Projection-based Registration Using a Multi-view Camera for Indoor Scene Reconstruction

Transcription

1 Projecton-based Regstraton Usng a Mult-vew Camera for Indoor Scene Reconstructon Sehwan Km and Woontack Woo GIST U-VR Lab. Gwangju , S.Korea {skm, wwoo}@gst.ac.kr Abstract A regstraton method s proposed for 3D reconstructon of an ndoor envronment usng a mult-vew camera. In general, prevous methods have a hgh computatonal complexty and are not robust for 3D pont cloud wth low precson. Thus, a projecton-based regstraton s presented. Frst, depth are refned based on temporal property by excludng 3D ponts wth a large varaton, and spatal property by fllng holes referrng neghborng 3D ponts. Second, 3D pont clouds acqured at two vews are projected onto the same mage plane, and two-step nteger mappng enables the modfed KLT to fnd correspondences. Then, fne regstraton s carred out by mnmzng dstance errors. Fnally, a fnal color s evaluated usng colors of correspondng ponts and an ndoor envronment s reconstructed by applyng the above procedure to consecutve scenes. The proposed method reduces computatonal complexty by searchng for correspondences wthn an mage plane. It not only enables an effectve regstraton even for 3D pont cloud wth low precson, but also need only a few vews. The generated model can be adopted for nteracton wth as well as navgaton n a vrtual envronment. 1. Introducton Image-based 3D reconstructon of a real envronment plays a key role n provdng vsual realsm for navgaton n and nteracton wth a vrtual envronment (VE. Convectonal modelng of a real envronment wth 3D modelng tools s tme-consumng and the generated models are not realstc. Though the reconstructon method usng actve range sensors, combned wth a camera, generates an accurate and realstc model, they requre expensve sensng equpments and tme-ntensve reconstructon processng. Furthermore, algnment of 3D pont cloud wth a texture map s also requred. On the other hand, mage-based 3D reconstructon methods not only preserve realsm but also provde a rather smple modelng procedure. Especally, off-the-shelf mult-vew cameras, provdng color as well as depth mages n real-tme, enables to generate mage-based models more easly. Therefore, a delcate regstraton s requred to regster 3D pont clouds, acqured from the mult-vew camera n a few drectons, for 3D reconstructon of a real envronment. Varous regstraton methods were proposed. Besl et al. proposed ICP (Iteratve Closest Pont algorthm [1], and Johnson presented Color ICP to reconstruct an ndoor envronment [][3]. Blas et al. exploted a smulated annealng to mnmze a cost metrc based on total dstance between all matches [4]. On the other hand, Nshno presented an optmzaton method based on M-estmator to mplement a robust regstraton for several range mages [5]. Especally, Pull developed a data acquston devce and adopted a projectve regstraton employng planar perspectve warpng [6]. Sharp defned nvarant features to mprove ICP [7], and Fsher appled projectve ICP to Augmented Realty applcatons [8]. But, most methods depend on expensve equpments and requre much tme to generate 3D models [4][5][7]. In addton, f 3D pont clouds have large error bound t s hard to guarantee the accuracy of the regstraton results [1][][3]. Furthermore, stereo cameras are usually used for object modelng, and not for an ndoor scene reconstructon [6]. To address these problems, a novel projectonbased regstraton method s proposed. Frst, depth mage s refned based on spato-temporal property of 3D pont cloud usng adaptve uncertanty regon. Second, 3D pont clouds acqured at two adjacent vews are projected onto the same mage plane, and corre- Ths research was supported by the MIC, Korea, under the ITRC support program supervsed by the IITA /05 $ IEEE

2 spondences are searched for wthn an overlappng area through the modfed KLT (Kanade-Lucas- Tomas feature tracker. Then, two sets of 3D pont cloud are regstered by mnmzng Eucldean dstance errors wth Levenberg-Marquardt algorthm. Fnally, each trangulated pont s evaluated referrng correspondng ponts, and a new color s assgned to each pont n the overlappng area. Consequently, we reconstruct an ndoor envronment by applyng the above procedure to consecutve scenes. The proposed 3D reconstructon method for a real envronment has the followng characterstcs. Frst of all, although a mult-vew camera provdes 3D pont cloud whch has low precson, ts pervasveness provdes a