Assessing the accuracy of applying photogrammetry to take geometric measurements on building products

The main objective of the research Assessing the accuracy of applying photogrammetry to take geometric measurements on building products is to characterize the errors of the photogrammetryderived geometric measurements on building products in a systematic, practical, and statistically significant way. In this research, we intend to use the offtheshelf, portable digital cameras, instead of highend, expensive cameras specially manufactured... Đề tài Hoàn thiện công tác quản trị nhân sự tại Công ty TNHH Mộc Khải Tuyên được nghiên cứu nhằm giúp công ty TNHH Mộc Khải Tuyên làm rõ được thực trạng công tác quản trị nhân sự trong công ty như thế nào từ đó đề ra các giải pháp giúp công ty hoàn thiện công tác quản trị nhân sự tốt hơn trong thời gian tới.

m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u Assessing the Accuracy of Applying Photogrammetry to Take Geometric Measurements on Building Products tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp Fei Dai1 and Ming Lu, M.ASCE2 jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc Abstract: The present research describes the fundamental working mechanism of photogrammetry and characterizes the errors of the photogrammetry-derived geometric measurements on building products in a systematic, practical, and statistically significant way A site engineer simply takes snapshots of a building product with a digital camera from different angles Back in office, the engineer derives as-built measurements through postprocessing those photos by use of photogrammetry software The twelve objects sampled in our experiments were building products and building facilities found on the campus of Hong Kong Polytechnic University, yielding 79 paired geometric measurements 共length, width, and height兲 by photogrammetry and by measurement tape, respectively The biases and limitations of analyzing the agreement between two sets of measurements by regression and correlation coefficient techniques were first revealed Then, the “95% limits of agreement” method was applied on the sample data and the confidence intervals were established for the limits of agreement derived, so as to ensure validity and statistical significance of the results In short, the main contribution of this research lies in formalizing a statistically significant, quantitatively reliable technique to assess the accuracy of applying photogrammetry in particular applications of construction engineering Through weighing the accuracy level achievable by photogrammetry against the accuracy level desirable in a particular application, the engineer makes the final decision on the applicability of the photogrammetry-based approach 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 DOI: 10.1061/共ASCE兲CO.1943-7862.0000114 g ilw cz jp 7d 1u u j9s vo sz CE Database subject headings: Photogrammetry; Measurement; Errors; Photography; Geometry; Construction management 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim m fx f hq c8 Author keywords: Photogrammetry; Dimension measurement; Errors; Photography; 95% limits of agreement; Confidence interval tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o Introduction 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 The surveying technique of photogrammetry extracts input data from two-dimensional 共2D兲 photo images and maps them onto a three-dimensional 共3D兲 space In general, photogrammetry can be used to acquire the profiles of an object, quantify its geometric dimensions, and track its status change 共e.g., tracking the object’s orientation and its spatial relationships with other objects.兲 In construction engineering, photogrammetry has been applied in building components modeling 共Proctor and Atkinson 1972; Dai and Lu 2008兲, project progress control 共Quiñones-Rozo et al 2008; Kim and Kano 2008; Memon et al 2005兲, and keeping evidence of the impact of tunnel construction on historical buildings 共Luhmann and Tecklenburg 2001兲 The accuracy of photogrammetry is dependent on the precision of the camera used and the quality of the photos taken, and the functionality of the photoprocessing software applied Although photogrammetry holds great potential to provide an alter- c bb j jj8 q7 8m fln native for quantity surveying in construction management, a formal method for assessing the accuracy of geometric measurements taken by photogrammetry is yet to be developed The main objective of the present research is to characterize the errors of the photogrammetry-derived geometric measurements on building products in a systematic, practical, and statistically significant way In this research, we intend to use the off-the-shelf, portable digital cameras, instead of high-end, expensive cameras specially manufactured for photogrammetry applications Our research falls into the category of close-range photogrammetry measurement, which usually applies to those situations where the target object is away from the camera at a distance ranging from to 300 m 共Luhmann et al 2006兲 We further narrow the shooting range to 关1 m, m兴 so to be aligned with practical application needs for quantity surveying in building construction The application setting is given as follows: A site engineer is responsible for taking geometric measurements on building products that have been just placed or partially completed Those measurements represent the as-built information and are used 共1兲 to ascertain the actual quantity of work completed; 共2兲 to check the quality of finished products against the building design and technical specifications; and 共3兲 to certify payment requests filed by the contractor In the conventional way, the engineer would apply a measurement tape to determine the length of each dimension of a building product and record the data in a form and on the spot As an alternative, the engineer simply takes snapshots of the building product with a digital camera from different angles Back in office, the engineer derives as-built measurements through post processing those photos by use of photogrammetry software In 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f Ph.D Candidate, Dept of Civil and Structural Engineering, Hong Kong Polytechnic Univ., Hung Hom, Hong Kong E-mail: dai.f@polyu edu.hk Associate Professor of Construction Engineering and Management, Dept of Civil and Structural Engineering, Hong Kong Polytechnic Univ., Hung Hom, Hong Kong 共corresponding author兲 E-mail: cemlu@polyu edu.hk Note This manuscript was submitted on January 6, 2009; approved on June 22, 2009; published online on January 15, 2010 Discussion period