miru2006_cr.dvi
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- かずまさ みやくぼ
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1 y;yy yy y y;yy yy y;yy y yy NEC yftomoka-s,sei-i,kanbara,yokoyag@is.naist.jp, yyiketani@cp, n-nakajima@ay.jp.nec.com (structure from motion), structure from motion,,, Video Mosaicing for Curved Documents Based on Structure from Motion Tomokazu SATO y;yy, Akihiko IKETANI yy, Sei IKEDA y, Masayuki KANBARA y;yy, Noboru NAKAJIMA yy,andnaokazu YOKOYA y;yy y Nara Institute of Science and Technology, Takayama-cho, Ikoma-shi, Nara, Japan yy Internet System Lab., NEC, , Takayama-cho, Ikoma-shi, Nara, Japan yftomoka-s,sei-i,kanbara,yokoyag@is.naist.jp, yyiketani@cp, n-nakajima@ay.jp.nec.com Abstract A number of methods for video mosaicing have already been investigated. However, these methods often assume that the target object is flat or very far from the camera to avoid the disparity problem. In this report, we proposeanovel video mosaicing method for curved documents based on 3-D reconstruction. With the proposed method, the mosaic image of geometrically restored target document is generated, even if the document has a curved surface. Experiments on curved documents have shown the feasibility of the proposed method. Key words video mosaicing, structure from motion, shape estimation, feature tracking, camera parameter estimation 1. ( ) 1(a)
2 (a) (b) (c) 1 [1], [2] 1(b) Brown [3] Yamashita [4] NURBS Cao [5] Brown [6] 2 ( ) [7] [11] Homography. Homography Homography [11] 1(c) [12] [13] [11] (structure from motion)
3 PDA (A) Initial 3-D reconstruction by feature tracking (B) Parameter refinement and target shape estimation (a) Detection of reappearing features (b) Global optimization (c) Surface fitting to 3D point cloud Iterate until convergence (C) Mosaic image generation structure from motion (A) (B) (C) (A) (C) 2. 1 S p =(x p;y p;z p) f x fp =(u fp ;v fp ) f M f S p x fp (au fp ;av fp ;a) T = M f (x p;y p;z p; 1) T ; (1) a x fp 1 ^x fp =(^u fp ; ^v fp ) (,,, ) x fp f p x 0 fp =(u 0 fp;vfp) 0, (1) S p x fp f p E fp E fp = jx fp x 0 fpj 2 (2) 2. 2 M f S p ( (A)) [14] M f 0 p S p (u 1p;v 1p; 1) (B) (f >1) M f ( ) Harris [15] RANSAC [16] ( ) (u 0 fp;vfp) 0 S p =(x p;y p;z p) M P f (2) p E fp Levenberg-Marquadt p S p ( ) P f p Eip i=1 S p =(x p;y p;z p) ( ) [14] M f S p
4 3-D D points of features Compensate for Distortion Matching n m Vmin: direction of minimum principal curvatures (i) (ii) (iii) (iv) 3 ; (i), (ii), (iii), (iv) 2. 3 ( (B)). 2(B) (a) (b) (c) (a) (c) (2) (a) (c) (i) 3(iii) 4 Plane P Projected points V2 Vmax: direction of maximum principal curvatures Vmin: Normal of projection plane V1: first principal direction of projected points y = f (x) (a) (c) [17] E all = X f X p E fp (3) (a) E fp 3(ii) (b) 1 4 (b) p S p R p R p z = ax 2 + bxy + cy 2 + dx + ey + f (4)
5 1 0 V min =(vm x;vm y;vm z) V min P (x; y; z) = vm xx + vm yy + vm zz = 0 S p P V1 =(v1 x;v1 y;v1 z) V1 V min V2 =(v2 x;v2 y;v2 z)=v1 V min S p V1; V2 (μx; μy) ψ! ψ! μx p V1 = S p (5) μy p V2 (μx; μy) (a 0; ;a m) μy = f(μx) = mx i=0 a iμx i (6) AIC [18] m (a) 2. 4 ( (C)) (m; n), (μx;f(μx); μz) (m; n) =( Z μx 0 r 1+f d dx f(x)g2 dx; μz) (7) (7) (m; n) (μx; f(μx); μz). 0 au f av f a 1 0 C A = M f V1 V2 V min 1 C A T 0 μx f(μx) μz 1 C A (8) ( ) 90 (m; n) I(m; n) I(m; n) = P 1 f W f X f W f I f (u f ;v f ) (9) W f = jcos f j (10) I f (u f ;v f ) f (u f ;v f ) f (m; n) (μx;f(μx); μz) f ( ) (m; n) m m (m; n) I(m; n) I new(m; n). I new(m; n) = I max I(m; n) max(i(m + u; n + v); 8(u; v) 2 W ) (11) W ( ) W I max ( 255) W 3.
