Close Range Angles Deformation Monitoring by Telescope Camera of Total Station MS50 Using Automatic Detection of Coded Targets

Transcription

1 -3 September 5, Istanbul - TURKEY Close Range Angles Deformaton Montorng by Telescope Camera of Total Staton MS5 Usng Automatc Detecton of Coded Targets Yueyn Zhou Andreas Wagner Thomas Wunderlch Peter Wasmeer College of Surveyng and Char of Geodesy Char of Geodesy Char of Geodesy Geo-Informatcs Technsche Unverstät Technsche Unverstät Technsche Unverstät Tongj Unversty München München München Shangha, Chna München, Deutschland München, Deutschland München, Deutschland ag-yue@63.com a.wagner@tum.de th.wunderlch@tum.de peter.wasmeer@tum.de Abstract Wth the development of Image Asssted Total Statons, some orgnal calbraton methods whch were tested on prototypes can be mproved for new nstruments. Ths paper proposes an mproved calbraton method n telescope camera of total staton MS5. Coded Targets are detected automatcally wth the help of open source lbrary OpenCV. Wth enough number of the pxel coordnates obtaned by CTs and the angular readngs obtaned from total staton, we can calculate all the calbraton parameters at a certan focus poston. ew group of parameters can be nterpolated by focus poston. To accomplsh a hghly accurate measurement, some detals should also be consdered. Dstance measurement s not nvolved n ths method because of ts relatvely low accuracy compared wth the angular measurement n close range. Thus only the two-dmensonal relatonshp between angles and mage coordnate values are studed. Fnally, the longtme stablty of ths method s tested by a longtme montor example whch verfed the stablty and accuracy of ths method. The standard devaton of calculated angles from the mage pxels can be no more than.mgon wth the gven condtons. Instead of automated target recognton technque whch requres prsms for each target poston, estmated angles obtaned from mage pont usng coded targets save much cost and are more convenent for applcaton n montorng. Keywords Image Asssted Total Staton; Coded Targets; Stablty of Montor; Calbraton I. ITRODUCTIO Image asssted total staton (IATS) s a promsng soluton to replace human vson n some tradtonal measurements. It combnes all the advantages of total staton and cameras such as hgh automatzaton, few personal errors and so on. MS5 s one of the Geo-robot produced by Leca whch has step servo motors and s equpped wth two vdeo cameras: overvew camera and telescope camera. They have dfferent feld-of-vew (FoV). The calbraton method n ths paper s for the bult-n telescope camera whch has a small FoV. The maxmum resoluton of telescope camera s 56 9 and the camera axs s paralleled wth the collmaton axs. One of the prncpal problems n IATS s to establsh the relatonshp from mage ponts to ts correspondng angles n theodolte coordnate system, whch s the calbraton procedure n IATS. Most of exstng calbraton methods are tested on dfferent self-made prototypes (e.g. [], [], [3]). Reference [3] made an overvew of tradtonal actve automated target recognton (ATR) technque and ts lmtatons, whle adaptaton of approprate CCD camera can help solve some of these problems. Automatc detecton of targets on mage helps mprove the effcency of IATS applcatons and has varous ways to accomplsh such as ellpse detecton, cross lne detecton, template matchng and so on. For actual applcatons, coded targets (CTs) are perhaps the best method because by CTs we can obtan both the pxel coordnate value and the ID of the target on mage at the same tme. CTs are one of the basc tools n photogrammetry and prmarly used for ntal exteror orentaton determnaton [4]. There are two man types of CTs, concentrc rngs and dot dstrbuton [5]. We choose the frst one because t s more robust n detecton. CTs n ths paper are studed to automatcally detect the pxel coordnate of the target n the 53