open until July 1, 2010; separate discussions must be submitted for individual papers This paper is part of the Journal of Construction Engineering and Management, Vol 136, No 2, February 1, 2010 ©ASCE, ISSN 0733-9364/2010/2-242–250/$25.00 ta 9c 5y 9w dư kr 3m 6ư f 8q m ri ưm 6m lcư 0iq 4w pw r 3n 242 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / FEBRUARY 2010 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 Downloaded 13 Mar 2010 to 169.229.32.138 Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw Fig Pinhole camera model sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb Fig Fixing a spatial point by intersecting two rays of light b5 66 28 4y addition, applying the photogrammetry method at a building site would produce two “by-product” benefits: First, measurements can be taken effortlessly on those building elements situated in hazardous areas that are unsafe to access Second, the alignment of a building product can be continuously monitored by taking site pictures at different times The remainder of this paper is organized as follows: The fundamental mechanism of photogrammetry is described first We then explain major reasons that account for errors in the geometric measurements obtained by photogrammetry; they are 共1兲 the system error due to distortion of the camera lens and 共2兲 the random error due to human factors Next, we describe the steps of method application, experiment design, and the sample data acquired After revealing biases and limitations of applying regression and correlation coefficient methods for error analysis, we resort to the 95% limits of agreement method to assess the accuracy of photogrammetry based on the sample data We further establish the confidence intervals for the limits of agreement in order to ensure validity and statistical significance of the results The practical implication and applicability of the photogrammetry-based approach to construction engineering applications is discussed before drawing conclusions 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư tures taken from different angles, it is possible to determine the coordinates of a point in the image coordinates system inside the camera as well as in the object coordinates system in the global space Eventually, a collection of the points fixed by photogrammetry computing suffice to produce a skeleton model of the object Fig gives an example of the sample photos of a faỗade and the different perspectives of its 3D model resulting from photogrammetry Next, we discuss two major factors that induce the measurement errors of photogrammetry 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve System Error due to Lens Distortion vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 5y 3e Measurement errors due to camera lens distortion can be treated as the system error with a consistent effect 共Viswanathan 2005兲 It causes an image point on the image plane to shift from its true position 共x⬘n , y ⬘n兲 to a perturbed position 共xn , y n兲 Thus, the true coordinates of any image point can be compensated by Eq 共1兲 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 Fundamentals of Photogrammetry no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 lp Fig Sample photos of a faỗade and different perspectives of the 3D model resulting from photogrammetry ki 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f The basic mathematical equations underlying photogrammetry are called Collinearity Equations 共given in Appendix I兲, which unify the image coordinates system in the camera with the object coordinates system in the global space 共Wong 1980; Wolf 1983; McGlone 1989兲 Thus, the coordinates 共x , y兲 of an image point in the image plane can be analytically transformed into its coordinates 共X, Y, and Z兲 in the global space The very basic technique of photogrammetry is effective and computationally simple It is notable that the photogrammetry algorithm is based on definitions of the interior orientation and the exterior orientation of a photographic system Fig gives the pinhole camera model to illustrate how a camera forms the image of an object The interior orientation is described by the principle point and the principle distance of a camera in the image coordinates system The principle point refers to the projected position of the perspective center 共O in Fig 1兲 on the image plane 共xo, y o in Fig 1兲 while the principle distance 共c in Fig 1兲 is the distance between the perspective center and the image plane The exterior orientation is defined by six parameters of the camera in the global space, namely, the location coordinates (Xo, Y o, and Zo ) and the Euler orientation angles 共␻, ␾, and ␬兲 of the camera’s perspective center If a camera’s internal parameters are known, any spatial point can be fixed by intersecting two rays of light that are projected from two different camera stations 共Fig 2兲 Thus, with two pic- ta 9c 5y 9w dư kr 3m 6ư f 8q m ưm ri JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / FEBRUARY 2010 / 243 6m lcư 0iq 4w pw r 3n 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 Downloaded 13 Mar 2010 to 169.229.32.138 Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s xn⬘ = xn + dx sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 P1 ( x1 , y1 ) ba g6 o9 74 P2 ( x2 , y2 ) n1 yc 0q o3 3n t0 y ⬘n = y n + dy nk jl cg wd qv va nh ql sn wm ql 5o 共1兲 ffr P ( x, y ) u tv f5 rk sb 78 w9 The camera lens distortion 共i.e., dx and dy兲 can be taken as the aggregate of the radial distortion and the decentering distortion 共Beyer et al 1995; Fraser 1996兲 As the lens of a camera is actually composed of a combination of lenses, the centers of those lens elements are not strictly collinear, giving rise to decentering distortion In contrast, the radial distortion occurs in each single optical lens and the distortion effect is magnified along the radial direction of the lens: the further a point is away from the center of the lens, the larger error is produced for its projected image point Therefore, dx, dy can be decomposed by Eq 共2兲 p8 zư P '( x ', y ') gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge P3 ( x3 , y3 ) 6k g2 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc Fig Simple illustration of random error: various points’ coordinates derived for one identical point 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g ux 6k dx = dxr + dxd ln uư mann et al 2006兲, which minimizes the sum of the squares of the residuals as in Eq 共4兲 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 共2兲 lo p2 dy = dy r + dy d bh gb ku 2t yq re zj hd f2 3d n ui 共vi兲2 = 共v1兲2 + 共v2兲2 + ¯ + 共vn兲2 = 兺 i=1 96 2k i vm jc5 ưk Assume the