robot equpped wth an omndrectonal camera. We represent the envronment usng a collecton of one-dmensonal panoramc mages formed by averagng the center scanlnes of a cylndrcal vew. Such 1D mages can be stored and processed wth few resources, allowng a farly dense samplng of the envronment. Image matchng proceeds n real tme usng dynamc programmng on scale-nvarant features extracted from each crcular vew. By analyzng the shape of the matchng curve, the relatve orentaton of pars of vews can be recovered and utlzed for navgaton. When navgatng, the robot contnually matches ts current vew aganst stored reference vews taken from known locatons, and determnes ts locaton and headng from the propertes of the matchng results. Experments show that our method s robust to occluson, repeatng patterns, and lghtng varatons. I. INTRODUCTION Vson-based robot navgaton and localzaton s challengng due to the vast amount of vsual nformaton avalable, requrng extensve storage and processng tme. To deal wth these challenges, we propose the use of features extracted from one-dmensonal panoramc mages taken durng navgaton. Ths work bulds on pror work for extractng stable features from the scale space of one-dmensonal panoramc mages [1] and for the global matchng of two vews usng dynamc programmng [2]. In ths paper we demonstrate the utlty of ths approach for robot navgaton and localzaton. Fgure 1 shows the robot equpped wth an omndrectonal camera, a sample panoramc vew, the 1D crcular mage formed by averagng the center scanlnes, and an eppolarplane mage (EPI) [3],.e., the evoluton of the 1D mage over tme as the robot travels. A. Motvaton One-dmensonal mages can be processed quckly wth low storage requrements, enablng dense samplng and realtme analyss of vews. The reduced dmensonalty also ads greatly n mage matchng, snce fewer parameters need to be estmated. However, there are also some factors that make t dffcult to extract stable, globally nvarant features from 1D omndrectonal mages. Frst, for global nvarance to vewponts, the maged scene must le n the plane traversed by the camera (the eppolar plane). Ths requres that the robot travels on a planar surface, whch lmts the applcablty to ndoor envronments. Even then, extractng a sngle scanlne from an omndrectonal vew s problematc snce t s dffcult to precsely mantan the camera s orentaton due to vbratons [4]. Fg. 1. Our robot wth omndrectonal camera, a sample panoramc vew, the crcular 1D mage formed by averagng the center scanlnes of the panoramc vew, and the eppolar plane mage (EPI), a stack of one-dmensonal mages over tme as the robot travels. Instead, we form our 1D mages by averagng of the center scanlnes of the cylndrcal vew, typcally subtendng a vertcal vewng angle of about 15 degrees. We thus trade true dstance-nvarant ntenstes for robustness. Ths s not a problem n practce snce ntenstes change smoothly wth dstance whch n turn causes smooth changes n the scale space, from whch features are extracted. A second dffculty of the 1D approach s that onedmensonal mages do not carry very much nformaton. Dstnct features that can be matched relably and unquely over wde ranges of vews are rare. A unque descrptor would have to span many pxels, ncreasng the chance of occluson. We thus forego global unqueness of features n favor of a large number of smple features, and use a global matchng technque that not only matches ndvdual features, but also consders ther spatal relaton. B. Related work There has been much recent work on nvarant features n 2D mages, ncludng Lowe s SIFT detector [5], [6], and the nvarant nterest ponts by Mkolajczyk and Schmd [7], [8]. Such features have been used for object recognton and mage retreval, as well as robot localzaton and navgaton [9], [1]. A comparson of local mage descrptors can be found n [11]. The classc eppolar-plane mage (EPI) analyss approach [3] has been appled to panoramc vews wth explct mage stablzaton for 3D reconstructon by Zhu et al. [4]. Ishguro and Tsuj [12] descrbe a method for robot localzaton from memorzed omndrectonal vews, whch are stored usng Fourer coeffcents; smlarly, Pajdla and Hlaváč [13] use the mage phase of a panoramc vew for robot localzaton. Cauchos et al. [14] present a method for robot localzaton by correlatng real and syntheszed omndrectonal mages, but they can only handle small vewpont changes. Matsumoto et 1