2 -3 September 5, Istanbul - TURKEY mage based on open source lbrares [6]. II. MATHEMATICAL MODEL OF CALIBRATIO Exstng lterature [7] orgnally proposed a camera calbraton method wthout real control array. It s sutable not only for the bult-n telescope camera, but also for other cameras whch s rgdly nstalled on the telescope. But for the telescope camera n MS5 whose accuracy of dstance measurement s relatvely lower than that of angular measurement for most of total statons. It demands more strngent requrements for the dstance measurement f we want to obtan hgher accuracy of 3D coordnate. Thus, dstance measurement s not nvolved n ths method and we only concentrate on the D transformaton relatonshp between angular measurement and mage coordnate. Pxel coordnate s a left handed (LH) coordnate. The orgn pont s the left top pont n the mage. We defne the mage coordnate also as a LH coordnate. The orgn s the dstorton center of the lens and has a value, x y whch Fg. Relatonshp between pxel coordnates and mage coordnates Supposng there s a vrtual plane whch s perpendcular to the collmaton axs, we also defne the 3D telescope LH coordnate system n whch the Z axs s opposte to the pontng drecton and Y axs s the horzontal axs. The X and Y axs n vrtual plane coordnate system are paralleled to the telescope axs, so X and Y coordnate value n vrtual plane are the same n telescope coordnate. Besdes, the telescope camera axs s always paralleled to the collmaton axs n MS5. The relatonshp s shown n Fg.. can be fxed at the center of mage n pxel coordnate. The relatonshp between the two coordnate sets s as shown n Fg., and we have: xi = y yp yi = x + xp () where xp, yp are pxel coordnates and xi, yi are mage coordnates. Dstorton occurs nevtably n lens system especally n wde FoV lenses ([8], [9]). But n our case where the FoV s.5 dagonal, the dstorton error s much smaller. Thus, we only consder one radal dstorton parameter. Expermental result shows t s suffcent. The corrected mage coordnate s: xi _ c xi xi K r yi _ c yi yi K r () Fg. Relatonshps among telescope coordnate, vrtual plane and mage plane The vrtual constant should be always fxed because the shape n vrtual plane can change by a scalar factor n dfferent vrtual constant as shown n Fg. 3. We set 5 c (unt: pxel). where xi _ c, yi _ c are corrected mage coordnates, r xi yi and K s the radal dstorton parameter. 54

3 -3 September 5, Istanbul - TURKEY pontng to the zenth drecton and the X axs s pontng to ntal zero drecton. Dfferent nstrument errors wll always nfluence the angular measurement. So before usng the angles to do the coordnate transformaton, we need to compensate these nstrument errors frst. These errors are brought by the nstrument tself and should be ndependent to the calbraton parameters. We use the same mathematcal model for calculatng the theodolte axs errors n [] and we wll not dscuss t here. The compensated angles are Hz _ thc and V _ thc. Wth the help of the crosshar n telescope we can Fg. 3 Dfferent vrtual constant can have dfferent shape sze n vrtual plane calculate the nstrument errors before calbraton. Ths s one of the major dfferences between Walser s method and ours. The coordnate n vrtual plane s obtaned from mage coordnate by 4 affne transformaton parameters (Fg. 4). These 4 parameters ( a, a, b, b ) are equvalent to those n Walser s method [] whch s expressed as s, s for the scale factor n both drectons, s for shear factor and for rotaton angle. x y Fg. 5 Relatonshp between theodolte coordnate and telescope coordnate There are two steps to do the 3D coordnate transfer from telescope coordnate to the theodolte coordnate. The frst Fg. 4 Affne transformaton between mage coordnate and vrtual plane coordnate The formula s qute smple and easy for dfferentaton: where x _ tel a xi _ c a yi _ c y _ tel b xi _ c b yi _ c x _ tel and y _ (3) tel are telescope coordnates and have the same value n vrtual plane coordnate. For each target pont we can always have a 3D coordnate value x _ tel; y _ tel; c, and from telescope coordnates we can also get the correspondng theodolte coordnates by two rotaton angles - horzontal angle and vertcal angle. For a leveled nstrument, the theodolte Z axs should be step s to rotate - V _ thc Then rotate We have : around Y_tel along clockwse. Hz _ thc around Z_tel along counter clockwse. x _ the x _ tel y _ the ( Hz _ thc) ( V _ thc ) y _ tel Rz Ry z _ the c x _ tel R y _ tel c where Ry ( V _ thc ), Rz ( Hz) and R are rotaton matrx n 3 3 (4) 55