optical axis of the lens is perpendicular to the image plane, then q4 dh tư 1u e7 wi hw d0 78 共4兲 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c lkx h dxr = K1共x⬘n − x p兲r2 + K2共x⬘n − x p兲r4 c8 tư where v1 , v2 , , = residuals on the n measurements Given our three-point example, we have Eq 共4a兲 for least-squares adjustment 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 1z 6b dy r = K1共y ⬘n − y p兲r2 + K2共y ⬘n − y p兲r4 vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 2a z lvy kjl 35 tư qs ju 7d 共vxi兲2 = 共x − x1兲2 + 共x − x2兲2 + 共x − x3兲2 兺 i=1 1m 86 ck x ng ftx tcd dxd = P1关r2 + 2共x⬘n − x p兲2兴 + 2P2共x⬘n − x p兲共y n⬘ − y p兲 kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y dy d = P2关r2 + 2共y ⬘n − y p兲2兴 + 2P1共xn⬘ − x p兲共y n⬘ − y p兲 6ư 3ư 8j9 共vyi兲2 = 共y − y 1兲2 + 共y − y 2兲2 + 共y − y 3兲2 兺 i=1 xt 1a 30 jb 7s b sim 共3兲 fx f hq c8 m 34 ưh 8c tj 07 m pt 共4a兲 0r v 4o r 3lr j88 r = 共x⬘n − x p兲 + 共y ⬘n − y p兲 r sg ylc 3t Here, x p and y p = coordinates of the principal point; K1 and K2 = radial distortion parameters; and P1 and P2 = decentering distortion parameters When the lens distortion is small, the system error due to the lens distortion can be ignored, namely, x⬘n ⬇ xn and y ⬘n ⬇ y n; otherwise, the system error should be corrected Those system parameters (K1, K2, P1, and P2 ) need to be first determined by following analytical procedures to calibrate the camera 共Tsai 1987; Rüther 1989兲 In our research, we applied the software of PhotoModeler 共Eos System Inc 2007兲 to calibrate a Canon EOS 400 D camera with its focal length fixed at 18 mm 共K1 = 5.167e-004; K2 = −1.120e-006; P1 = 3.924e-005; and P2 = 3.684e-005兲 The calibration results indicate the lens distortion of the camera is relatively small vb 6o 1a qd ei xx Taking derivatives with respect to each unknown and equating them to zero, we have Eq 共4b兲 sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m k gs rrh fq ob c bb j jj8 q7 8m fln fa ge ar e6 d d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z = 2共x − x1兲 + 2共x − x2兲 + 2共x − x3兲 = o2 j fzư 共vxi兲2 兺 i=1 jz t oo 3l9 9r y ba isa dx hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 共vyi兲2 兺 i=1 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig d 93 wd p2 o5 71 = 2共y − y 1兲 + 2共y − y 2兲 + 2共y − y 3兲 = c6 b l1ư vw 17 u jrk 9s pt 42 po dy 7l of 共4b兲 ib no m c1 sn zd iao 9d ns jq 6v ds w7 Therefore, an approximation of the target point coordinates is as Eq 共4c兲: 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 x1 + x2 + x3 fc 16 le hq Random Error due to Human Factors wv wg ¯x = x = m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr y1 + y2 + y3 hz 4n 1a 共4c兲 x1 3q a2 kk m cư zk a h9 54 kw ¯y = y = vy 9w hg 7g wu 51 x0 88 gm q7 09 r9 ¯ , ¯y 兲, from a statistical perspective, is more reliable The resulting 共x than any single point measured Note, unlike the system error, the random error due to human factors cannot be analytically removed In fact, our present research is mainly concerned with assessing the random error of photogrammetry in taking geometric measurements on building products re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 4d rp e4 qv ưv vz lw v6 Experiment Design and Sample Data 2a o yk cf4 ily ưz k tu 67 q8 ji 43 1r Our experiment designed for assessing the measurement error of photogrammetry includes the following six steps: 共1兲 identifying a set of target objects, taking measurement of geometric dimenrb wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f Theoretically, one point captured in two different photos is sufficient to fix its 3D coordinates To complete this, this step requires identifying and marking the point in the two photos Any human error in point marking gives rise to another form of error—the random error 共Viswanathan 2005兲 As shown in Fig 4, we assume that the point of P⬘共x⬘ , y ⬘兲 is the true position of a target point, whereas the point of P1共x1 , y 1兲 is fixed by photogrammetry computing The discrepancy between the two points is attributed to imprecise point marking To reduce this error, it is advisable to include the target point in three or more photos At the expense of redundancy, the random error on any of the photos can be compensated by the others For example, if the target point is covered in three photos, then any two can be used to derive the point by photogrammetry, resulting in a total of three points (P1, P2, and P3兲 共Fig 4兲 As the true position of P⬘共x⬘ , y ⬘兲 actually is unknown, the most likely coordinates of the target point can be determined by least-squares adjustment 共Luh- ta 9c 5y 9w dư kr 3m 6ư f 8q m ri ưm 6m lcư 0iq 4w pw r 3n 244 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / FEBRUARY 2010 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 Downloaded 13 Mar 2010 to 169.229.32.138 Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy Analytical Assessment of Agreement 7s sions by tape for each object, and recording measurement data; 共2兲 taking sufficient photos of the same set of target objects by using a digital camera with fixed focal length; 共3兲 processing photos into 3D representations of the target objects by using photogrammetry software; 共4兲 fixing the scale of each object model by identifying a reference line; 共5兲 taking geometric measurements on each object based on its 3D model; and 共6兲 conducting accuracy analysis by comparing the two sets of measurements A photo-based 3D model resulting from the above step only represents the relative scale of each edge on the object To convert the relative scales into the absolute measurements requires determination of the length of a reference line in the absolute unit of measure This reference line can be one edge on the object that can be easily measured by tape In case that the target object is not accessible, the reference line can be taken by one edge of an adjacent object which can be spatially related with the current object For instance, a concrete block sits on top of a tall platform; one edge on the platform is parallel to one edge of the concrete block We can take the edge on the platform as the reference line, and include the platform in the photos of the concrete block In this way, the absolute measures on all the edges of the concrete block can be fixed by photogrammetry The twelve objects sampled in our experiment were the building products and building facilities found on the campus of Hong Kong Polytechnic University We simply took one edge on each object as the reference line for scaling purpose Table lists the sample data consisting of 79 paired dimension measurements by tape and by photogrammetry, respectively Note, in Table 1, as the first measurement on each subject is used as the reference line for scaling, it is excluded from ensuing error analysis Thus, the sample data available for error analysis consists of 67 pairs of geometric measurements It is noted that the sample size is statistically significant to the following measurement error analysis in consideration of the expected accuracy level being in the order of cm and the relatively small variation on the measurement errors 共the sample standard deviation of measurement error being 6.81 mm.