Abstract

We present a new method for measuring camera vibrations such as camera shake and shutter shock. This method successfully detects the vibration trajectory and transient waveforms from the camera image itself. We employ a time-varying pattern as the camera test chart over the conventional static pattern. This pattern is implemented using a specially developed blinking light-emitting-diode array. We describe the theoretical framework and pattern analysis of the camera image for measuring camera vibrations. Our verification experiments show that our method has a detection accuracy and sensitivity of 0.1 pixels, and is robust against image distortion. Measurement results of camera vibrations in commercial cameras are also demonstrated.

© 2017 Optical Society of America

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References

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    [Crossref]

2014 (1)

2013 (2)

B. Ferrer, J. Espinosa, A. B. Roig, J. Perez, and D. Mas, “Vibration frequency measurement using a local multithreshold technique,” Opt. Express 21(22), 26198–26208 (2013).
[Crossref] [PubMed]

N. Aoki, H. Kusaka, and H. Otsuka, “Measurement and description method for image stabilization performance of digital cameras,” Proc. SPIE 8659, 86590O (2013).
[Crossref]

2011 (2)

S. C. Shin, W.-S. Ohm, S.-M. Kim, and S. Kang, “A method for evaluation of an optical image stabilizer in an image sensor module,” Int. J. Precis. Eng. Manuf. 12(2), 367–370 (2011).
[Crossref]

H. S. Choi, J. H. Cheung, S. H. Kim, and J. H. Ahn, “Structural dynamic displacement vision system using digital image processing,” NDT Int. 44(7), 597–608 (2011).
[Crossref]

2010 (3)

H.-S. Jeon, Y.-C. Choi, J.-H. Park, and J. W. Park, “Multi-point measurement of structural vibration using pattern recognition from camera image,” Nucl. Eng. Technol. 42(6), 704–711 (2010).
[Crossref]

N. Joshi, S. B. Kang, C. L. Zitnick, and R. Szeliski, “Image deblurring using inertial measurement sensors,” ACM Trans. Graphics 29(4), 30 (2010).

K. Yue, Z. Li, M. Zhang, and S. Chen, “Transient full-field vibration measurement using spectroscopical stereo photogrammetry,” Opt. Express 18(26), 26866–26871 (2010).
[Crossref] [PubMed]

2009 (1)

R. Safaee-Rad and M. Aleksic, “Handshake characterization and image stabilization for cell-phone cameras,” Proc. SPIE 7241, 72410V (2009).
[Crossref]

2008 (1)

2007 (1)

B. Golik and D. Wueller, “Measurement method for image stabilizing systems,” Proc. SPIE 6502, 65020O (2007).
[Crossref]

2006 (1)

J. J. Lee and M. Shinozuka, “A vision-based system for remote sensing of bridge displacement,” NDT Int. 39(5), 425–431 (2006).
[Crossref]

2004 (1)

M. Ben-Ezra and S. K. Nayar, “Motion-based motion deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 689–698 (2004).
[Crossref] [PubMed]

2003 (2)

A. M. Wahbeh, J. P. Caffrey, and S. F. Masri, “A vision-based approach for the direct measurement of displacements in vibrating systems,” Smart Mater. Struct. 12(5), 785–794 (2003).
[Crossref]

P. Xu, Q. Hao, C. Huang, and Y. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35(7), 547–552 (2003).
[Crossref]

1993 (1)

K. Sato, S. Ishizuka, A. Nikami, and M. Sato, “Control techniques for optical image stabilizing system,” IEEE Trans. Consum. Electron. 39(3), 461–466 (1993).
[Crossref]

1983 (1)

H. Kondo, H. Imazeki, and T. Tsuruta, “Measurement of image blur due to intrinsic vibration of the camera body by applying speckle photography,” J. Appl. Photogr. Eng. 9(5), 138–142 (1983).