4 -3 September 5, Istanbul - TURKEY coordnate. T _ x the y the z the s theodolte If we defne the postve drecton of the rotaton matrx s counter clockwse, we have : cos sn Ry sn cos cos sn Rz sn cos where s the rotaton angle. (5) Wth the 3D theodolte coordnate obtaned by (4), we can get the correspondng horzontal angle, vertcal angle and slope dstance of the target. We don t need the slope dstance n our method. y _ the Hz _ tar arctan x _ the z _ the V _ tar arctan x _ the y _ the (6) So every tme we pont to the target drecton wthn the FoV of telescope camera, we can get the pxel coordnate n the target and the estmated horzontal and vertcal angles of the target wth the method above. The parameters to be estmated are : where X ˆ aˆ ˆ ˆ ˆ ˆ ˆ ˆ a b b K Hz V (7) Ĥz and ˆ V are estmated angles of the target n theodolte coordnate. The 5 parameters ahead determne the relatonshp between pxel coordnates and the correspondng angles of the target n theodolte system at a specfc focus poston. Each pont par can establsh two observaton equatons, so we need at least 4 pont pars to calculate the parameters. A least-squares adjustment method s used to estmate the varables wth an dentcal weght matrx and an ntal value: a, a, b, b, K, x 8, y 96 Hz mean Hz thc V mean V thc ( _ ( )), ( _ ( )) T (8) We must be aware that the 5 parameters ahead wll change when the focus poston changes. As s mentoned n lterature (e.g. [3], []), the calbraton parameters are potentally subject to varatons. So every tme we need to fx the focus poston when calculatng those parameters at a specfc focus poston. Once we get dfferent calbraton parameters n dfferent focus poston, we can nterpolate unknown parameters by cubc polynomal functon and a new focus poston. III. AUTOMATIC DETECTIO OF CODED TARGETS Actually CTs detecton s another edge-based measurement method. As s descrbed n [], edge-based method s the most precse detecton method compared wth template-based method and pont-based method. In lterature [3], detecton based on mage processng algorthms has specal benefts compared wth Automated Target Recognton (ATR) functons. Detaled comparsons are gven n that paper, so we wll not dscuss agan. For CTs, we can also get the ID of each target whch makes the detecton a fully automaton procedure. CTs have been used n photogrammetry for decades. In lterature [], dfferent types of CTs were summarzed and a crcular CTs automatc detecton was presented. The CTs we are usng can be obtaned by PhotoModeler and many other photogrammetry software. After some basc processng such as Gauss flter and mage bnarzaton wth a gven threshold, we use Canny algorthm [3] to get the edges n mage. Wth all the edges, we can ft the correspondng ellpse boxes. These fundamental functons are nvolved n OpenCV lbrares whch are open and can be compled n dfferent platforms [6]. The most mportant thng n CTs detecton of concentrc rngs reles on two crucal steps. One s to correctly fnd nner ellpse for poston; the other s to obtan the robust and unque code n the outer code regon for ID. The whole detecton procedure s shown n Fg.6. A. Correct Ellpse Capture Accordng to each contours, we can obtan the area and permeter as, S L by countng pxels. Wth the Count Count exstng ellpse fttng method [4], we can calculate the estmated area and permeter for each ellpse box: S ab Est L b 4 a b Est (9) where a s sem-major axs and b s sem-mnor axs. Besdes, we defne the center of the th ellpse: C, C () x y 56

5 Decode the code Start Capture ellpse Y Defne max and Get 5 Y Y Start End Choose th ellpse mn sze of ellpses Start Defne the radus of code rng as k tmes nner crcle Fnd all contours Import mage Separate code rng nto Bts=4 part Choose th contour Convert to grey mage Calculate 4 coordnate values n each local ellpse coordnate Enough to ft an ellpse Go to next contour Gauss flter processng Transform local coordnate to mage pxel coordnate parameters of boundng box Bnary mage Input a threshold G Get bnary values from the mage at each pxel coordnate Defne the radus of code rng as k tmes nner crcle Defne some restrctons: Wthn defned sze Wthn mage coordnate Rato of major and mnor axs n a certan range Edge detected by Canny algorthm Sort at dfferent startng postons but the same order whch generate a dfferent number Is t the frst code rng? Capture ellpse Y Choose the smallest decmal number as the code Satsfed wth all the restrctons Decode the code Choose the smallest decmal number as the code =+ Add to ellpse lst End code=code Is t the last contour? Y Y Add pxel poston and code to CTs lst Is t the last ellpse? End -3 September 5, Istanbul - TURKEY Fg.6 Flow chart of automatc CTs detecton 57

