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1 Journal of Computer2Aided Design & Computer Graphics Vol. 22 No. 2 Feb. 200 ), ), ), 2), ) ) ( 0090) 2) ( 0004) ia. ac. cn) :,,,,., ;, ;,, : ; ; : TP39 Automatic Reconstruction of Distant Scenes from Wide Baseline Images Zhang Feng ), Xu Zhenhui ), Shi Limin ), Sun Fengmei 2), and Hu Zhanyi ) ) ( N ational L aboratory of Pattern Recognition, I nstitute of A utomation, Chinese A cadem y of Sciences, Bei j ing 0090) 2) ( I nstitute of I mage Processing and Pattern Recognition, N ort h China Universit y of Technology, Bei j ing 0004) Abstract : When images are taken f rom a relatively long distance, t he resultant disparity variation is usually small, consequently non2coplanar space point s could be mistakenly reconstructed to a plane if t he traditional pinhole camera model is employed, which will drastically affect t he reconstructed scene visual appearance. Aimed at t his p ro blem, an auto matic met hod for distant scene reco nst ructio n is proposed in t his work. The main contributions include : a more suitable perspective camera model for distant scene reco nst ructio n, a ro bust self2calibratio n met hod based o n affine camera model and t he efficient f usion of reconstructed partial result s is carried out via a combination of t he factorization met hod and t he bloc2based bundle adjust ment technique. Extensive experiment s with distant outdoor images are reported and validate our method. Key words : camera model ; 3D reconstruction ; self2calibration [ ].,,, : Tomasi [2 ],, ; Poelman [3 ], : ; : : (2006BA K3B04) ; ( ) ; (2007AA0Z34). (979 ),,, ; (984 ),,, ; (977 ),,, ; (956 ),,,, ; (96 ),,,,, China Academic Journal Electronic Publishing House. All rights reserved.

2 2, : 257,, ; Pollefeys [4 ],,,,, ; [526 ],, ; Snavely [728 ], (500 ),,, EXIF, EXIF,, 2, ; Pollefeys [9 ],,,, (3),,,. X = [ X Y Z ] T, x = [ x y ] T, x = P X, 0 (),, P 3 4, Q R2, P, K = f s x 0 0 f y P = K[ R t ] (2), R = r r2 r3 r2 r22 r23 r3 r32 r33, t = K, f,, s, ( x0 y0 ), R t () (2) x = f ( r X + r2 Y + r3 Z + t ) + s( r2 X + r22 Y + r23 Z + t2 ) ( r3 X + r32 Y + r33 Z + t3 ) y = f ( r2 X + r22 Y + r23 Z + t2 ) ( r3 X + r32 Y + r33 Z + t3 ) + y0 + x0 t t2 t3 (3), f a = f t3, sa = s x = ( f ( r X + r2 Y + r3 Z + t ) )Πt3 + ( r2 X + r22 Y + r23 Z + t2 )Πt3 ( r3 X + r32 Y + r33 Z)Πt3 + y = ( f ( r2 X + r22 Y + r23 Z + t2 ) )Πt3 ( r3 X + r32 Y + r33 Z)Πt3 + t3, = t3, (3) + y0 x = f a ( r X + r2 Y + r3 Z + t ) + sa ( r2 X + r22 Y + r23 Z + t2 ) ( r3 X + r32 Y + r33 Z) + y = f a ( r2 X + r22 Y + r23 Z + t2 ) ( r3 X + r32 Y + r33 Z) +, ( r3 X + r32 Y + r33 Z)Πt3, + y0 + x0 + x0 = 0, (4), (4) x = f a ( r X + r2 Y + r3 Z + t ) + sa ( r2 X + r22 Y + r23 Z + t2 ) + x0. y = f a ( r2 X + r22 Y + r23 Z + t2 ) + y0, x0 = 0, y0 = 0, x = AX (5) China Academic Journal Electronic Publishing House. All rights reserved.

3 A = f a s a 0 f a r T r T 2. (4), = 0, (5), 0, (4) 2, 2. [2 ],, m n, (5) S = x xn x m xnm = A X Xm (6) S (6) 2 n 3 3 m, S 3. S S = U V T, U V, S, S i. = diag (, 2, 3,0,,0),U V U V 3, A An = U, X Xm = V T An (7) (7), 2. 2 [3,0 ], 3 3 H H A H = f s 0 f Ai H = f i s 0 f i (8) r T r T 2 r T i r T 2 A HH T A T = f 2 + s 2 s f s f 2 f 2 Ai H H T Ai T = f 2 i + s 2 s f i s f i 2 f 2 i, i = 2,3,, n, i = 2,3,, n (8) (9), 0.. s 0, s f ,, 0. 9 f i f n, f i f f 2., i = 2,, , i = 2,, n; (9) f 2 A HH T A T f 2 Ai H H T Ai T , i = 2,3,, n f (0) A HH T A T Ai H H T Ai T (0) H H,, i = 2,3,, n () = H H T, ai, ai2 ( i =,2,, n) Ai, () ( a a T - ) = ( a2 a 2 T - ) = ( a2 a 2 T - a a T ) = ( a a 2 T ) = ( ai a i T - ) = 0, i = 2,3,, n 0. 2 ( ai2 a i2 T - ) = 0, i = 2,3,, n 0. 2 ( ai2 a i2 T - ai a i T ) = 0, i = 2,3,, n 0. 0 ( ai a i2 T ) = 0, i = 2,3,, n (2) (2),. n,, 0, 5 + n, 5 ( ),, n. (2) 3 n, 3,, Cholesky H, H ( Xj ) m j =, (8) China Academic Journal Electronic Publishing House. All rights reserved.