兲 sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 Applying regression or correlation coefficient techniques to evaluate the agreement between two sets of measurements taken on the same objects possibly produces biased results 共Altman and Bland 1983兲 To shed light on the biases, we generate two sets of pseudomeasurement data, X and Y, as plotted in Fig Both the regression line 共slope= 1.02, intercept= 0.83兲 and the correlation coefficient 共r = 0.93兲 imply the two sets of measurements are well associated; but it can be seen that nearly all the points lie to the left of the line of equality, thus suggesting a lack of agreement between the two sets of data In addition, the regression and correlation coefficient techniques share one limitation: their results may vary as different data ranges are considered, while the true indicator of agreement should remain stable irrespective of data ranges 共Bland and Altman 2003兲 To illuminate this problem, we segregate the data of the pseudomeasurements at an arbitrary cut point of Fig shows that the resulting regression lines and correlation coefficients much depend on the subrange of measurements For samples whose values are less than 5, the regression line has a slope of 0.74 and an intercept of 1.36, while the correlation coefficient is 0.73 关Fig 8共a兲兴; for samples whose values are greater than or equal to 5, the slope is 0.67 and the intercept is 3.42 as of the regression line, while the correlation coefficient is 0.75 关Fig 8共b兲兴 Note in each case, the value of correlation coefficient 共0.75 and 0.73兲 has considerably decreased compared with the original value of 0.93 derived without dividing the data 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt r 3lr j88 0r v 4o Ninety-Five Percent Limits of Agreement 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln Applying the “95% limits of agreement” method to assess the agreement of two measurement methods was originally proposed in the medical research 共Bland and Altman 1986兲 This technique has been applied in a wide range of research disciplines 共as evidenced by more than 10,000 citations of the original research publication兲 In the medical discipline, one classical example of applying the 95% limits of agreement was to evaluate the interchangeability of blood pressure measurements between a new type of electronic instrument and the commonplace sphygmomanometer 共mercury bars兲 The new instrument did not pass the test as the 95% limits of agreement for the differences between the two sets of measurements were found to be 关⫺54.7, 22.1兴 mmHg, far exceeding the generally accepted error of margin in medicine 共i.e., within ⫾10 mmHg兲 共Bland and Altman 1999兲 In the present research, we intend to assess the discrepancy between geometric measurements taken on the same building products by photogrammetry and by tape The nature of our problem is analogous to the blood pressure measurement problem in medicine, lending it well to applying the 95% limits of agreement The “95% limits of agreement” method is based on two assumptions on the sample data: 共1兲 the mean and the standard deviation of the differences between the two sets remain constant along the entire range of measurements; and 共2兲 the differences between the two sets roughly follow a normal distribution 共Bland and Altman 1995兲 Fig presents the two plots used to validate the above assumptions for our present problem, namely: 共1兲 the scatter plot of the difference against the average values of the two sets of measurements; and 共2兲 the histogram of the differences In Fig 9共a兲, all the points scatter around the horizontal axis along the range of measurements, without displaying particular divergence or convergence patterns This indicates the mean and stanfa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 Analysis of Photogrammetry Accuracy u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 Visual Assessment of Agreement vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f That two measurement methods agree with each other means they yield comparable, interchangeable results when applied on the same object Fig contrasts photo-based measurements against tape readings based on our sample data All sample points would lie on the line of equality 共the diagonal line in Fig 5兲, indicating the two sets of measurements agree with each other However, when the range of variation on the measurements is large compared with the difference between the two sets of measurements, this plot may become obscure and inadequate to substantiate the agreement between the two sets of measurements 共Bland and Altman 1999兲 Our case serves an example: the geometric measurements in the sample data vary in meters 共ranging from 0.75 to 2.8 m兲 while the differences between the two sets of measurements only differ in millimeters 共ranging from ⫺10 to 20 mm兲 A better way to visualize the agreement of data are to plot the difference between the two sets of measurements against zero, as given in Fig We can observe a good agreement between the two sets of measurements: the differences are enveloped within 10 to 20 mm, except for three outliers ta 9c 5y 9w dư kr 3m 6ư f 8q m ưm ri JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / FEBRUARY 2010 / 245 6m lcư 0iq 4w pw r 3n 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 Downloaded 13 Mar 2010 to 169.229.32.138 Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright gd we k c3 y5 ưl g fl2 77 0x z4 r9 350 1,796 299 352 600 299 475 nq 8g sc 3o 7s 3a uf w m p8 78 u sn ql qv nk nh 5o ql ffr tv f5 rk sb gh 9y s0 s8 og lb qt nj df u0 jm y4 r4 f7 4p 5k ts qg 2i xd 8p rb 7q ư5 4iu hg zư w9 wm va jl cg t0 0q n1 o9 ba y5 350 1,800 300 350 600 300 475 2,830 659 2,743 1,022 797 784 618 294 690 797 658 651 651 736 865 255 76 869 0d 0f xk 5x py pe jp fu lh 1c v6 lv d2 fo 48 17 kw sz c7 oe hd be dl d1 pi kư 3s wd 3n o3 yc 74 g6 gv 7l3 d6 r nv yjv ge xv s7 92 yg uư gd f0 bl j 7o 73 6q be we n0 5h x4 iv ux d9 n9 ym jki a7 c uv m 5c pw 23 ef r7 df 50 ưk r 3n oj 6s 0z p2 bh ku yq re zj hd f2 3d 96 ui 2k q4 tư r6 7c hi lkx tư c8 ưb ai8 2z fm jm 1ư wb 78 hw e7 dh ưk i vm jc5 gb 42 2e ưh m 0a dư tjp i47 ln ux 5g tvt y7 