2 al. [15] present a smlar method based on smply comparng cylndrcal gray-level mages. None of the above methods computes explct feature correspondences or can tolerate large changes n vewponts or partal occluson. The dea of matchng two panoramc mages (or, more generally, crcular feature sequences) usng dynamc programmng orgnates wth the work by Zheng and Tsuj [16], who coned the term crcular dynamc programmng. They match vertcal lne segments across two panoramc vews, and do not model unmatched features explctly, but allow a lne n one mage to match multple lnes n the other mage. Vertcal edges n omndrectonal mages are also used by Yag et al. [17]. In contrast to exstng work, our method matches two crcular sequences of sparse features whle explctly accountng for unmatched features, thus toleratng occluson. We also contrbute a novel way of estmatng the poston of each eppole (the respectve other vewpont) from the shape of the matchng curve. C. Organzaton of the paper The remander of the paper s organzed as follows. Secton II revews the detecton and matchng of scale-space features. Secton III dscusses the estmaton of vewpont change and relatve orentaton from the matchng curve. Secton IV presents our localzaton and navgaton results n real envronments, and we conclude n Secton V. II. SCALE-SPACE FEATURES We start wth a bref revew of the feature detecton and matchng ntroduced n [1] and [2]. A. Feature detecton The key dea s to compute the scale space S(x, σ) of each 1D omndrectonal mage I(x), x [, 2], over a range of scales σ, and to detect locally scale-nvarant nterest ponts or keyponts n ths space. The scale space s defned as the convoluton of the mage wth a crcular Gaussan kernel G(x, σ), usng a logarthmc scale for σ, so that neghborng values of σ n the dscrete representaton of S are a constant factor k apart. We typcally use k = 2 1/3,.e., 3 samples per octave (doublng of σ). Note that we compute the scale space of the lumnance (gray-level) mage, whle color nformaton s stll utlzed by storng t n each keypont s descrptor. The second mage of Fgure 2 shows an example. Gven a dscretzed scale space, dfferences are computed both vertcally (between neghborng smoothng scales σ), and horzontally (between neghborng mage locatons x), resultng n the dfference scale spaces D σ and D x, respectvely. Ths s equvalent to convolvng the orgnal mage wth dfference-of-gaussan (DoG) operators, whch approxmate frst and second dervatves of the scale space. Interest pont selecton then proceeds by fndng the mnma and maxma of D σ and D x (see the bottom two mages n Fgure 2). We obtan subpxel estmates of both locaton x and scale σ by fttng a quadratc surface to the 3 3 neghborhood of each extremum. Ths also provdes estmates of the local curvature. Fg. 2. Feature computaton. From top to bottom: part of the crcular panorama shown n Fgure 1, the gray-level scale space S of the average of all scanlnes, dfferences of rows D σ, and dfferences of columns D x wth marked mnma and maxma, whch are canddate features. The appeal of fndng extrema n scale space s that t provdes automatc estmates of both poston and scale of features. Intutvely, at each mage locaton, the DoG kernel that best matches the underlyng mage ntenstes s selected. Dependng on ts vertcal (σ) poston n scale space, an extremum can thus represent an mage feature of any sze, rangng from small detals, such as table legs, to large features, such as a couch or a wall of a room. B. Feature matchng The extrema n both dfference scale spaces D σ and D x are our canddate features. We exclude clearly unstable features wth a small absolute value at the extremum or low curvature around t. Gven a typcal 1D frame, a crcular scanlne of 1 pxels depctng a cluttered ndoor scene, we are then left wth about 2 4 features. For each feature, we store nformaton about the local shape of the scale space and the orgnal ntenstes and colors of the correspondng mage locaton n a feature descrptor. We defne the matchng score between two features as the nverse Eucldean dstance between ther descrptor vectors. In the absence of narrow occludng objects, the features vsble from two dfferent locatons wll have the same relatve orderng. Ths observaton, known as the orderng constrant, enables an effcent dynamc programmng (DP) algorthm for fndng the globally optmal soluton to the feature matchng problem. Ths algorthm, descrbed n detal n [2], fnds the set of matches that maxmzes the total matchng score for arbtrary rotatons of both vews under the orderng constrant whle leavng some features