6 -3 September 5, Istanbul - TURKEY All the ellpses n the mage should satsfy these basc constrants below: a k b, a RMax, b RMn (.a) S L k k, k k (.b) Count Count SEst LEst C k a w, C k a h (.c) x 6 y 6 where w and h are the wdth and heght of the mage resoluton respectvely; R Max and R Mn are predefned maxmum and mnmum ellpse sze n mage. (.a) restrcts the length of estmated sem axs whch can avod large eccentrc-errors when the surface of CTs s not perpendcular to amng drecton. (.b) can help delete part of wrong shapes. (.c) can make t sure that the detected complete target s wthn the mage boundng. In our case, we set k, k k.9, k k., k B. Decodng Code regon s the outer rng of the ftted ellpse whch s separated nto some specfc sectons. The code-bt determnes the number of sectons. Suppose we use code-bt as 4. Standard ellpse s shown as Fg.7(a). We can calculate the coordnate of 4 red dots (.e. code pont) as: Fg. 7 Code regon (red crcles) (c) We can check the bnarzaton mage by code pont coordnate n mage. Then a 4bt bnary code s obtaned. If we choose a dfferent startng pont, the bnary value s also dfferent. But we can choose the smallest value among 4 codes as the unque code. In Fg.7(c) for example, the smallest code value s and the correspondng decmal number s 399 whch s used as ts ID code. Correct nner ellpse capturng s the prerequste of correct decodng. But we can never make t sure the nner ellpse s always correctly captured n front of complex background. We use two groups of code ponts to check the code regon. As s shown n Fg. 8 (a) and (b), two code rngs are k 7 and k 8 larger n sze of nner ellpse whch s green and blue rng respectvely. The decmal number obtaned by these two group rngs should be the same result; otherwse the nner ellpse s wrong. Here we set k7.9 and x a cos( ) 4,,,...,3 y bsn( ) 4 () k8.5. where x and y are local ellpse coordnate. In fact, the ellpse s not always standard and has a rotaton angle (Fg. 7(b) blue ellpse) and the center s Cx, C y n the mage coordnate. Thus, the coordnate of code pont n mage coordnate s: x Cx x cos( ) y sn( ) (3) y Cy x sn( ) y cos( ) Fg.8 Check of codes (a) (b) Fg.9 Wrongly detected ellpses (a) (b) We must be aware that not all the codes can be used for detecton. Some codes can be wrongly detected qute often by the background. As s shown n Fg.9, even a part of the code rng can easly be detected as ellpse by mstake. We can 58

7 -3 September 5, Istanbul - TURKEY nvestgate a more complex ellpse detecton algorthm to avod ths problem but we need to pay more for the cost of effcency. In a smpler way, we solve ths problem by abandon the correspondng codes whch are lsted n Tab.. TABLE I. Abandoned codes accuracy than the latter one. Thus, the absolute accuracy of the fnal result s manly determned by the angular accuracy of total staton tself. But f the amng drecton of the telescope remans stable, the relatve deformaton captured from the telescope camera can be precsely detected. Once the precse relatonshp from pxel ponts to correspondng angles s establshed, we can get at least no lower accuracy of angular montorng compared wth the tradtonal way whch uses ATR functons wth prsms. Because of the nstrument manufacturng, the angular readngs wll be a lttle dfferent f we am at the same target from dfferent telescope postons. Exstng lterature [] solves ths problem by amng to the target randomly and ths systematc error wll be averaged to all the calbraton parameters. To avod ths error whch wll nfluence the accuracy of calbraton result, we always need to preserve the same procedure when translatng the telescope to target drecton. Fg. shows the way how we translate from left-top corner to the target P each tme we do the measurement n calbraton. IV. ACCURACY ASSESSMET The FoV of telescope camera s.5 dagonal and the resoluton s 3 pxel dagonal. If the CTs detecton has subpxel accuracy poston ([], []), the correspondng angular accuracy s.5mgon. Accordng to least-squares method, we have: res A xˆ L res _ Hz Hz ˆ Hz _ tar (4) ˆ res _ V A x Vˆ V _ tar where res s the resdual vector of observatons, A s lnearzed desgn matrx, x ˆ s correctons of varables usng dentcal weght matrx. It s an teratve procedure wth an ntal value gven by formula (8). The posteror varance of unt weght s: Fg. The translaton way of telescope to a target P V. EXPERIMET A. Preparatons Warmng-up procedure s the frst crucal preparaton. The nternal temperature can nfluence the output of angles and mage pont. Ths ssue has been studed and tested n prevous lteratures (e.g. [], []). T res res ˆ = r (5) where r s the degree of freedom. There are 7 varables to estmate n ths method. If there are n pars of observatons, we obtan r n 7. The value of reflects the qualty of orgnal observatons. ˆ From equatons ()~(6), we can see that there are two knds of observatons: one s the angular measurements obtaned by total staton; the other s the detected pxel coordnates obtaned by CTs. The former one has much lower (a) (b) Fg. Angle, pxel devaton and nner temperature n warmng-up procedure Ths procedure s shown as Fg.. It s mnutes nterval between each experment ndex. We can see from Fg.(a) that horzontal angle can devate for. mgon and vertcal angle wll stay stable. Fg.(b) tells that warmng-up 59