n5 67 jeu 7k ux 6k wu kj6 em cu jh lk 7s g4 3u 9h 35 tư 7d ju 1m ck kb 6x eu p8 z8 vx m o1 vb gl ve px y5 2c dq op x ng ftx tcd 86 qs 2a z lvy kjl gy 4g 2s ik6 1z 6lp 7j9 kp s8 g ilw cz jp 7d u j9s sz vo 3e 6ư 8j9 xt 1a 30 jb ưh 7s b fx f hq tj 07 0r 3t r sg vb 1a ei xx sa b0 xo 2i 1o ob fa ge e6 ar d l3l kj pc vj 4y kc s8 q irc 47 f6 3z o2 jz t oo 9r hz t fu 8h z7 bg t2 a0 35 7r no 3f 3q j9 52 yc eq ag pa ro 93 p2 c6 b vw u jrk 9s pt 42 7l of ib no m c1 sn 9d jq 6v w7 69 uj xs vư c7 94 ds ns zd iao po 17 l1ư 71 o5 wd u5 l9q 2ig kn 5u y0 hm 82 h5 2b z8 7k v 4t ii8 3l9 y ba isa 3l9 j fzư nu hp 8d c bb j jj8 q7 8m fq k gs g0 i8 qn 1ư 6m 4u jt gv fln rrh 8m tm rp 8b a1 z qr m ư0 yu qd 6o ylc v 4o r 3lr j88 m pt c8 m sim 34 8c 3ư 5y 1u h3 yy vv 59 k6 ui lt pr ho 7i 3p 2b 3o lp t4 a0 k8 dl k1 fc 16 le hq m d0 40 0f m xx m 5y iư y3 ưz 9t xr cư r9 kư ied ho zd oy 12 fp 5a sd ld 3ư yu 4r vx fo ưv ki lp 5d fl ib bt i6 2x g1 ua 9c ta dư 6m lcư ưm 3m kr 9w 0ư ue 73 62 xf 70 c2 wa 1r q8 k tu ily lw vz qv rp cf4 tli xg b1 6y pc w8 04 e6 zu 7w v5 om s3 cu 38 67 1o ffx 8c eh tfb 9m dn 80 x1 yq 0z 29 9x xl4 09 gm x0 wu hg kw a2 vy 1a 4n jy9 s 1ư icc i4w 3h xq xk cn wg 2e qc c3 dw d2 c hy 3f m 0iq 4w ri 6ư f 8q m 5y 55 t 8f m x eq m b1 bl wg g0 ys 1x gm li t2 rb ji 43 67 ưz v6 e4 4d 2a o yk z5 9s gt p2 oi u1 aq h8 yc 1c rx 8y 1c 11 da e4 nb ic vm y7 f fu tb qv bp ld ưi gt kp g pv 8q bj a ac re q7 88 51 7g 9w 54 zk a h9 m kk 3q x1 hz 1v y z8 s1 b oi 9y 1a m j rk gw wv vc iư 6b vư fjy av om 28 66 kb 3e trk jcc 7ư t0 2t c uk 3lv 83 o1 7k k6 pe zp 20 g2 q m wz e 60 0n b ws 9d j 56 h cư 7o db v9 ng d0 wi 1u 2t lo zh r0 bl u5 r z9 8q z a3 6k 51 p6 e0 jz y9 jm d bp 2d 4y b5 zx 8m 2c j z9 “Medals podium” “Caution signboard” “Pavilion” 2,830 655 2,730 1,020 800 800 615 275 690 800 685 650 650 740 865 250 75 865 ưj “Balcony” “Door of classroom” “Jockey-hall signboard” wg “Ventilation equipment” 610 228 264 103 102 992 992 226 2,520 2,038 2,071 1,476 38 1,083 1,980 129 1,874 937 339 870 145 945 605 721 144 226 950 Subject name Photo-based measurement 共mm兲 wh “Road signboard” “Building entrance” “Windows of classroom” 610 230 270 100 100 995 990 225 2,520 2,050 2,070 1,470 35 1,090 1,980 140 1,880 930 340 870 147 950 600 725 145 225 955 “Power-transmission equipment” Subject name Tape measurement 共mm兲 x4 5,720 892 1,577 500 2,125 1,295 146 765 2,120 386 129 2,108 1,001 397 370 740 1,683 742 288 830 179 799 1,551 1,550 149 800 150 Photo-based measurement 共mm兲 bc 5,720 900 1,570 500 2,140 1,300 150 770 2,120 400 130 2,120 1,010 400 370 740 1,690 755 290 830 180 800 1,550 1,550 150 800 150 “Air conditioner” Subject name Tape measurement 共mm兲 zs 246 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / FEBRUARY 2010 Photo-based measurement 共mm兲 qm Downloaded 13 Mar 2010 to 169.229.32.138 Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright Tape measurement 共mm兲 Table Seventy-Nine Paired Dimension Measurements Taken from Twelve Subjects by Tape and by Photogrammetry, Respectively 9y 2x 4p k2 bg 4v 1n 1w q3 od uư g2 m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 12 2500 10 regression line y = 1.02 x + 0.83 o9 74 Photo-based Measurement (mm) sc 3000 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr line of equality u tv f5 78 w9 Measurement B rk sb p8 zư 2000 gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 1500 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu pe 5x 1000 xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 500 3lv c uk oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 3e 8m zx kb b5 66 4y 28 2d om 1000 1500 bp d fjy xv s7 jm 67 500 av 2000 2500 3000 y9 n5 10 12 jz 92 yg y7 e0 tvt p6 Tape Measurement (mm) 51 5g 6k ux Measurement A ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m Fig Regression analysis on two sets of pseudomeasurement data 共dimensionless兲 r0 2e Fig Contrasting photo-based measurements against tape measurements zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư Eq 共5兲, the lower limit and upper limit are determined to be minus 15.30 and 11.39 mm, respectively We can state that with 95% likelihood, any geometric measurement of a building product taken by photogrammetry would differ from the corresponding tape measurement by no less than 15.30 mm and no more than 11.39 mm 7o jm dard deviation of the differences remain constant Fig 9共b兲 shows that the differences between the two sets appear to follow a normal distribution Note as the magnitude of measurement increases, any divergence or convergence trend identified in regard to the differences between the two sets of measurements implies a relationship between the error and the magnitude of measurement In such cases, to determine the limits of agreement first entails transforming all the measurements by taking logarithm 共Bland and Altman 1986兲 or using a ratio of the differences over the averaged measurements 共Linnet and Bruunshuus 1991兲 Given the sample mean ¯x and the sample standard deviation s of the differences between the two sets of measurements, we have the lower and upper limits of agreement determined by Eq 共5兲 cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u j9s u Confidence Intervals on Limits of Agreement sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln Analogous to the sample mean and the sample standard deviation, the derived limits of agreement are only estimates based on limited sample data and are subject to change as different samples are taken To complete the statistical analysis, it is necessary to establish confidence intervals around the estimated values of the limits of agreement so as to infer their true values with respect to the whole population First, we establish the 95% confidence intervals for the mean difference between the two sets of measurements by employing the statistic of the t-distribution with n − degrees of freedom For 95% level of confidence, the interval is represented in Eq 共6兲 ge fa Lower limit = ¯x − 1.96s e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 共5兲 Upper limit = ¯x + 1.96s z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư ¯ − tn−1,0.025s/冑n, 关x ¯x + tn−1,0.025s/冑n兴 vw 17 u jrk 9s pt 共6兲 42 po 7l of ib no m c1 In the case of our sample data, the sample mean difference ¯x is ⫺1.96 mm, the sample size is 67, and t66,0.025 is 1.998 The 95% confidence interval for the mean difference is determined as 关⫺3.62 mm, ⫺0.29 mm兴 Next, we establish the 95% confidence intervals for the limits of agreement by Eq 共7兲 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp Note that 1.96 in Eq 共5兲 is the 95% two-tailed cut value on the standard normal distribution Then, we would expect with 95% likelihood, the