4 2, : ,,, (4) ;, = 0, f a, sa,, x0, y0, R, t, t2 X,,, [22 ], : ) 4 ; 2),, ; 3), 3,,, 4,,2,3,4 4,,2,3 2, 3,4 xi = Ai X + bi, i =,2,3 (3) xi = Bi X + ci, i = 2,3,4 (4) ( 3 ) ( 4 ), H = M3 3 T3 0 (5) (6) H, 4 A2 b2 = B2 c2 H (5) A3 b3 = B3 c3 H (6) A4 b4 = B4 c4 H (7),,, Ai, bi ( i =, 2,, n) Xj ( j =,2,, m). F = n m i = j = d ( xij, Ai X j + bi) 2 (8). xij i X j. : Step. SIF T [324 ] Step2. Step2.. 3 ; Step2. 2. (5) (7) 2 ; Step2. 3. (8) ; Step2. 4. Step2. 2 Step2. 3, Step3. Step ; Step3. 2. (8) A, K, R, T; Step3. 3., ; Step ,, 3,.. (3 4 ), , 30 m ; China Academic Journal Electronic Publishing House. All rights reserved.

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262 22 0 3 Πmin Πmin Πmin 98. 473 0 2. 223 2 08. 06 8 9 878 2 7. 7 7 2. 029 3 78. 45 2 3 007 3 286. 202 8 7. 7 5 308.

8 2, : 263,, ( References) : [ ] Hartley R, Zisserman A. Multiple view geometry in computer vision [ M ]. 2nd ed. Cambridge : Cambridge University Press, 2000 [ 2 ] Tomasi C, Kanade T. Shape and motion from image streams under orthography : a factorization method [J ]. International Journal of Computer Vision, 992, 9 (2) : [ 3 ] Poelman C J, Kanade T. A paraperspective factorization met hod for shape and motion recovery [J ]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 997, 9 (3) : [ 4 ] Pollefeys M. Visual modeling with a hand2held camera [J ]. International Journal of Computer Vision, 2004, 59 (3) : [ 5 ] Zhang Guofeng, Qin Xueying, Dong Zilong, et al. Camera tracking based on structure and motion recovery for augmented video [J ]. Chinese Journal of Computers, 2006, 29 (2) : (in Chinese) (,,,. [J ]., 2006, 29 ( 2) : 204-2) [ 6 ] Zhang G F, Qin X Y, Hua W, et al. Robust metric reconstruction from challenging video sequences [ C] ΠΠ Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,Minneapoils, 2007 : - 8 [ 7 ] Snavely N, Seitz S T M, Szeliski R. Photo tourism : exploring photo collections in 3D [J ]. ACM Transactions on Graphics, 2006, 25 (3) : [ 8 ] Snavely N, Seitz S M, Szeliski R. Skeletal graphs for efficient structure from motion [ C] ΠΠProceedings of IEEE Conference on Computer Vision and Pattern Recognition, Anchorage, 2008 : - 8 [ 9 ] Pollefeys M, Nist r D, Frahm J M, et al. Detailed real2time urban 3D reconstruction from video [J ]. International Journal of Computer Vision, 2008, 78 (2Π3) : [ 0 ] Pollefeys M. Self2calibration and metric 3D reconstruction from uncalibrated image sequences [ D]. Stockholm : KTH Royal Institute of Technology, 200 [ ] Triggs B, Mclauchlan P F, Hartley R I, et al. Bundle adjust ment a modern synthesis [ M ] ΠΠLecture Notes in Computer Science. Heidelberg : Springer, 2000, 883 : [ 2 ] Lourakis M I A, Argyros A A. The design and implementation of a generic sparse bundle adjustment software package based on t he Levenberg2Marquardt algorithm [ R]. Heraklion : Institute of Computer Science of the Foundation for Research and Technology2Hellas, 2004 [ 3 ] Lowe D G. Object recognition from local scale2invariant features [ C] ΠΠProceedings of the International Conference on Computer Vision, Corfu, 999 : [ 4 ] Lowe D G. Distinctive image features from scale2invariant keypoint s [J ]. International Journal of Computer Vision, 2004, 60 (2) : 9-0 [ 5 ] Labatut P, Pons J P, Keriven R. Efficient multi2view reconst ruction of large2scale scenes using interest point s, Delaunay triangulation and graph cuts [ C] ΠΠProceedings of the t h International Conference on Computer Vision, Rio de Janeiro, 2007 : China Academic Journal Electronic Publishing House. All rights reserved.

2 3. 1,,,.,., CAD,,,. : 1) :, 1,,. ; 2) :,, ; 3) :,; 4) : Fig. 1 Flowchart of generation and application of 3D2digital2building 2 :.. 3 : 1) :,

2 3. 1,,,.,., CAD,,,. : 1) :, 1,,. ; 2) :,, ; 3) :,; 4) : Fig. 1 Flowchart of generation and application of 3D2digital2building 2 :.. 3 : 1) :, 3 1 Vol. 3. 1 2008 2 CAA I Transactions on Intelligent Systems Feb. 2008, (,210093) :.,; 3., 3. :; ; ; ; : TP391 :A :167324785 (2008) 0120001208 A system f or automatic generation of 3D building models