8 -3 September 5, Istanbul - TURKEY procedure wll nfluence the CTs detecton by 4. pxel on the mage. Theodolte axes errors should also be consdered before calbraton. As s mentoned n lterature [], theodolte axes errors always occur when some axes condtons are not met. These errors nvolve vertcal-ndex error, collmaton error and tltng-axs error whch can be determned and elmnated. The relevant formulas have been dscussed before, so we wll not dscuss t n ths paper. These errors are calculated by exstng formulas. calbraton postons and there are many CTs on the plate, and we only choose one of the CTs as our study target. We have pars amng drectons near our study target to estmate the calbraton parameters for each focus poston of CTs. Dfferent focus poston of CTs means dfferent parameter relatonshps between theodolte system and mage system. We obtaned 8 postons and the relatonshp between focus poston and dstance from CTs s shown n Fg.3. B. Image Capturng and Correspondng Measurement Fg.3 Relatonshp between focus poston and dstance from CTs VI. RESULTS AD AALYSIS Fg. Experment at focus poston of 83 After the preparatons mentoned before, we can start to obtan calbraton data then. As s descrbed n lterature [7] for case of sngle target, every tme we translate to a poston near the target, we can obtan a par of angular readngs and pxel coordnates of detected CTs. Fg. shows one of the Accordng to the mathematcal model and formula (5), we can estmate all the calbraton parameters and the accuracy of the result by least-squares method n dfferent postons. TABLE II. Calculated results of 8 postons Focus Poston D Dstance (m) a a b b K ( 6 ) ˆ ( ) mgon

9 -3 September 5, Istanbul - TURKEY The results above are estmated based on equal weghts. Wth the estmated parameters n Tab., we can obtan all the new parameters by nterpolatng focus postons wth a new focus poston. As s descrbed n lterature (Knoblach, 9), we can also establsh polynomal functons between focus poston and these calbraton parameters. More focus postons mean more precse samplng of the parameters for modelng. One thng needed to keep n mnd s the vrtual constant shown n Fg. should always be fxed both n calbraton and applcaton. Dfferent vrtual constants wll obtan dfferent groups of calbraton parameters because of a scale factor. Fg.4 and Tab. 3 show resduals of estmated angles n 6 drectons nearby the same target wth dfferent methods at a new focus poston of The longtme stablty s rather mportant for a method. To test t n ths method, we montored the CTs at focus poston of 75 for 3 hours and 4 mnutes. Inner temperature fnally stablzed at From formulas () to (6), we can calculate horzontal and vertcal angles of the target n theodolte coordnate system based on theodolte readngs, detected pxel postons on mage and the nterpolated parameters. We choose a part of the stable observatons whch lasted for mnutes (Fg.5). (a). Gnomonc projecton (b). Walser s method Fg.5 Devaton of estmated angles by ths paper s method at 38.8 (c). Method n ths paper Fg.4 Resduals of dfferent calbraton approaches usng the same data at focus poston of 58 Fg.4(a) and Fg.4(b) refers to the same calbraton methods and parameters n lterature [5], Fg.4(c) s the resdual result calculated n ths method. TABLE III. Resduals of target angles calculated by dfferent methods(unt:mgon) Gnomonc Pont Walser s method Ths method projecton ndex Hz V Hz V Hz V The standard devaton of calculated horzontal and vertcal angle are: Hz V.53mgon.6mgon VII. COCLUSIO AD EXPECTATIO (6) There s an exact relatonshp between telescope camera coordnate and total staton coordnate. We can use CTs nstead of ATR functons whch always requre prsms for each pont to automatcally fnd the target. Hgher accuracy of CTs detecton can help mprove the qualty of the fnal results n further study. Once we combned angles from total staton and mages from the bult-n camera, we can use varous mage processng algorthms such as template matchng, edge detecton or mage segmentaton accordng to dfferent specfc applcatons wth motorzed reflectorless total staton. CTs n ths paper are only one of the varous photogrammetry tools. In dfferent knds of applcatons we can use dfferent target detecton strateges on mage. Ths method wll not be lmted to close range 6