6 5 8 1st frame 100th frame 200th frame 6 ( ) (a) before shading removal (a) top view (b) side view 7 ( ) PC(Pentium Xeon 3.2GHz, Memory 2GB), IEEE1394 (Aplux C104T, VGA, 15fps) Tsai [19] ( ) 2m cm 200 VGA (b) after shading removal 9 ( ) 3 8 AIC [18] 5 4 ( : ) 9 (a) (b) (A) 27 ( 7.4fps) (B) 71 (C)
7 , (b) 90 1 [ : ( : )] target average maximum minimum std.dev. left side 356.1(100.0) 362.0(101.7) 349.0(98.0) 3.19(0.90) right side 353.6(100.0) 360.0(101.8) 348.0(98.4) 2.56(0.72) 10 1st frame 50th frame 100th frame 11 ( ) 2 [ : ] target average maximum minimum std.dev. left side right side VGA AIC 2 ( : ) ( ) 13 ( ) (6) 2
8 4. 1 [1] T. Wada, H. Ukida and T. Matsuyama: Shape from Shading with Interreflections Under a Proximal Light Source: Distortion-Free Copying of an Unfolded Book," Int. J. of Computer Vision, Vol. 24, No. 2, pp , [2] Z. Zhang, C. L. Tan and L. Fan: Restoration of Curved Document Images through 3D Shape Modeling," Proc. IEEE Conf. on Computer Vision and Pattern Recognition, Vol. 1, pp , [3] M. S. Brown and W. B. Seales: Document Restoration Using 3D Shape: A GeneralDeskewing Algorithm for Arbitrarily Warped Documents," Proc. Int. Conf. on Computer Vision, Vol. II, pp , [4] A. Yamashita, A. Kawarago, T. Kaneko and K. Miura: Shape Reconstruction and Image Restoration for Non-flat Surfaces of Documents with a Stereo Vision System," Proc. Int. Conf. on Pattern Recognition, Vol. 1, pp , [5] H. Cao, X. Ding and C. Liu: A Cylindrical Surface Model to Rectify the Bound Document Image," Proc. Int. Conf. on Computer Vision, Vol. 1, pp , [6] M. S. Brown and Y. C. Tsoi: Undistorting Imaged Paint Materials using Boundary Information," Proc. Asian Conf. on Computer Vision, Vol. 1, pp , [7] R. Szeliski: Image Mosaicing for Tele-Reality Applications," Proc. IEEE Workshop on Applications of Computer Vision, pp , [8] N. Chiba, H. Kano, M. Higashihara, M. Yasuda and M. Osumi: Feature-based Image Mosaicing," Proc. IAPR Workshop on Machine Vision Applications, pp. 5 10, [9] C. T. Hsu, T. H. Cheng, R. A. Beuker and J. K. Hong: Feature-based Video Mosaicing," Proc. IEEE Int. Conf. on Image Processing, Vol. II, pp , [10] U. Bhosle, S. Chaudhuri and S. D. Roy: A Fast Method for Image Mosaicing Using Geometric Hashing," IETE J. of Research, SpecialIssue on VisualMedia Processing, Vol. 48, No. 3-4, pp , [11],,,,, : ", D-II), Vol. J88-D-II, No. 8, pp , [12] P. Grattoni and M. Spertino: A Mosaicing Approach for the Acquisition and Representation of 3D Painted Surfaces for Conservation and Restoration purpose," Machine Vision and Applications, Vol. 15, No. 1, pp. 1 10, [13] W. Puech, A. G. Bors, J. M. Chassery and I. Pitas: Mosaicing of Paintings on Curved Surfaces," Proc. IEEE Workshop on Applications of Computer Vision, pp , [14] T. Sato, M. Kanbara, N. Yokoya and H. Takemura: Dense 3-D Reconstruction of an Outdoor Scene by Hundredsbaseline Stereo Using a Hand-held Video Camera," Int. J. of Computer Vision, Vol. 47, No. 1-3, pp , [15] C. Harris and M. Stephens: A Combined Corner and Edge Detector," Proc. Alvey Vision Conf., pp , [16] M. A. Fischler and R. C. Bolles: Random Sample Consensus: A Paradigm for ModelFitting with Applications to Image Analysis and Automated Cartography," Communications of the ACM, Vol. 24, No. 6, pp , [17] B. Triggs, P. McLauchlan, R. Hartley and A. Fitzgibbon: Bundle Adjustment A Modern Synthesis, pp , LNCS, Springer Verlag, [18] K. Kanatani: Geometric Information Criterion for Model Selection," Int. J. of Computer Vision, Vol. 26, No. 3, pp , [19] R. Y. Tsai: An Efficient and Accurate Camera Calibration Technique for 3D Machine Vision," Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pp , 1986.
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