1978 (1)

S. Ueha, N. Magome, and J. Tsujiuchi, “Comments on speckle interferometry with regard to displacements of the camera during an exposure,” Opt. Commun. 27(3), 324–326 (1978).
[Crossref]

1965 (1)

1964 (1)

Y. Yeh and H. Z. Cummins, “Localized fluid flow measurements with an He–Ne laser spectrometer,” Appl. Phys. Lett. 4(10), 176–178 (1964).
[Crossref]

Ahn, J. H.

H. S. Choi, J. H. Cheung, S. H. Kim, and J. H. Ahn, “Structural dynamic displacement vision system using digital image processing,” NDT Int. 44(7), 597–608 (2011).
[Crossref]

Aleksic, M.

R. Safaee-Rad and M. Aleksic, “Handshake characterization and image stabilization for cell-phone cameras,” Proc. SPIE 7241, 72410V (2009).
[Crossref]

Aoki, N.

N. Aoki, H. Kusaka, and H. Otsuka, “Measurement and description method for image stabilization performance of digital cameras,” Proc. SPIE 8659, 86590O (2013).
[Crossref]

Ben-Ezra, M.

M. Ben-Ezra and S. K. Nayar, “Motion-based motion deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 689–698 (2004).
[Crossref] [PubMed]

Caffrey, J. P.

A. M. Wahbeh, J. P. Caffrey, and S. F. Masri, “A vision-based approach for the direct measurement of displacements in vibrating systems,” Smart Mater. Struct. 12(5), 785–794 (2003).
[Crossref]

Chen, S.

K. Yue, Z. Li, M. Zhang, and S. Chen, “Transient full-field vibration measurement using spectroscopical stereo photogrammetry,” Opt. Express 18(26), 26866–26871 (2010).
[Crossref] [PubMed]

E. Kee, S. Paris, S. Chen, and J. Wang, “Modeling and removing spatially-varying optical blur,” in Proceedings of IEEE Conference on Computational Photography (IEEE, 2011), pp. 1–8.

Cheung, J. H.

H. S. Choi, J. H. Cheung, S. H. Kim, and J. H. Ahn, “Structural dynamic displacement vision system using digital image processing,” NDT Int. 44(7), 597–608 (2011).
[Crossref]

Choi, H.

Choi, H. S.

H. S. Choi, J. H. Cheung, S. H. Kim, and J. H. Ahn, “Structural dynamic displacement vision system using digital image processing,” NDT Int. 44(7), 597–608 (2011).
[Crossref]

Choi, Y.-C.

H.-S. Jeon, Y.-C. Choi, J.-H. Park, and J. W. Park, “Multi-point measurement of structural vibration using pattern recognition from camera image,” Nucl. Eng. Technol. 42(6), 704–711 (2010).
[Crossref]

Cummins, H. Z.

Y. Yeh and H. Z. Cummins, “Localized fluid flow measurements with an He–Ne laser spectrometer,” Appl. Phys. Lett. 4(10), 176–178 (1964).
[Crossref]

Espinosa, J.

Farrell, J.

F. Xiao, A. Silverstein, and J. Farrell, “Camera-motion and effective spatial resolution,” in Proceedings of International Congress of Imaging Science (Society for Imaging Science and Technology, 2006), pp. 33–36.

Ferrer, B.

Golik, B.

B. Golik and D. Wueller, “Measurement method for image stabilizing systems,” Proc. SPIE 6502, 65020O (2007).
[Crossref]

Hao, Q.

P. Xu, Q. Hao, C. Huang, and Y. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35(7), 547–552 (2003).
[Crossref]

Hashi, H.

K. Hayashi, M. Tanaka, H. Kusaka, and H. Hashi, “New approach on multi-axial analysis of camera shake,” in Proceedings of IEEE Conference on Consumer Electronics (IEEE, 2010), pp. 39–40.
[Crossref]

Hayashi, K.