chance to smplfy 3D reconstructon of a real envronment [9][10]. For ths purpose, the proposed method estmates camera pose usng projected D correspondences nstead of 3D coordnates. Thus, regstraton s carred out effectvely even f the precson of acqured 3D pont cloud s relatvely low compared to that of precse optcal sensor. Besdes, computatonal complexty s reduced as t searches for the correspondences n a D mage plane. Ths also enables a more convenent and fast reconstructon, combned wth the mult-vew camera whch provdes 3D nformaton n real-tme. In addton, the proposed method smplfes 3D reconstructon by placng a mult-vew camera only at a few postons n an ndoor envronment. The paper s organzed as follows. In Chapter, we explan the depth mage refnement. Fne regstraton s mentoned n Chapter 3. Then, color selecton for the overlappng area and extenson to the consecutve scenes are descrbed n Chapter 4. After expermental results are analyzed n chapter 5, conclusons and future work are presented n chapter 6.. Depth Image Refnement.1. Erroneous 3D Ponts Unlke optcal sensor-based methods whch use actve range sensng technque, passve technques use the mages generated by lght reflected by objects. However, dsparty estmaton results n nherent stereo msmatchng errors, usually at depth dscontnuty and on homogeneous areas. The errors cause poor regstraton results. Thus, unrelable regons should be elmnated before regstraton. In ths regard, a depth mage s refned by employng ts spato-temporal property. In the frst step, erroneous ponts are removed usng the temporal property that erroneous depth values change dramatcally n 3D space wth tme. In the second step, holes are flled on the bass of the spatal property that there s a spatal correlaton between neghborng pxels. Fgure 1 s a flow dagram for 3D reconstructon of two scenes n a real envronment. Two sets of color data & dsparty maps Nose removal usng Gaussan dstrbuton propertes of dsparty map value Medan Flterng Hole Fllng Projecton-based Regstraton Color Selecton Regstered 3D pont clouds Fgure 1. Flow dagram for 3D reconstructon To analyze the characterstcs of 3D pont cloud, mean and standard devaton are calculated for each pxel after acqurng N f depth mages for the same scene. However, depth values of some parts have large varatons even n a statc scene. The reason s that although the materals of objects are assumed to obey the propertes of Lambertan surface, some parts do not satsfy the postulaton. In general, depth values drft wth tme, camera poston, llumnaton condtons of a scene, etc. These factors nduce large varatons n depth values, especally at depth dscontnuty areas as well as on homogeneous areas, when dsparty s estmated. Thus, these unstable parts should be removed. In the depth mage of a statc scene, depth varaton of each pxel s modeled as a Gaussan dstrbuton. After nvestgatng depth value of each pxel, we get rd of the pxels whose depth varaton s larger than the threshold value for the th pxel as follows. Th (1 where represents a standard devaton for depth varaton of the th pxel. and Th denote a scale factor and a threshold value for the th pxel, respectvely. However, note that the threshold values depend on 3D coordnates of a scene wth respect to the optcal center of the mult-vew camera. Ths s because the dsparty estmaton error ncreases as an object moves away from the camera. Therefore, Th must be reexpressed as a functon of 3D coordnates wth respect to the optcal center of the camera... Adaptve Uncertanty Regon To decde Th n terms of 3D coordnates for a scene, error bounds of each axs should be calculated for /05 $ IEEE

3 every ray, whch starts from the optcal center and passes through correspondng pxel on the mage plane. A 3D pont wthn the estmated error bound cannot be dstngushed from the error due to the nherent dsparty estmaton errors. The above descrpton derves us to conclude that an adaptvely changng shape appears to be ellpsodal n 3D space, and we call t Adaptve Uncertanty Regon. The mult-vew camera has correlaton errors n dsparty estmaton and calbraton errors. For a multvew camera wth a constant Feld Of Vew (FOV, we assume that Gaussan nose dstrbuton lnearly ncreases wth the dstance along x and y axes; and Gaussan nose dstrbuton ncreases monotoncally wth the dstance along z axs as shown n Fgure [11]. Based on 3D coordnates for x, y and z axes, we determne tolerances for each axs. Gaussan dstrbuton FOV Image plane