unmatched. Fgures 3 and 4 show sample matchng results under dffcult condtons. Fgure 3 demonstrates that our method can handle arbtrary rotatons (crcular shfts) as well as sgnfcant lghtng changes. It shows two mages taken by a robot from the same locaton but at dfferent orentatons. In addton the celng lghts were turned off n one of the mages. The observed matchng curve s very close to the expected curve, a straght lne at a 45-degree angle (whch wraps around snce the frames are crcular), despte the fact that only few features could be matched. Fgure 4 show an EPI of the robot navgatng between bookshelves, as well as the curve resultng from matchng the frst wth one of the last frames. The S- 2

3 Fg. 3. The matchng curve for two omndrectonal mages from the same vewpont under dfferent rotatons and n dfferent lghtng condtons. shaped curve, dscussed n detal n the next secton, ndcates a sgnfcant change n vewng angle perpendcular to the robot s headng. Despte the large vewpont change and the locally ambguous repettve patterns, our algorthm recovers the correct matches. The entre matchng process s qute fast. Our current mplementaton on a 3 GHz Pentum 4 takes about 7 ms to match two frames (35 ms for feature extracton and local matchng cost computaton, and 35 ms for the global matchng). Taken together wth 25 ms for unwarpng the orgnal mage, averagng the scanlnes, and computng the scale space, the total processng rate s about 1 Hz. III. ESTIMATION OF VIEWPOINT CHANGE AND ROTATION We now descrbe how to extract the relatve orentaton and poston of two vews from the matchng curve. A. Fndng the eppoles The characterstc S-shape of the matchng curve n Fgure 4 results from the fact that features on ether sde of a translatng robot move n opposte drectons, whle features drectly n front and behnd the robot reman statonary. The precse locaton at whch there s no vsual moton s called the eppole. Geometrcally, the eppole s the projecton (mage) of the other vewpont. Snce the mages are panoramc, there are two eppole locatons, exactly apart. In terms of vsual moton, the front eppole locaton s the center of expanson and the rear locaton s the center of contracton. Clearly, all possble matchng curves have to pass through both eppole locatons, whle the shape of the rest of the curve depends on the dstance to the observed scene ponts. In general, the shape of the matchng curve s constraned to le n two trangular regons, as shown n Fgure 5. The top fgure llustrates the case of a robot translatng forward n a straght Fg. 4. Top: EPI of an mage sequence wth repettve patterns taken by a translatng robot. Bottom: The global matchng curve between the frst frame and one of the last frames. lne,.e., both vews beng algned wth the drecton of travel. We assume n ths paper that mage locaton corresponds to the front of the robot, and mage locaton to the rear. In ths case, the eppole locatons E 1 and E 2 are (, ) and (, ). The more general case, n whch each vew s orentaton s ndependent of the drecton of translaton, s shown n the bottom of Fgure 5. Here, the drecton of translaton s offset by θ n the frst vew and by φ n the second vew. Ths results n a shfted matchng curve n a crcular fashon snce the dagram wraps around such that the eppoles now le at (θ, φ ) and (θ +, φ + ). The queston s now, gven an arbtrary matchng curve, how can we fnd the eppoles and recover θ and φ? The answer s that for a correct, S-shaped matchng curve there s ndeed only one way of placng the feasble trangular regons such that the curve s fully contaned, and thus only one soluton for the eppole locatons. If the S-shape s not very pronounced, however, estmatng the eppole locatons becomes unstable. As the amount of translaton goes to zero, the matchng curve approaches a straght lne and the eppole locatons become undefned. In fact, ths s the stuaton of Fgure 3. It s easy, however, to determne the relatve rotaton of the two vews δ = φ θ from the amount of shft of the lne, even f the poston of the eppoles along the lne s uncertan. Thus, the frst step of our algorthm s to estmate δ, the ntercept of the straght lne φ = θ + δ through the eppole locatons. Let the matchng curve be the functon φ = f(θ). We assume that f has been unwrapped n the 3