K. Hayashi, M. Tanaka, H. Kusaka, and H. Hashi, “New approach on multi-axial analysis of camera shake,” in Proceedings of IEEE Conference on Consumer Electronics (IEEE, 2010), pp. 39–40.
[Crossref]

Hayashi, S.

Huang, C.

P. Xu, Q. Hao, C. Huang, and Y. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35(7), 547–552 (2003).
[Crossref]

Imazeki, H.

H. Kondo, H. Imazeki, and T. Tsuruta, “Measurement of image blur due to intrinsic vibration of the camera body by applying speckle photography,” J. Appl. Photogr. Eng. 9(5), 138–142 (1983).

Ishizuka, S.

K. Sato, S. Ishizuka, A. Nikami, and M. Sato, “Control techniques for optical image stabilizing system,” IEEE Trans. Consum. Electron. 39(3), 461–466 (1993).
[Crossref]

Jeon, H.-S.

H.-S. Jeon, Y.-C. Choi, J.-H. Park, and J. W. Park, “Multi-point measurement of structural vibration using pattern recognition from camera image,” Nucl. Eng. Technol. 42(6), 704–711 (2010).
[Crossref]

Joshi, N.

N. Joshi, S. B. Kang, C. L. Zitnick, and R. Szeliski, “Image deblurring using inertial measurement sensors,” ACM Trans. Graphics 29(4), 30 (2010).

Kang, S.

S. C. Shin, W.-S. Ohm, S.-M. Kim, and S. Kang, “A method for evaluation of an optical image stabilizer in an image sensor module,” Int. J. Precis. Eng. Manuf. 12(2), 367–370 (2011).
[Crossref]

Kang, S. B.

N. Joshi, S. B. Kang, C. L. Zitnick, and R. Szeliski, “Image deblurring using inertial measurement sensors,” ACM Trans. Graphics 29(4), 30 (2010).

Kee, E.

E. Kee, S. Paris, S. Chen, and J. Wang, “Modeling and removing spatially-varying optical blur,” in Proceedings of IEEE Conference on Computational Photography (IEEE, 2011), pp. 1–8.

Kim, J.-P.

Kim, S. H.

H. S. Choi, J. H. Cheung, S. H. Kim, and J. H. Ahn, “Structural dynamic displacement vision system using digital image processing,” NDT Int. 44(7), 597–608 (2011).
[Crossref]

Kim, S.-M.

S. C. Shin, W.-S. Ohm, S.-M. Kim, and S. Kang, “A method for evaluation of an optical image stabilizer in an image sensor module,” Int. J. Precis. Eng. Manuf. 12(2), 367–370 (2011).
[Crossref]

Kim, W.-C.

Kondo, H.

H. Kondo, H. Imazeki, and T. Tsuruta, “Measurement of image blur due to intrinsic vibration of the camera body by applying speckle photography,” J. Appl. Photogr. Eng. 9(5), 138–142 (1983).

Kusaka, H.

N. Aoki, H. Kusaka, and H. Otsuka, “Measurement and description method for image stabilization performance of digital cameras,” Proc. SPIE 8659, 86590O (2013).
[Crossref]

K. Hayashi, M. Tanaka, H. Kusaka, and H. Hashi, “New approach on multi-axial analysis of camera shake,” in Proceedings of IEEE Conference on Consumer Electronics (IEEE, 2010), pp. 39–40.
[Crossref]

Lee, J. J.

J. J. Lee and M. Shinozuka, “A vision-based system for remote sensing of bridge displacement,” NDT Int. 39(5), 425–431 (2006).
[Crossref]

Li, Z.

Magome, N.

S. Ueha, N. Magome, and J. Tsujiuchi, “Comments on speckle interferometry with regard to displacements of the camera during an exposure,” Opt. Commun. 27(3), 324–326 (1978).
[Crossref]

Mas, D.

Masri, S. F.