Object boundary Adaptve uncertanty regon Fgure. Adaptve uncertanty regon Each 3D pont, calculated from correspondng D pxel, generates an ellpsodal uncertanty regon n 3D space. Thus, threshold, Th, s determned referrng the adaptve uncertanty regon that changes accordng to 3D coordnates of a scene, and s descrbed as follows. ( x xc ( x ( y yc ( y ( z zc ( z 1 ( where (x c, y c, z c denotes a translaton vector from optcal center of the camera to center of the uncertanty regon. x, y and z represent uncertanty dstances along each axs. However, the ellpsod should be rotated wth respect to the optcal center reflectng the drecton of the ray. Therefore, after the ellpsod of Eq. (3 s rotated wth respect to the optcal center usng Eq. (4, t moves to (x c, y c, z c. x ( x y ( y z ( z 1 (3 R x' x xc y' R1R y yc z' z zc R1 0 zc / d yc / d 0 yc / d zc / d d 0 xc d y c z c xc 0 d, (4 where (x, y, z s a fnal uncertanty regon n terms of 3D coordnates of a scene wth respect to the optcal center. Therefore, Eq. (1 s reexpressed reflectng 3D coordnates, (x c, y c, z c, wth respect to optcal center of the camera as well as drecton of ray as follows. Th x, y, z (5 ( c c c Through the above step, some parts of a scene, whch do not meet the assumpton of Lambertan surface, are removed. The boundary of an object and homogeneous areas are also excluded. Then, Medan flter s appled to remove spot noses. However, hole fllng s requred on the holes, generated durng the above step, and homogeneous areas where dsparty may not be estmated. Thus, spatal property for a current pont,.e. spatal correlaton among 3D ponts of four neghborhood pxels, s exploted [11]. However, ths step may generate errors f depth dfference between adjacent pxels s large. Therefore, ths step s appled only when the depth dscontnuty s less than a threshold, Th dd. After nvestgatng the 3D coordnates of each of four drectons, we apply ths step only to the holes whose sze s so small that we can consder each of them as a plane. 3. Regstraton usng Correspondences The depth mage refnement removes nherent stereo msmatchng errors, and reduces error bound of 3D pont cloud. However, precson of 3D pont cloud s stll low for regstraton. The regstraton explotng the conventonal ICP, whch employs the shortest dstance, s napproprate snce error bound of 3D pont cloud s relatvely large. Thus, a projecton-based regstraton method s proposed to carry out a parng process that searches for correspondences between 3D pont clouds of destnaton and source vews. Fgure 3 shows the projecton-based regstraton of Fgure 1 n detal /05 $ IEEE

4 3D data from source vew 3D data from destnaton vew Projecton of 3D data acqured from destnaton vew onto destnaton vew Projecton of 3D data acqured from source vew onto destnaton vew Correspondng features searchng usng KLT Feature Tracker Eucldean dstance errors between correspondences wthn the overlappng area n terms of projecton matrx of a source vew. Accordngly, fne regstraton should be accomplshed to compensate the errors nduced by dsparty estmaton, camera calbraton, and so forth. Cost functon mnmzaton usng Levenberg-Marquardt algorthm Rotaton and translaton matrx update Rgd transformaton of source pont set S NO MSE < threshold STOP Fgure 3. Flow dagram for projecton-based regstraton 3.1. Intal Regstraton A mult-vew camera s attached to a moble robot and ts pose s estmated by detectng and trackng features of a scene. Frst, a coplanar calbraton pattern and structural constrants of the mult-vew camera are used for ts calbraton [1][13]. Then, ntrnsc parameters and camera pose are estmated wth respect to a reference poston n a real envronment. Fnally, a rgd-body transformaton s appled to 3D coordnates of feature ponts at each camera vew to estmate the poses of the camera at each vew. Therefore, partal 3D pont clouds, acqured at each poston, are ntally regstered. Even though the ntal regstraton provdes a combned 3D pont cloud for a scene, t stll requres fne regstraton that provdes a correct camera pose. 3.. Fne Regstraton YES Fgure 4. Projecton of 3D pont cloud onto mage plane projecton of 3D pont cloud of destnaton vew onto ts own vew projecton of 3D pont cloud of source vew onto the destnaton vew In general, projecton of 3D pont cloud of the source vew onto the destnaton vew generates floatng-pont numbers. Thus, some pxels do not have any value as shown n Fgure 6. These unprojected pxels can generate false alarms when