(bundle adjustment) 8),9) ),6),7) GPS 8),9) GPS GPS 8) GPS GPS GPS GPS Anai 9) GPS GPS GPS GPS GPS GPS GPS Maier ) GPS GPS Anai 9) GPS GPS M GPS M inf

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1 GPS GPS solve this problem, we propose ()novel model about GPS positioning which enables more robust estimation with extended bundle adjustment, and ()outlier removal for GPS positioning using video information. Concretely, we have employed a simple assumption that true GPS position exists within a certain range from the observed GPS position and the size of the range depends on the GPS positioning confidence. The proposed method estimates camera parameters by minimizing an energy function that is defined by using the reprojection error and the penalty term for GPS positioning. Additionally, outliers are removed by checking the consistency between vision and GPS information. GPS GPS GPS GPS ( ) () GPS () GPS GPS GPS GPS GPS GPS GPS Extrinsic Camera Parameter Estimation Using Video Images and GPS Considering GPS Positioning Confidence and Outlier Hideyuki Kume, Takafumi Taketomi, Tomokazu Sato and Naokazu Yokoya This report proposes a method for estimating extrinsic camera parameters using video images and temporally sparse position data acquired by GPS. In conventional methods, the accuracy of estimated camera position largely depends on the confidence of GPS positioning data because they implicitly assume that GPS position error is very small or normally distributed. In order to. ) Structure from Motion ) Visual SLAM 3) GPS ),4) 9) 4),5) 4) 5) GPS ),6) 9) GPS GPS GPS ),6),7) Graduate School of Information Science, Nara Institute of Science and Technology c Information Processing Society of Japan

2 (bundle adjustment) 8),9) ),6),7) GPS 8),9) GPS GPS 8) GPS GPS GPS GPS Anai 9) GPS GPS GPS GPS GPS GPS GPS Maier ) GPS GPS Anai 9) GPS GPS M GPS M influence function GPS 8),9) GPS GPS GPS GPS GPS (RTK-fix RTK-float ) GPS GPS GPS GPS 3 4. GPS GPS GPS GPS GPS GPS GPS 8),9) GPS (A) (B) 4) ( f ) GPS (GPS G f ) GPS GPS (C) (A) (C) (D) GPS (C) (D) c Information Processing Society of Japan

3 Fig. (A) 特徴点の追跡によるカメラ位置 姿勢の推定 (B) 特徴点の三次元位置の推定, 追加 削除 f G Y N (C)GPS 測位の外れ値を考慮した GPS 測位値を用いた狭区間最適化 (C-)GPS 測位値を用いた狭区間最適化 (C-3)GPS 測位の外れ値の判定, 除外 外れ値か N f 回目の繰り返し (C-) 再投影誤差の平均, 標準偏差の計算 Y (D)GPS 測位値を用いた全体最適化 Flow diagram of the proposed method.. GPS GPS E i Φ i GPS Ψ i E = Φ i + Ψ i () i F i G F G GPS Φ i GPS Ψ i.. Φ i Φ i = µ j(q ij ˆq ij) () P i j P i P i i q ij i j ˆq ij j µ j j j (w m) w 4) µ j = s j = m + ( w i=w m (q ij ˆq ij ) ) s j j.. GPS 8),9) GPS GPS 8) ˆΨ i = ω(m i g i d) (4) 9) ˆΨ i = ω τ (Migi d) (5) M i i GPS d GPS g i i GPS GPS ω Φ i τ GPS GPS RMS GPS GPS GPS GPS GPS (RTK-fix RTK-float ) GPS GPS GPS Ψ i (3) 3 c Information Processing Society of Japan

4 x i y i z i Ψ i = GPS 測地座標系 z ( 鉛直上 ) ( 東 ) y x GPS 測地座標系におけるGPS 測位位置 : g i ( 南 ) h( p) r( p) M i カメラ座標系 カメラ座標系におけるGPS 受信機の位置 : GPS 受信機の推定位置 M d i g i GPS 測位位置 GPS Fig. Penalty for GPS positioning. ( ) n ( ) n x r(p) i + yi + h(p) z i (6) = M i d g i (7) M i i GPS r h / p GPS n n GPS Ψ i Ψ i 8),9) Φ i Ψ i GPS GPS (DGPS RTK- GPS) RTK-GPS (RTK-fix RTK-float) DOP GPS RTK-GPS (RTK-fix RTK-float) d p p r(p), h(p) GPS. GPS GPS.. GPS GPS (C) (D) (A) (B) (A) (B) ( ) ( ) (D) (C) (f l) ( f ) () E GPS (D) (A) (C) E.. GPS GPS GPS (C) ( f ) GPS GPS Φ f GPS GPS GPS GPS Φ f, σ f (C-) 4 c Information Processing Society of Japan