4 B A θ φ E 2 E 1 C φ* θ* E 1 δ* { E 2 φ 2 C E 2 A B E 1 θ 2 φ 2 φ* E 1 θ* E 2 θ 2 Fg. 5. Top: Two panoramc vews whose orentatons are algned wth the drecton of translaton. Each vew s orentaton (.e., robot headng) s ndcated wth an arrow n the pcture on the left; ths headng corresponds to mage locaton. For any observed scene pont (such as A, B, and C), the pont s par of mage locatons (θ, φ) must le wthn the shaded regon n the dagram on the rght. Bottom: Two vews wth arbtrary orentatons θ and φ wth respect to the drecton of translaton. Ther relatve rotaton δ = φ θ determnes the offset of the dagonal lne. In both fgures, the eppole locatons are marked E 1 and E 2. φ drecton so that t s monotone ncreasng on [, 2] wth range [f(), f() + 2]. We defne δ to be the offset that results n equal amounts of the curve of f above and below the straght lne φ = θ + δ : δ = arg mn δ # θ (f(θ) > θ + δ) # θ (f(θ) < θ + δ), (1) where # θ counts the number of dscrete angles (pxel locatons) for whch ts argument s true. The optmal offset δ can be found quckly by searchng over a small set of dscrete angles. Next, we compute the area A between ths reference lne and the matchng curve as an ndcaton of the amount of translaton between the two vews (see Fgure 6 top). Let g(θ) = f(θ) (θ+δ ) be the vertcal dstance of the matchng curve to the reference lne. Then A = 2 g(θ) dθ. (2) Note that the average absolute vertcal dstance v = 1 2 A (3) measures the average vewpont change,.e., the average (angular) vsual moton between correspondng features. In the absence of odometry nformaton or other knowledge about the absolute sze or poston of scene features, ths s our only way of quantfyng the amount of translaton between vews. Ideally, at ths pont, the matchng curve would ntersect the reference lne at two locatons, θ and θ +, yeldng the eppoles E 1 and E 2. In practce, however, the matchng curve s affected by nose and occluson, and the ntersectons may not be exactly apart. It s also possble that the curve crosses the reference lne more than twce. In fact, the (extreme) case of matchng two unrelated vews would yeld an arbtrary matchng curve. We thus need not only a robust way of estmatng the eppoles, but also a measure for the confdence of the result. Gven a canddate locaton ˆθ for the frst eppole, recall that we expect the frst half of the matchng curve to be below the reference lne, and the second half above t (the shaded areas n Fgure 5). That s, we expect g(θ ˆθ) to be negatve on [, ], and postve on [, 2]. Usng the sgn functon { 1, θ < h(θ) = (4) 1, θ < 2 we defne the sgned area between the matchng curve and the reference lne for a canddate offset ˆθ as S(ˆθ) = 2 h(θ)g(θ ˆθ)dθ (5) We fnd the eppole locaton by maxmzng ths area: θ = arg max S(ˆθ), (6) ˆθ and denote the maxmal sgned area S = S(θ ). Agan, the optmum can be found quckly by searchng over the dscrete values of ˆθ. B. Match confdence Fgure 6 shows two matchng curves. The top curve results from matchng two frames under a sgnfcant vewpont change, but wthout occluson. In such a case, the matchng curve fully obeys the S-shape rule, ensurng that an optmal θ value can been found such that the curve only enters the postve areas. In ths case the sgned area S s equal to the absolute area A. In the presence of occluson, or when attemptng to match unrelated scenes, the curve shape becomes more rregular. Even for the optmal value of θ, there are regons n whch the area s negatvely weghted. Ths s llustrated n the bottom of Fgure 6, where we attempt to match two frames from entrely dfferent vewponts. Thus, negatvely weghted areas ndcate a matchng error, or lack of confdence n the current match (and consequently, n the estmates of the eppole locatons). Snce the area that s weghted negatvely s proportonal to the dfference between absolute and sgned areas, we defne the error measure as e = 1 2 (A S ). (7) Ths measure ndcates the relablty of matchng: the greater e, the more lkely the matchng s erroneous. In practce, e s typcally less than 1 degree for correct matches. 4