correspondng features are searched for through a modfed KLT feature tracker. Therefore, to preserve an orgnal mage as well as to remove unprojected pxels, a specal care should be taken. A two-step nteger mappng s presented to meet these requrements. In Fgure 5, grd ponts are on the lnes. Whte crcles represent grd ponts, and black crcles denote projected pxels of 3D pont cloud of the source vew onto the destnaton vew. Projected pont Grd pont Correct parng plays an essental role n accurate regstraton. Fgure 4 and Fgure 4 are the projecton results of 3D pont clouds, whch are acqured at the destnaton and source vews, onto the destnaton vew. Md-lumnance value s assgned to unprojected area to dfferentate t from projected one. It should be noted that the projecton of 3D pont cloud of source vew onto the destnaton vew creates self-occluson. Ths s elmnated based on the rays that orgnate at the camera center and pass though each pxel on the mage plane. Theoretcally, Fgure 4 should exactly overlap wth Fgure 4. However, dscrepances occur due to the errors n dsparty estmaton, camera calbraton, etc. Therefore, accurate geometrc relatonshp between two vews s found by mnmzng Search range for 1 st step Search range for nd step Fgure 5. Two-step nteger mappng At the frst step, a search range s set to 0.5 ~ 0.5 along x and y axes, respectvely, for each grd pont. The color of each grd pont s evaluated by consderng weghts, whch are decded by relatve dstances wth all pxels wthn the search range. In most cases, only one projected pont s ncluded n the fst range. However, there exst grd ponts whch do not nclude any projected pont at the frst step. At the second step, the search range s expanded to 1.0 ~ /05 $ IEEE

5 and a smlar procedure s accomplshed. Fgure 6 shows the results. Fgure 6 s an enlarged part of Fgure 4, and Fgure 6 s the result after the twostep nteger mappng s appled. The presented method mproves the modfed KLT feature trackng performance by removng unmapped grd ponts and preservng an orgnal mage as t s, at the same tme. Fgure 6. Two-step nteger mappng before after We search for correspondng feature ponts, and use Eucldean dstance between them to defne a total cost functon wthn the overlappng area. To guarantee the correct parng, RANSAC s also appled. By mnmzng the followng cost functon, a fnal pose of the source vew s estmated. That s, we can estmate the pose of source vew {R, T }, wth respect to the pose of destnaton vew {R, T } through mnmzng the dstance errors on N feat feature ponts as follows. Gven two sets of correspondng ponts, Fnd { R such that arg mn E where E N feat 1 0, T { R, T} ( x } w. r. t { R, x,, T ( y }, y, (6 where (x,, y, and (x Srt,, y, represent ponts on projected D mage planes of 3D pont cloud of the destnaton and source vews, respectvely. E denotes Eucldean dstance between them. The total dstance error s mnmzed by Levenberg-Marquardt algorthm. 4. Surface reconstructon of 3D pont cloud After the estmaton of the camera parameters of source vew wth respect to destnaton vew, trmmng and color selecton, for duplcate 3D pont clouds wthn the overlappng area, are carred out. After regstraton of two vews, each grd pont of the overlappng area n the destnaton vew has ts own correspondence n the source vew. Ths means that we can obtan the correspondng features n 3D pont cloud of the orgnal source vew. Thus, fnal 3D coordnates are calculated by a lnear trangulaton method for the overlappng area [14]. Then, color adjustment s requred to consder changes n lghtng condtons dependng on camera poston. We suppose that all materals wthn a captured scene satsfy the propertes of Lambertan surface. R' R G' v G B' B R u G B /( u v (7 where u and v are dstances from left and rght borders of the overlappng area to the current pxel, respectvely. R (or G, B and R (or G, B are red (or green, blue component of a current pxel for both mages. On the other hand, R (or G, B means fnal colors for the overlappng area. To reconstruct a fnal surface, after placng a multvew camera at several postons successvely and acqurng mages and 3D pont clouds, we apply the above procedure to them. Fgure 7 shows a conceptual dagram descrbng an ndoor scene reconstructon. Indoor Envronment Calbraton Pattern [RT] 0 Captured Areas by a Mult-vew Camera [RT] 1 [RT] [RT] 3... [RT] 01 [RT] 1 [RT] 3... Fgure 7. Indoor scene reconstructon As shown n Fgure 7, we frst place a calbraton pattern whose relatve