5 Φ f = Φ i (8) G f i G f σ f = (Φ i G f Φ f ) (9) i G f G f = {i G f l i < f} () G f f GPS (C-) (C-3) Φ f > Φ f + σ f () G f Anai 9) GPS M 3. RTK-GPS GPS.. 3. GPS GPS (6) p r(p), h(p) GPS p RTK-GPS (RTK-fix RTK-float) 3.. RTK-GPS (TOPCON GR-3 ±mm, ±5mm) 5 GPS Hz RTK-GPS RTK Fig. 3 (a) RTK-fix (b) RTK-float 3 GPS Distribution of GPS positions in the fixed-point observation 3.. GPS RTK-fix GPS RTK-GPS 3 (a) (b) 5% 3 GPS GPS.. (b) r(p) h(p) GPS r(p), h(p) [mm] Table Maximum errors for each solution type [mm]. (a) (b) RTK-fix RTK-float c Information Processing Society of Japan

6 (a) (b) - 4 RTK-float Fig. 4 Trace of the moving average in RTK-float () GPS GPS.5 (b).5 37mm 5mm 3..3 GPS GPS 4 RTK-float 3 GPS 3 m 3. GPS 3.. (Sony VCL-HG758) (Sony DSR- 5fps 4 km.5 37mm 5 cm.5 5mm PD-5) 7m ( fps ) RTK-GPS (TOPCON GR-3) GPS GPS RTK-fix GPS (TOPCON Tools) GPS RTK-float GPS GPS d GPS (4) (5) GPS ω = 8 (6) n = 7, l = GPS A: GPS B: GPS GPS 8) C: GPS GPS 9) D: ( ) E: ( ) B,C A GPS 3 B C 3..3 GPS GPS c Information Processing Society of Japan

7 (a) (b) A 5 GPS ( ) Fig. 5 Estimated GPS positions (horizontal) f f Φ f () Φ f + σ f 7 GPS 8 8 A C A 5 6 B RTK-float B GPS GPS GPS ( ) Fig. 6 Estimated GPS positions (altitude) Fig. 7 7 Reprojection errors for each frame. C ( E) GPS B RTK-float RTK-float RTK-fix C RTK-float RTK-float 4 RTK-float 5% t 7 c Information Processing Society of Japan

8 Fig. 8 Position errors for each frame. Table [mm] Comparison of position errors [mm]. A B C E C 4. GPS GPS GPS GPS GPS GPS GPS GPS GPS GPS ( (A) No.96) (SCOPE) ) Pollefeys, M., Nistér, D., Frahm, J., Akbarzadeh, A., Mordohai, P., Clipp, B., Engels, C., Gallup, D., Kim, S., Merrell, P. et al.: Detailed real-time urban 3D reconstruction from video, Int. J. of Computer Vision, Vol.78, No.-3, pp (8). ) Pollefeys, M., VanGool, L., Vergauwen, M., Verbiest, F., Cornelis, K., Tops, J. and Koch, R.: Visual Modeling with a Hand-Held Camera, Int. J. of Computer Vision, Vol.59, No.3, pp.7 3 (4). 3) Klein, G. and Murray, D.: Parallel Tracking and Mapping for Small AR Workspaces, Proc. Int. Symp. on Mixed and Augmented Reality, pp.5 34 (7). 4) (D-II) Vol.J86-D-II, No., pp (3). 5) Bleser, G., Wuest, H. and Stricker, D.: Online camera pose estimation in partially known and dynamic scenes, Proc. Int. Symp. on Mixed and Augmented Reality, pp (6). 6) Agrawal, M. and Konolige, K.: Real-time localization in outdoor environments using stereo vision and inexpensive GPS, Proc. Int. Conf. on Pattern Recognition, Vol.3, pp (6). 7) Schleicher, D., Bergasa, L. M., Ocana, M., Barea, R. and Lopez, E.: Real-time hierarchical GPS aided visual SLAM on urban environments, Proc. Int. Conf. on Robotics and Automation, pp (9). 8) GPS : Vol.47, No.SIG5(CVIM3), pp (6). 9) Anai, T., Fukaya, N., Sato, T., Yokoya, N. and Kochi, N.: Exterior orientation method for video image sequences with considering RTK-GPS accuracy, Proc. Int. Conf. on Optical 3-D Measurement Techniques, Vol.I, pp.3 4 (9). ) Maier, D. and Kleiner, A.: Improved GPS Sensor Model for Mobile Robots in Urban Terrain, Proc. Int. Conf. on Robotics and Automation, pp (). 8 c Information Processing Society of Japan