5 Postve area (θ*, φ *) Negatve area Postve area (θ*, φ *) Fg. 6. Top: A good matchng curve, whch has only postve-sgned area (blue/dark). Bottom: A bad matchng between two unrelated vews wth sgnfcant amount of negatve-sgned area (red/lght). C. Evaluatng the vewpont change We can expermentally evaluate the accuracy of our measure v for vewpont change as follows: Gven an mage sequence taken by the robot, we choose a small set of reference frames, for example every 1-th or 2-th frame. We then select for each frame of a dfferent sequence the closest reference frame based on the computed vewpont change v between the two frames. Fgure 7 shows the results for two sequences taken along smlar paths, but under dfferent lghtng condtons and occlusons. It can be seen that the vewpont change between frames and reference frames correlates wth the actual dstance, and that the selected closest reference frame only brefly oscllates for vews halfway between reference frames. We have performed such experments for other pars Fg. 7. Top: Two EPIs of sequences taken along smlar paths wth dfferent lghtng and occluson. Every 1-th frame of the frst sequence was stored as a reference frame. Mddle: The ndex of the closest reference frame for each frame of the second sequence. Bottom: The vewpont change v to the closest reference frame,.e., the average absolute change n vewng angle n degrees. of sequences and for sparser sets of reference frames, wth smlar results. Overall we have found that the measure v s robust n the presence of lghtng changes and some occluson. IV. LOCALIZATION AND NAVIGATION In ths secton we demonstrate the feasblty of relable navgaton from 1D omn-drectonal vews n ndoor envronments. A. World model We represent the envronment usng a collecton of 1D panoramas assocated wth locatons n an absolute coordnate system. For each such reference vew, we store the 1D mage, the 1D set of features, the poston and orentaton n the world coordnate system, and a tmestamp of when the vew was recorded. 5

6 Fg. 8. A sample world model. The small (red) crcles represent the locatons and orentatons of the reference vews. The thn (blue) vsblty lnes ndcate whch pars of reference vews can be matched and are used for path plannng. The black lnes llustrate the envronment features such as walls, table, and doorways, but are not part of the robot s model. When buldng a world model, we manually gude the robot through the envronment and take vews that are spaced by about 25cm to acheve a farly dense samplng of the surroundngs. We derve the global coordnates from the ntal odometry values, followed by a global correcton to acheve loop closng and algnment wth known locatons, necessary to compensate for odometry errors. Fgure 8 shows the layout of one of our world models, acqured from a sngle run. In practce we store reference vews from multple runs performed at dfferent tmes of day to get a samplng of dfferent lghtng condtons. Note that the archtectural features (walls, doorways, tables) are only sketched for llustraton, but are not part of the world model. In our current system, each reference locaton requres approxmately 6kB of memory (uncompressed). About 8% s used to store the features and ther descrptors, the rest for the panoramc vew. Because of the relatvely low cost per locaton, we are able to store many reference mages, and can also afford to store multple lghtng condtons. The robot could, however, stll navgate usng sparser models. Also, the global accuracy of the locatons s not crtcal snce the robot localzes tself wth respect to nearby mages. B. Localzaton The key component of our system s the accurate localzaton of the robot from a small set of nearby reference vews. Durng navgaton, the robot s approxmate locaton s known, and we can match the closest reference frames frst, untl a large enough set of reference vews has been found whose matchng error s below a threshold. If the robot s placed at an unknown locaton, however, we must match all reference vews untl enough good matches have been found. Whle the vewpont change v of the matched reference vews can be used for a frst locaton estmate, the most precse locaton and orentaton estmate of the robot can be obtaned from the eppole angles. Formally, localzaton nvolves estmatng the robot s poston (x R, y R ) and orentaton θ R from a set of good matches M (.e., matches for whch e s below a certan threshold). For each reference vew M, we denote ts known absolute locaton and orentaton (x, y, φ ), and ts eppolar angles derved from the matchng curve wth the robot s current vew as θ and φ. We frst estmate the robot s headng θ R. For each M we get a separate estmate θ R = φ θ + φ. (8) We combne these estmates usng a weghted average, where the weghts reflect the match qualty. The next step s to fnd the robot s poston. Gven an estmate for ts locaton (x R, y R ) and the known poston (x, y ) of reference vew, the lne connectng the two has orentaton γ = arctan y y R x x R. (9) From the match of these two vews we also obtan a measured value for ths angle: γ = φ φ. (1) Our goal s thus to fnd