poston from an ndoor envronment s already known. Then, based on the pattern, we estmate ntrnsc and extrnsc parameters of a mult-vew camera wth respect to the orgn of the world coordnate system. We calculate [R T] 0 by explotng Intra-/Inter-calbraton whch employs Tsa s algorthm and structural nformaton of the camera [11]. Through the above-mentoned procedure, we estmate the pose of the second vew wth respect to the frst vew, [R T] 01. That s, we can calculate the pose of the second vew from the reference pont, [R T] 1. Thus, we can get the camera pose of the th vew from the reference pont, [R T] -1, and carry out 3D surface reconstructon. By usng the proposed method, we do not need a dense depth estmaton process employng the mult-baselne stereo technque. Thus, we can reduce computatonal complexty /05 $ IEEE

6 5. Expermental Results and Analyss The experments were carred out under a normal llumnaton condton of a general ndoor envronment. We used Dgclops, an IEEE 1394 mult-vew camera for color mage and 3D pont cloud acquston, and a Xeon.8 GHz CPU computer [9]. We employed a coplanar pattern wth 75 grd ponts to get an ntal camera pose from the orgn of the world coordnate system. ance between two consecutve ponts of the pattern s 10.6 cm. Fgure 8 shows the results of depth mage refnement. Fgure 8 and Fgure 8 depct orgnal and correspondng dsparty mages. 3D pont cloud acqured from a camera and the results of depth refnement and hole fllng are demonstrated n Fgure 8(c and Fgure 8(d, respectvely. In ths regard, we set N f as 30 and Th dd as Intal value of N feat s set as 00. We can observe from the results that nvald areas, such as object boundary, homogeneous areas and non- Lambertan surface, are effectvely removed. Holes, whose depth dfference s very small, are also flled. source and destnaton vews, respectvely. We can see that the dstances between correspondences are effectvely mnmzed. (c (d Fgure 9. Correspondng features projecton of 3D pont cloud of destnaton vew onto ts own vew projecton of 3D pont cloud of source vew onto the destnaton vew (c enlarged area of before error mnmzaton (d enlarged area of after error mnmzaton Fgure 10 llustrates the regstraton results. Fgure 10 and Fgure 10 show a combned 3D pont cloud of both vews and a regstered 3D pont cloud after applyng the proposed method, respectvely. On the other hand, Fgure 10(c and Fgure 10(d are enlarged areas for the correspondng scenes. By observng the boundary of a crcle, Chnese and Englsh characters, we can see that the regstraton works well. (c (d Fgure 8. Depth refnement orgnal mage depth mage (c 3D pont cloud before depth refnement (d 3D pont cloud after depth refnement Fgure 9 demonstrates the results of mnmzng the Eucldean dstances between correspondng features. That s, we appled the modfed KLT feature tracker to Fgure 4 and Fgure 4, and mnmzed the dstances between them. Fgure 9 and Fgure 9 are projected mages of 3D pont clouds, whch are acqured at the destnaton and source vews, onto the destnaton vew. Correspondng features are also marked. Enlarged areas are also shown n Fgure 9(c and Fgure 9(d at the ntal and fnal steps. Red and whte markers represent correspondng features of (c (d Fgure 10. Regstraton results combned 3D pont cloud regstered 3D pont cloud (c enlarged area of (d enlarged area of /05 $ IEEE

7 The regstraton results for one wall of an ndoor envronment are shown n Fgure 11. We let the multvew camera located around a wall, and acqured color mages and 3D pont clouds. As shown n Fgure 11, we moved the camera four tmes around the wall and regstered partal 3D pont clouds to generate a depthpreserved 3D wall. Fgure 11 and Fgure 11(c are scenes seen from left and front sdes. The rght part of Fgure 11(c s enlarged n Fgure 11(d. On the other hand, the front vew of the regstraton results for the vews acqured at sx postons s llustrated n Fgure 11(e and a zoomed-n scene s shown n Fgure 11(f. As demonstrated, by applyng the proposed regstraton method to a few sets of 3D pont cloud, we can acheve dense 3D reconstructon for an ndoor envronment. (d (e (c (f Fgure 11. Indoor scene reconstructon top vew of 4 regstered vews left vew (c front vew (d enlarged area of (c (e front vew of 6 regstered vews (f zoomed-n scene We compared the proposed method wth conventonal ICP and color ICP on the bass of PSNR (Peak Sgnal to Nose Rato, whch represents the vsual qualty of regstered results, n Fgure 1. From