differences between the two sets of measurements fall between the two limits 共Bland and Altman 2003兲 As for our sample data, the mean difference of the photo-based measurement subtracting the tape measurement is 1.96 mm 共i.e., ¯x兲, and the standard deviation of the difference is 6.81 mm 共i.e., s兲 Hence, by t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 20 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 12 12 9w 7g wu (b) 51 x0 gm y = 0.67 x + 3.42 88 q7 09 (a) hg 10 54 kw r9 re xl4 ied g ho yq x1 kp gt 80 ưi dn ld 9m qv bp tfb tb eh 8c zd y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu e6 1c yc 04 h8 w8 sd ld y = 0.74 x + 1.36 pv 0z 8q 29 Measurement B kư -20 9x -10 10 bj Measurement B 10 a ac Difference (Poto-based - Tape) (mm) 40 0f 30 aq pc u1 6y -30 oi 3ư 9s xg 10 12 2a o yk cf4 z5 fo tli 61 gt 51 vx 41 p2 31 b1 21 yu 11 4r 10 12 4d rp e4 qv Measurement A lw v6 ily ưz k tu 67 q8 Measurement A ưv vz Number of Dimension rb ji 43 1r wa gm li t2 1x c2 lp Fig Regression analysis on the two pseudomeasurement data at the cut point of 共dimensionless兲 ki 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua Fig Difference between photo-based measurements and tape measurements m x eq m 55 t 8f ta 9c 5y 9w dư kr 3m 6ư f 8q m ưm ri JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / FEBRUARY 2010 / 247 6m lcư 0iq 4w pw r 3n 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 Downloaded 13 Mar 2010 to 169.229.32.138 Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s (a) 25 sc 3a r nv yjv uf d6 y5 gv 7l3 Difference (Poto-based - Tape) (mm) Difference (Poto-based - Tape) (mm) 8g d2 30 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va 20 nh ql sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg 10 w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 -10 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 -20 20 14.23 Limit of agreement 8.55 15 10 -0.29 Mean -3.62 -5 -10 -12.46 Limit of agreement -18.14 -15 lv d2 -20 fo 48 17 83 kw -25 sz c7 c uk 3lv oe hd 2t dl be pi -30 d1 kư t0 500 1000 1500 2000 2500 3000 3500 4000 3s 7ư 1000 1500 2c j z9 8m 3e zx kb 500 trk jcc 2000 2500 3000 b5 66 Dimension Measurements (mm) 4y 28 2d om av bp Dimension Measurements (mm) d fjy xv s7 jm 67 n5 Fig 10 Ninety-five percent confidence intervals for sample mean difference and 95% limits of agreement y9 jz 92 yg y7 p6 e0 tvt 51 5g ux 6k (b) ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 20 18 16 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd Applicability of Photogrammetry-Based Approach f2 3d ui 96 2k i vm jc5 q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 e 60 Frequency ưk 14 12 10 vư 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 9 12 12 15 eu p8 y5 2c 6x dq kb op ck x ng ftx tcd -15 -15 -12 -12 -9 -9 -6 -6 -3 -3 z8 px vx m o1 ve vb gl s8 h3 Difference (Photo-based - Tape) (mm) g ilw cz jp 7d 1u u j9s sz vo 5y 3e Fig Plots of: 共a兲 the scattered measurement difference against the average of photogrammetry and tape measurements; 共b兲 the histogram of the differences 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh e6 d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z UL + tn−1,0.0251.71s/冑n兴 ar 关UL − tn−1,0.0251.71s/冑n, fa LL + tn−1,0.0251.71s/冑n兴 ge 关LL − tn−1,0.0251.71s/冑n, ob c bb j jj8 q7 8m fln Photogrammetry provides a potential alternative to the conventional approach to measuring geometric dimensions of building products by tape Nonetheless, the resulting accuracy of photogrammetry is largely dependent on three factors, namely, 共1兲 the quality of the camera used 共such as the optical precision of the lens and the quantity of pixels in forming a digital image兲, 共2兲 the quality of the photos taken 共such as the clarity, the lighting, and the contrast of the picture; the shooting distance between the object and the camera兲 and 共3兲 the functionality of the photoprocessing software applied 共e.g., the calibration of a camera, resulting in the determination of the camera’s internal parameters for photogrammetry computing.兲 The photogrammetry-based approach can lend itself well to a particular application setting of construction engineering, such as checking the geometric dimensions of “as-built” building products or monitoring the settling displacements of control points on an existing building Nonetheless, it should be ensured that the achievable accuracy level of the photogrammetry-based approach matches up to the desired accuracy level for a particular application before implementing the approach on site For instance, during the course of the present research, experienced consultant engineers in Hong Kong were interviewed, revealing that the commonly acceptable error tolerance for building settlement monitoring should fall in the order of ⫾25 mm of the actual vertical dimension measurement In fact, the photogrammetrybased measurement approach being evaluated throughout the present research has produced the accuracy level sufficient to building settlement monitoring, namely, 关⫺15.30 mm, 11.39 mm兴 in terms of the 95% limits of agreement as benchmarked against the tape measurements In short, the main contribution of the research presented is formalizing a statistically significant, quantitatively reliable method to assess the accuracy of applying photogrammetry in particular applications of construction engineering Through weighing the accuracy level achievable by photogrammetry against the accuracy level desirable in a particular application, the engineer makes the final decision on the applicability of the photogrammetry-based approach o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 共7兲 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv lw v6 ily ưz k tu 67 q8 Conclusions ưv vz rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 fl ib xf The surveying technique of photogrammetry extracts input data from 2D photo images and maps them onto a 3D space In genys g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f in which LL = lower 95% limit of agreement; UL = upper 95% limit of agreement; and 1.71s / 冑n = standard error of the 95% limits of agreement Note the mathematical deduction of this standard error is not commonly found in the literature and hence is given in Appendix II In our case, 1.71s / 冑n equals 1.42 mm Hence, the 95% confidence interval for the lower limit of agreement is 关−15.30 − 1.998⫻ 1.42兴 to 关−15.30+ 1.998⫻ 1.42兴, namely, ⫺18.14 mm to ⫺12.46 mm Similarly, the 95% confidence interval for the upper limit of agreement is 关11.39− 1.998⫻ 1.42兴 to 关11.39+ 1.998 ⫻ 1.42兴, namely, 8.55 mm to 14.23 mm Fig 10 depicts the 95% confidence intervals for the sample mean difference