the robot poston that mnmzes the error functon O(x, y) = M γ γ 2. (11) See Fgure 9 for llustraton. We solve ths non-lnear mnmzaton problem usng the Levenberg-Marquardt algorthm. We have also mplemented a dfferent localzaton algorthm that computes a weghted average of the ntersecton ponts of the lnes assocated wth all pars of γ values. The two algorthms yeld comparable results n practce. C. Navgaton Gven a goal locaton, the robot frst plans a path from ts current locaton to the goal, then travels t whle orentng tself usng reference vews. For smplcty, our current path planner uses the graph of vsblty edges between reference vews,.e., edges between reference vews that can be matched. Ths graph s constructed once and stored. Notce that the localzaton scheme descrbed above permts navgaton n areas that are not part of ths graph. 6

7 y γ γ * Reference vew ( x, y, φ ) Locaton estmate ( x,, θ ) R y R R presence of lghtng changes, repeatng patterns, and some occluson. In future work we wll explore ways to reduce the number of stored reference vews by analyzng the redundancy of the data. The goal s to acheve a sparser samplng of both vewponts and lghtng condtons wthout affectng the navgaton relablty. x Fg. 9. Localzaton based on drecton constrants. Sold lnes represent possble robot locatons based on the eppole angles derved from a match wth each reference vew. The optmal robot locaton mnmzes the dfference between measured angles γ and measured angles γ. For each navgaton task, the robot s estmated poston and the goal locaton are added to the vsblty graph, and the shortest path s computed usng Djkstra s algorthm. Ths path s approxmated wth a small set of straght-lne segments, whch form the robot s target trajectory. The robot then navgates along ths trajectory whle localzng tself n real tme usng nearby reference frames. In each localzaton cycle, the robot tres to match up to 12 reference frames wth the goal of achevng 5 good matches, from whch the locaton s estmated. We have found that ths acheves a good balance between accuracy and speed. Each cycle takes typcally less than 1 second (on the robot s 5MHz processor), allowng the robot to travel at an average speed of about 2 cm/s. D. Dscusson Our experments demonstrate that the robot can successfully navgate varous ndoor envronments n the presence of moderate scene and llumnaton changes, some occluson, and repeatng patterns. Large amounts of occluson or uneven surfaces can hnder the matchng. Strong lghtng changes (e.g., day vs. nght), however, can be handled by storng multple reference vews, whose tmestamps allow the robot to select whch vews to match frst. Featureless areas such as long corrdors can be ambguous globally, but usually contan enough nformaton for local navgaton when the robot has an estmate of ts poston. V. CONCLUSION We have presented a new method for navgaton and localzaton of a moble robot usng one-dmensonal panoramc mages. Our method employs scale-space features and uses crcular dynamc programmng for mage matchng. The reduced dmensonalty allows dense samplng of reference vews and real-tme analyss of vews. We have presented a new method for computng the relatve orentaton and poston of two vews from the omndrectonal matchng curve. Accurate robot localzaton s acheved by combnng the angle and dstance estmates from a small set of nearby reference vews. Expermental results demonstrate that moble robot navgaton from 1D panoramas s feasble n ndoor envronments n the ACKNOWLEDGMENTS The authors are grateful to Carrck Detweler and Peter Mullen for ther contrbutons to our feature matchng system. Support for ths work was provded n part by the Natonal Scence Foundaton under grant IIS and by Mddlebury College. REFERENCES [1] A. Brggs, C. Detweler, P. Mullen, and D. Scharsten, Scale-space features n 1D omndrectonal mages, n Omnvs 24, the Ffth Workshop on Omndrectonal Vson, May 24, pp [2] A. Brggs, Y. L, and D. Scharsten, Matchng features across 1D panoramas, n Omnvs 25, the Sxth Workshop on Omndrectonal Vson, Oct. 25. [3] R. C. Bolles and H. H. Baker, Eppolar-plane mage analyss: A technque for analyzng moton sequences, AI Center, SRI Internatonal, Tech. Rep. 377, Feb [4] Z. Zhu, G. Xu, and X. Ln, Panoramc EPI generaton and analyss of vdeo from a movng platform wth vbraton, n Proceedngs of the IEEE Conference on Computer Vson and Pattern Recognton, Fort Collns, June 1999, pp [5] D. G. 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