the results, we can observe that ICP and color ICP are dffculty n beng appled to the 3D pont cloud, whch has large dsparty estmaton errors. The reason s that those methods are just based on the closest dstance and do not consder neghborhood pxels. Projectonbased ICP just projects 3D pont cloud of source vew onto destnaton vew and searches for pared 3D pont. However, t s dffcult to guarantee correct correspondng features n case of the large error bound. On the other hand, the proposed method tracks the correspondng features by explotng surroundng nformaton for each block n a D mage plane. Then, t mnmzes the dstance between the correspondng features. Thus, we can see that the proposed method provdes results that are more relable. We took advantage of the followng measure for comparng performance n the overlappng area /05 $ IEEE

8 55 PSNR 0log10 ( db N 1 1 ( Y, Y, N 0 (8 where N s the number of pxels, whch are vald for both mages; and Y, and Y, denote the lumnance value of the th pont on each projected 3D pont cloud of source and destnaton vews, respectvely. The vsual qualty of the proposed method s superor to those of conventonal ICP and color ICP. Furthermore, the convergence of the proposed method s faster than that of [11] ( = 7.0, N B = 19 snce the proposed method employs the correspondng features. Besdes, vsual qualty s also better than that of [11]. Although t seems that the conventonal ICP and color ICP converge faster, they takes longer to search for correspondences than does the proposed method. The reason s that our method s based on a D mage plane whle the conventonal ICP and color ICP search for correspondences n 3D space. Fgure 1. Performance comparson 6. Conclusons and Future Work We proposed a novel regstraton method explotng color and depth nformaton acqured from a multvew camera to carry out 3D reconstructon for an ndoor envronment. We proved that even though the error of depth nformaton s relatvely large compared to that of laser-scanned data, 3D pont clouds are effectvely regstered between two vews. We also showed that an effectve reconstructon s possble usng a few vews of the real envronment nstead of many D mages. There are stll several remanng challenges. Frst, we have to reduce convergence rate for regstraton. Global regstraton should be optmzed to do 3D reconstructon for the entre ndoor envronment. Natural augmentaton of vrtual objects nto the reconstructed room envronment requres lght source estmaton and analyss to match llumnaton condton of the VE. Up to now, we lmt the proposed method to only ndoor scenes due to the dsparty estmaton errors. However, f the precson s enough hgh, t can be appled to outdoor scenes. 7. References [1] P. J. Besl and N. D. McKay, A Method for Regstraton of 3-D Shapes, IEEE Trans. on Pattern Recognton and Machne Intellgence, vol. 14, no., pp , 199. [] A. Johnson and S. Kang, Regstraton and Integraton of Textured 3-D Data, Tech. report CRL96/4, Dgtal Equpment Corporaton, Cambrdge Research Lab, Oct., [3] S. Kang and R. Szelsk, 3-D scene data recovery usng omndrectonal multbaselne stereo, Tech. report CRL-95-6 Oct [4] G. Blas and M. D. Levne, Regsterng multvew range data to create 3-D computer objects, IEEE Trans. PAMI, vol. 17, no. 8, pp , [5] K. Nshno and K. Ikeuch, Robust Smultaneous Regstraton of Multple Range Images Comprsng A Large Number of Ponts, ACCV00, 00. [6] K. Pull, Surface Reconstructon and Dsplay from Range and Color Data, Ph.D. dssertaton, Unversty of Washngton, [7] G. C. Sharp, S. W. Lee and D. K. Wehe, Invarant Features and the Regstraton of Rgd Bodes, IEEE Int l Conf., on Robotcs and Automaton, pp , [8] R. Fsher, Projectve ICP and Stablzng Archtectural Augmented Realty Overlays, Int. Symp. on Vrtual and Augmented Archtecture (VAA01, pp 69-80, 001. [9] Pont Grey Research Inc., [10] VIDERE DESIGN, [11] S. Km, K. Km and W. Woo, Projecton-based Regstraton usng Color and Texture Informaton for Vrtual Envronment Generaton, Lecture Notes n Computer Scence 3331, pp , 004. [1] R. Tsa, A versatle camera calbraton technque for hgh-accuracy 3d machne vson metrology usng offthe-shelf tv cameras and lenses, IEEE Journal of Robotcs and Automaton, vol. 3, no. 4, pp , [13] K. Km and W. Woo, Mult-vew Camera Trackng for Modelng of Indoor Envronment, Lecture Notes n Computer Scence 3331, pp , 004. [14] R. Hartley and A. Zsserman, Multple Vew Geometry n Computer Vson, Cambrdge Unversty Press, March /05 $ IEEE