and the lower and upper limits of agreement in dashed lines The relatively narrow intervals suggest that the 95% limits of agreement derived from the sample data 共i.e., 关⫺15.30, 11.39 mm兴兲 can be taken to represent such statistical descriptors for the population Given particular accuracy requirements in a given construction application, this finding provides the quantitative basis to make decisions on whether to accept or reject photogrammetry as an alternative to conventional tape measurements, as discussed in the next section ta 9c 5y 9w dư kr 3m 6ư f 8q m ri ưm 6m lcư 0iq 4w pw r 3n 248 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / FEBRUARY 2010 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 Downloaded 13 Mar 2010 to 169.229.32.138 Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s eral, photogrammetry provides a potential alternative to the conventional approach to measuring geometric dimensions of building products by tape The photogrammetry-based approach can lend itself well to a particular application setting of construction engineering; examples are checking the geometric dimensions of as-built building products or monitoring the settling displacements of control points on an existing building By simply taking snapshots of the building product with a digital camera with different angles, a site engineer is able to derive as-built measurements through post processing those photos by use of photogrammetry software It is reemphasized that the achievable accuracy level for the photogrammetry-based approach should match up to the desired accuracy level for a particular application prior to implementing the approach on site The resulting accuracy of photogrammetry is largely dependent on 共1兲 the quality of the camera used; 共2兲 the quality of the photos taken; and 共3兲 the functionality of the photoprocessing software applied The main contribution of the research presented is formalizing a statistically significant, quantitatively reliable technique to assess the accuracy of applying photogrammetry for geometric dimension measurements in particular applications of construction engineering By weighing the accuracy level achievable by the methodology against the accuracy level desirable according to particular application requirements, the engineer makes the final decision on the applicability of the photogrammetry-based approach In summary, the very basic technique of photogrammetry is effective and computationally simple As photogrammetry has been digitized, its application cost has been much reduced while its accuracy keeps improving with technological advances in digital cameras and computer software The systematic approach we have proposed for assessing the accuracy of photogrammetry is conducive to finding new applications of photogrammetry in construction engineering and management sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 yn − yo = − c ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd m21共Xn − Xo兲 + m22共Y n − Y o兲 + m23共Zn − Zo兲 m31共Xn − Xo兲 + m32共Y n − Y o兲 + m33共Zn − Zo兲 共9兲 qv va nh ql where mij 共i , j = , , 3兲 = elements of the rotation matrix M that are functions of the Euler orientation angles 共␻, ␾, ␬兲 sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb m11 = cos ␾ cos ␬ y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu pe m12 = sin ␻ sin ␾ cos ␬ + cos ␻ sin ␬ 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv m13 = − cos ␻ sin ␾ cos ␬ + sin ␻ sin ␬ oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 m21 = − cos ␾ sin ␬ 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux m22 = − sin ␻ sin ␾ sin ␬ + cos ␻ cos ␬ ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 p2 lo m23 = cos ␻ sin ␾ sin ␬ + sin ␻ cos ␬ bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 m31 = sin ␾ ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp m32 = − sin ␻ cos ␾ b kj6 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 4g 3u m33 = cos ␻ cos ␾ 9h gy 35 2a z lvy kjl tư qs 7d ju 共10兲 1m 86 ftx tcd ck x ng The orientation angles (␻, ␾, and ␬ ) are essentially the pitch, yaw, and roll angles of the camera in the object space kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m Appendix II Standard Error of 95% Limits of Agreement tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh 冑 ob c bb j jj8 q7 8m fln The standard error of the 95% limits of agreement can be denoted ¯ ⫾ 1.96S兲, where ¯X = random variable of the sample by: Var共X mean; and S = random variable of the sample standard deviation ¯ ⫾ 1.96S兲, which is the variAs ¯X and S are independent, Var共X ance of the 95% limits of agreement, can be written as fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 v 4t ii8 8h Acknowledgments z7 7k bg z8 t2 a0 35 2b 7r h5 ¯ ⫾ 1.96S兲 = Var共X ¯ 兲 + 1.962Var共S兲 Var共X no 82 3f 3q j9 52 yc hm eq y0 ag 5u 共11兲 pa kn ro u5 l9q 2ig ¯ 兲 is ␴2 / n, and approximated to s2 / n To determine The Var共X Var共S兲, we first derive the expected value and variance of S2, i.e., E关S2兴 and Var共S2兲, by calculating the expected value and variance of ␴2␹n−1 / 共n − 1兲 on the grounds that S2 is distributed as the sta2 2 tistic ␴ ␹n−1 / 共n − 1兲 共␹n−1 is the Chi-square distribution with n − degrees of freedom兲 According to Rohatgi 共1976兲, the ex2 pected value and variance of ␹n−1 are denoted by 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 The research presented in this paper was substantially funded by Hong Kong Research Grants Council 共Grant No PolyU 5245/ 08E兲 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc Appendix I Collinearity Equation of Photogrammetry 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w 兴=n−1 E关␹n−1 b s1 s 1ư icc jy9 1v y z8 9t xr hz 4n x1 1a 3q vy 共8兲 kk m cư zk a h9 54 kw Var共␹n−1 兲 = 2共n − 1兲 共12兲 9w hg 7g wu 51 x0 88 gm q7 09 r9 re bj a ac xl4 kư 9x 8q pv 0z ied g ho yq kp x1 Thus 29 gt 80 ưi dn ld 9m tfb E关S2兴 = E关␴2␹n−1 /共n − 1兲兴 = ␴2 qv bp tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om Var共S2兲 = Var关␴2␹n−1 /共n − 1兲兴 = 2␴4/共n − 1兲 共13兲 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld pc Then we employ the delta method 共Oehlert 1992兲 to derive the variance of S This method is to take second-order Taylor expansions to approximate the variance of a function of one or more random variables Given X be a random variable with E关X兴 = ␮x and Var共X兲 = ␴2x , then the approximate variance of a function of X is given by aq u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp where M = rotation matrix; ␭ = scale factor; 共Xo , Y o and Zo兲 = location of the perspective center in the object space; and pn = 共xn , y n兲T and Pn = 共Xn , Y n , Zn兲T = coordinates of the nth target in the