THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE. 630-0192 8916-5 E-mail: {kaduya-o,takafumi-t,goshiro,uranishi,miyazaki,kato}@is.naist.jp,.,,.,,,.,,., CG.,,, Camera pose estimation by considering intrinsic parameter change due to camera zoom Kazuya OKADA, Takafumi TAKETOMI, Goshiro YAMAMOTO, Yuki URANISHI, Jun MIYAZAKI, and Hirokazu KATO Graduate School of Information Science, Nara Institute of Schience and Technology 8916-5 Takayama, ikoma, Nara, 630-0192 Japan E-mail: {kaduya-o,takafumi-t,goshiro,uranishi,miyazaki,kato}@is.naist.jp Abstract In this paper, we propose a camera pose estimation method which can deal with camera zoom. In the proposed method, the camera pose and the intrinsic camera parameters are estimated by minimizing an energy function based on the epipolar constraint. The key idea of the proposed method is how the parameterization of intrinsic camera parameters change with the zoom value. In a simulated environment, we show the effectiveness of the proposed method by quantitative evaluation of its accuracy. In addition, in the real environment, a CG object is overlaid by using the proposed method. From the result of this experiment, we confirmed that the proposed method can achieve accurate camera parameter estimation even while zooming. Key words augmented reality, zoom camera, camera pose estimation, epipolar geometry 1. CG (AR) [1][2] [3][4]. AR,., AR,,.,,.,, 1
(a) (b) (c) 1 CG Fig. 1 Example of overlaying the CG object while zooming. 1. 1(a) 1., 1(b), 1(c). 1(b), CG.,,, 1(c) CG., [3].,,,,.,,,.,,.,,.,,. 2., [5][6][10] [7][8][9].,, n PnP (Perspective n-point problem),. Bujnak [5],, 4 1. Bujanak [6],,.,,, 2 6, [7][8]. [5-8],,.,., [9].,,, AR,AR [10].,, AR., [10] AR.,,. 3.,,,., f x,f y (u,v) z, 6 1.,, 1.,. 3.1 1 K. f x 0 u K = 0 f y v (1) 0 0 1,, 2, (f x,f y,u,v).,,., K z. 2
fxz P 1 P 2 fyz uz vz 2 1 Fig. 2 Parameterization of intrinsic camera parameters by zoom value K(z) = f x(z) 0 u(z) 0 f y(z) v(z) 0 0 1 3.2 (2), E ep E z E,. C t-1 p (t-1)1 p (t-1)2 R t-1 t t-1 R t t t R t 3 Fig. 3 Epipolar geometry p t1 p t2,t,r,k t (z) 7.,,KLT(Kanade- Lucas-Tomasi) [11]. 3.4,,., z t 1,z t. C t E = E ep +we z (3),w., E ep E z. 3.3 E ep, 3 2 E ep. 2 p 1,p 2,. p T 1(K 1 1 ) T [t] RK 1 p2 = 0 (4) 2,,R, t.,[t],. 0 t z t y [t] = t z 0 t x (5) t y t x 0, tt 1 E ep. E ep = 1 n ( n i=0 (p T (t 1)i(K 1 t 1) T [t] RK 1 t p ti) 2 ) (6),n.,t 1 K t 1, 6 E z = (z t 1 z t) 2 (7),. 3.5, E Levenberg- Marquardt(LM).,t 1 K t 1 PnP.,, z t 1.,. 4.,.,, CG.,.,.,,. 4.1,Sony HDR-AX2000(640 480,,30fps, )., 1 20, 3
焦点距離 4 Fig.4 Result of measuring the focal length for each zoom value 5 Fig. 5 Result of measuring the projection center for each zoom value Zhang [12]. f x,f y, u,v 4,5. f x(z),f y(z), u(z),v(z).. f x(z) = 0.5639z 4 17.236z 3 +186.12z 2 667.06z + 1280.2 (8) f y(z) = 0.5383z 4 16.336z 3 +175.61z 2 624.29z + 1221.9 (9) u(z) = 0.4343z + 315.59 (10) v(z) = 0.5447z + 229.7 (11),.,., f x(z),f y(z),u(z),v(z). 4.2,,500mm 500mm 500mm 100., 0pixel, 1.0pixel.,, (300 ), ARtoolkit[13]. PCCPU:Corei7 2.93GHz, :4.00GB.,,. 6,7,035,. 6,7,,. 1.064mm, 2.123mm 2, 25 6.8mm., 8,9,.,., R true R est. 1 2 Rd = R truer T est 2 Rd w 3 0.0894mm, 0.126., 0.05., 0.571pixel, 1.86pixel.,. 10,11 035. 2.75mm, 5.27mm 2, 23 8.35mm., 12,13,. 2.909mm, 0.217., 0.06., 0.484pixel, 1.245pixel.,,.,. 4.3 CG, CG., CG, 1., z = 1,. CG., z = 1. 14., 14(a),, 14(b)(c)(d), 4
焦点距離 焦点距離 6 () Fig. 6 Estimation result of focal length for each frame (Dolly) 7 ( ) Fig. 7 Estimation result of projection center for each frame (Dolly) 10 () Fig.10 Estimation result of focal length for each frame (No constraint) 11 () Fig. 11 Estimation result of projection center for each frame (No constraint) 8 () Fig. 8 Error in position for each frame(dolly) 12 () Fig. 12 Error in position for each frame(no constraint) 9 () Fig.9 Error in posture for each frame (Dolly) 13 () Fig. 13 Error in posture for each frame (No constraint),,., 4,z > 14,.,,,.,,,.,RANSAC. 5
(a) t = 20 (b) t = 70 (c) t = 120 (d) t = 400 14 (, ) Fig.14 Result of overlaid virtual cube object in each frame. the CG object is overlaid using fixed intrinsic parameters(top row) and using the proposed method (bottom row). 5.,,,.,,., CG,.,,. [1],, : :,. PRMU, 103(584), pp. 1-6, 2004. [2], :, 2009, pp. 1A2-B14, 2009. [3],,,,, :,, Vol.12, No.3, 2007, pp. 343-353, 2007. [4],,, P. Julien:,, Vol.J93-A, No.11, pp. 686-696, 2010. [5] M. Bujnak, Z. Kukelova, and T. Pajdla: A general solution to the P4P problem for camera with unknown focal length, Computer Vision and Pattern Recognition 2008, pp. 1-8, 2008. [6] M. Bujnak, Z. Kukelova, and T. Pajdla: New efficient solution to the absolute pose problem for camera with unknown focal length and radial distortion, Asian Conference on Computer Vision 2010, pp. 11-24, 2010. [7] H. Stewenius, D. Nister, F. Kahl, and F. Schaffalitzky: A minimal solution for relative pose with unknown focal length, Computer Vision and Pattern Recognition 2005, pp. 789-794, 2005. [8] H. Li: A simple solution to the six-point two-view focallength problem, European Conference on Computer Vision 2006, pp. 200-213, 2006. [9], :,, pp. 1-8, 2007. [10],,,, : AR, 56, pp. 581-582, 2012. [11] J. Shi, and C. Tomasi: Good Features to Track, Proceedings of the 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 593-600, 1994. [12] Z. Zhang: A Flexible New Technique for Camera Calibration, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.22, No.11, pp. 1330-1334, 2000. [13] : ARToolKit,, PRMU, 01-232, pp. 79-86, 2002. 6