10 -3 September 5, Istanbul - TURKEY applcatons as long as the sze of the target on mage s large enough to detect. Ths s one of the reasons why IATS s a promsng research drecton. ACKOWLEDGMET Ths paper s partly sponsored by Chna Scence Councl (o ) REFERECES [] B. Walser, Development and calbraton of an mage asssted total staton, PhD Thess, ETH-Zürch, 4. [] S. Knoblach, Entwcklung, Kalbrerung und Erprobung enes kameraunterstützten Hängetachymeters, PhD Thess, Technsche Unverstät Dresden, 9. [3] B. Bürk, S. Gullaume, P. Sorber and H.S. Oesch, DAEDALUS: A versatle usable dgtal clp-on measurng system for total statons, Internatonal Conference on Indoor Postonng and Indoor avgaton (IPI),. [4] S. Hattor, K. Akmoto, C. Fraser and H. Imoto, Automated procedures wth coded targets n ndustral vson metrology, Photogrammetrc Engneerng & Remote Sensng, 68(5):44-446,. [5] S. Hattor, K. Akmoto, C. Fraser, T. Ono and H. Imoto, Desgn of coded targets and automated measurement procedures n ndustral vson metrology, Internatonal Archves of Photogrammetry and Remote Sensng, Vol. XXXIII, Supplement B5,. [6] G. Bradsk, The OpenCV Lbrary Dr. Dobb s Journal of Software Tools,. [7] Y.D. Huang and I. Harley, A new camera calbraton method needng no control feld, Optcal 3-D measurement technques. Edtor Gruen and Kahmen. Wchmann, Karlsruh. pp.49-56, 989. [8] F. Devernay and O. Faugeras, Straght lnes have to be straght: automatc calbraton and removal of dstorton from scenes of structured envronment, Machne Vson and Applcatons, 3():4-4,. [9] R.Y. Tsa, A versatle camera calbraton technque for hgh accuracy 3D machne vson, Internatonal Journal of Robotcs and Automaton, 3(4):33-344, 987. [] P. Wasmeer, Grundlagen der Deformatonsbestmmung mt Messdaten bldgebender Tachymeter, PhD Thess, Technsche Unverstät München, 9. [] A. Reterer and A. Wagner, System consderaton of an mage asssted total staton - evaluaton and assessment, In: allgemene vermessungsnachrchten (avn), 9()3, 83-94,. [] S. J. Ahn and W. Rauh, Crcular coded target and ts applcaton to optcal 3D-measurement technques, Proc.. DAGM Symp. Mustererkennung, pp. 45-5, 998. [3] J. Canny, A computatonal approach to edge detecton, In: IEEE Trans. Pattern Analyss and Machne Intellgence, Vol. 8, o. 6, pp , 986 [4] A. Ftzgbbon, M. Plu, and R. B. Fsher, Drect least square fttng of ellpses, IEEE Trans. Pattern Analyss Machne Intellgence, :476-48, 999. [5] A. Wagner, P. Wasmeer, Flächen- und Feature-basertes Montorng mt Vdeotachymetern, Mult-Sensor-Systeme Bewegte Zukunftsfelder. Schrftrehe des DVW, Vol. 75, pp.75-88, 4. 6