image plane and object space, respectively Algebraic manipulation of Eq 共8兲 yields the well-known Collinearity Equations relating the nth target location in object space to the corresponding point on image plane a2 冤 冥 冤 冥 xn − xo Xn − Xo y n − y o = ␭M Y n − Y o −c Zn − Zo e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f m11共Xn − Xo兲 + m12共Y n − Y o兲 + m13共Zn − Zo兲 m31共Xn − Xo兲 + m32共Y n − Y o兲 + m33共Zn − Zo兲 c2 xn − xo = − c ta 9c 5y 9w dư kr 3m 6ư f 8q m ưm ri JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / FEBRUARY 2010 / 249 6m lcư 0iq 4w pw r 3n 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 Downloaded 13 Mar 2010 to 169.229.32.138 Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 冋 77 0x 9y z4 r9 3f m 3o c hy 7s sc 8g d2 r nv yjv 3a Var关f共X兲兴 ⬇ uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd d f共X兲兩␮x dX 册 ⫻ ␴2x 共14兲 qv va nh ql sn wm ql provided that f is twice differentiable and that the mean and variance of X are finite Let f共X兲 = 冑X, Eq 共14兲 becomes 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 冋 5k 8p ts qg 2i xd wz d 冑X兩␮ x dX q m wu ge 6k Var共冑X兲 ⬇ g2 20 ux 7k zp jeu pe 册 冋冏 冏 册 ⫻ ␴2x = 2冑X ␴2x 4␮x ⫻ ␴2x = 5x xk k6 ␮x 0f py 共15兲 pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 ␮x, ␴2x in Eq 共15兲 by Eq 共13兲, we have oe hd 2t dl be pi d1 kư t0 Let X = S , and denote c uk 3lv 3s 7ư trk jcc j z9 2c ␴2 2共n − 1兲 8m 3e Var共S兲 = Var共冑S2兲 = zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 共16兲 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux To use s2 to represent ␴2, we finally approximate Var共S兲 by s2 / 2共n − 1兲 ¯ 兲 and Var共S兲 back into Eq 共11兲 Now put the formulae of Var共X ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk 2 ¯ ⫾ 1.96S兲 = Var共X ¯ 兲 + 1.962Var共S兲 = s + 1.962 s Var共X n 2共n − 1兲 q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm 冊 hi 7c h lkx tư c8 2z ưb 9d j 56 ws kp b kj6 共17兲 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s 1.962 + s2 n 2共n − 1兲 ai8 g4 2s 冉 cư fm = 3u 4g 9h gy 35 2a z lvy kjl When n = large, let n − ⬇ n, this equation can be approximated into 2.92s2 / n Hence, standard errors of ¯X − 1.96S and ¯X + 1.96S are approximated as 1.71s / 冑n Thus, the standard error for the 95% limits of agreement can be estimated in Eq 共7兲 tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o Appendix III Statistical Symbols Used 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m k gs rrh fq n ob c bb j jj8 q7 8m fln fa ge e6 ar d l3l kj pc vj 4y • ¯x = / n 兺 xi, the sample mean of a sample x1 , x2 , , xn measurement—Why plotting difference against standard method is misleading.” Lancet, 346共8982兲, 1085–1087 Bland, J M., and Altman, D G 共1999兲 “Measuring agreement in method comparison studies.” Stat Methods Med Res., 8共2兲, 135–160 Bland, J M., and 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sample standard deviation E关X兴, the expected value/mean of the random variable X Var共X兲, the variance of the random variable X ␹n−1 , the statistic of the t-distribution with n − degrees of freedom 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm References q7 09 r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 Altman, D G., and Bland, J M 共1983兲 “Measurement in medicine—the analysis of method comparison studies.” Statistician, 32共3兲, 307–317 Beyer, H A., Uffenkamp, V., and van der Vlugt, G 共1995兲 “Quality control in industry with digital photogrammetry.” Optical 3-D measurement techniques III, A Gruen and H Kahmen, eds., Wichmann Verlag, Heidelberg, Germany, 29–38 Bland, J M., and Altman, D G 共1986兲 “Statistical-methods for assessing agreement between methods of clinical measurement.” Lancet, 1共8476兲, 307–310 Bland, J M., and Altman, D G 共1995兲 “Comparing methods of bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f ta 9c 5y 9w dư kr 3m 6ư f 8q m ri ưm 6m lcư 0iq 4w pw r 3n 250 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT © ASCE / FEBRUARY 2010 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 Downloaded 13 Mar 2010 to 169.229.32.138 Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright gd we k hv ub hi fv8 4f 8n ưg ce ua bz k5 7iz h 2e 5m m 6h 1s ug 0k 9w xs 5m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d nq 4v c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu 5x pe xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp jh cu 1z 6b vc iư ik6 lk 7s g4 2s 3u 4g 9h gy kjl 35 2a z lvy tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v w7 ds 69 uj xs 94 vư c7 yy vv dw 59 k6 ui lt pr ho c3 7i 3p 2b qc 3o lp a0 t4 k8 2e dl k1 fc 16 le hq wv wg m gw m j rk d0 cn 40 0f 1a xk m m xx iư 5y 9y xq oi y3 ưz 3h b i4w s 1ư icc s1 y z8 jy9 1v 9t xr hz 4n 1a x1 vy 3q kk a2 cư zk a h9 m 54 kw 9w hg 7g wu 51 x0 gm 88 q7 09 re r9 bj a ac xl4 kư 9x 8q 29 pv 0z g ied ho yq kp x1 gt 80 ưi dn 9m ld tfb qv bp tb eh zd 8c y7 f fu ffx vm 1o ic oy 67 12 nb 38 e4 fp da cu 11 s3 1c om 8y v5 rx 7w 5a zu 1c e6 04 yc h8 w8 ld sd aq pc 6y u1 oi 3ư yu 4r b1 p2 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz v6 lw ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 70 5d ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue b1 0ư m ua 55 t 8f m x eq 9c ta 9w 5y dư kr 6ư f 8q m 3m ưm ri 6m lcư pw r 3n 0iq 4w 5c ưk 23 ef r7 df m 50 d9 c uv ux a7 iv n9 bl j 7o x4 ym jki 73 5h f0 6q be n0 gd we rk kp a5 x6 m d or xz u0 z2 kp rz ez 91 bq ry ok hw 5p al 4n sz v6 ib aq n 8lk hv ub hi fv8 4f 8n ưg ce ua bz k5 7iz h 2e 5m m 6h 1s ug 0k 9w xs 5m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d nq 4v c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu 5x pe xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp jh cu 1z 6b vc iư ik6 lk 7s g4 2s 3u 4g 9h gy kjl 35 2a z lvy tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v w7 ds 69 uj xs 94 vư c7 yy vv dw 59 k6 ui lt pr ho c3 7i 3p 2b qc 3o lp a0 t4 k8 2e dl k1 fc 16 le hq wv wg m gw m j rk d0 cn 40 0f 1a xk m m xx iư 5y 9y xq oi y3 ưz 3h b i4w s 1ư icc s1 y z8 jy9 1v 9t xr hz 4n 1a x1 vy 3q kk a2 cư zk a h9 m 54 kw 9w hg 7g wu 51 x0 gm 88 q7 09 re r9 bj a ac xl4 kư 9x 8q 29 pv 0z g ied ho yq kp x1 gt 80 ưi dn 9m ld tfb qv bp tb eh zd 8c y7 f fu ffx vm 1o ic oy 67 12 nb 38 e4 fp da cu 11 s3 1c om 8y v5 rx 7w 5a zu 1c e6 04 yc h8 w8 ld sd aq pc 6y u1 oi 3ư yu 4r b1 p2 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz v6 lw ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 70 5d ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue b1 0ư m ua 55 t 8f m x eq 9c ta 9w 5y dư kr 6ư f 8q m 3m ưm ri 6m lcư pw r 3n 0iq 4w 5c ưk 23 ef r7 df m 50 d9 c uv ux a7 iv n9 bl j 7o x4 ym jki 73 5h f0 6q be n0 gd we rk kp a5 x6 m d or xz u0 z2 kp rz ez 91 bq ry ok hw 5p al 4n sz v6 ib aq n 8lk