A. M. Wahbeh, J. P. Caffrey, and S. F. Masri, “A vision-based approach for the direct measurement of displacements in vibrating systems,” Smart Mater. Struct. 12(5), 785–794 (2003).
[Crossref]

Nayar, S. K.

M. Ben-Ezra and S. K. Nayar, “Motion-based motion deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 689–698 (2004).
[Crossref] [PubMed]

Nikami, A.

K. Sato, S. Ishizuka, A. Nikami, and M. Sato, “Control techniques for optical image stabilizing system,” IEEE Trans. Consum. Electron. 39(3), 461–466 (1993).
[Crossref]

Nishi, K.

K. Nishi and R. Ogino, “3D camera-shake measurement and analysis,” in Proceedings of IEEE Conference on Multimedia and Expo (IEEE, 2007), pp. 1271–1274.

K. Nishi and T. Onda, “Evaluation system for camera shake and image stabilizers,” in Proceedings of IEEE Conference on Multimedia and Expo (IEEE, 2010), pp. 926–931.
[Crossref]

Ogihara, S.

Ogino, R.

K. Nishi and R. Ogino, “3D camera-shake measurement and analysis,” in Proceedings of IEEE Conference on Multimedia and Expo (IEEE, 2007), pp. 1271–1274.

Ohm, W.-S.

S. C. Shin, W.-S. Ohm, S.-M. Kim, and S. Kang, “A method for evaluation of an optical image stabilizer in an image sensor module,” Int. J. Precis. Eng. Manuf. 12(2), 367–370 (2011).
[Crossref]

Onda, T.

K. Nishi and T. Onda, “Evaluation system for camera shake and image stabilizers,” in Proceedings of IEEE Conference on Multimedia and Expo (IEEE, 2010), pp. 926–931.
[Crossref]

Otsuka, H.

N. Aoki, H. Kusaka, and H. Otsuka, “Measurement and description method for image stabilization performance of digital cameras,” Proc. SPIE 8659, 86590O (2013).
[Crossref]

Paris, S.

E. Kee, S. Paris, S. Chen, and J. Wang, “Modeling and removing spatially-varying optical blur,” in Proceedings of IEEE Conference on Computational Photography (IEEE, 2011), pp. 1–8.

Park, J. W.

H.-S. Jeon, Y.-C. Choi, J.-H. Park, and J. W. Park, “Multi-point measurement of structural vibration using pattern recognition from camera image,” Nucl. Eng. Technol. 42(6), 704–711 (2010).
[Crossref]

Park, J.-H.

H.-S. Jeon, Y.-C. Choi, J.-H. Park, and J. W. Park, “Multi-point measurement of structural vibration using pattern recognition from camera image,” Nucl. Eng. Technol. 42(6), 704–711 (2010).
[Crossref]

Park, K.-S.

Park, N.-C.

Park, Y.-P.

Perez, J.

Powell, R. L.

Ri, S.

Roig, A. B.

Safaee-Rad, R.

R. Safaee-Rad and M. Aleksic, “Handshake characterization and image stabilization for cell-phone cameras,” Proc. SPIE 7241, 72410V (2009).
[Crossref]

Sato, K.

K. Sato, S. Ishizuka, A. Nikami, and M. Sato, “Control techniques for optical image stabilizing system,” IEEE Trans. Consum. Electron. 39(3), 461–466 (1993).
[Crossref]

Sato, M.

K. Sato, S. Ishizuka, A. Nikami, and M. Sato, “Control techniques for optical image stabilizing system,” IEEE Trans. Consum. Electron. 39(3), 461–466 (1993).
[Crossref]

Shin, S. C.

S. C. Shin, W.-S. Ohm, S.-M. Kim, and S. Kang, “A method for evaluation of an optical image stabilizer in an image sensor module,” Int. J. Precis. Eng. Manuf. 12(2), 367–370 (2011).
[Crossref]

Shinozuka, M.

J. J. Lee and M. Shinozuka, “A vision-based system for remote sensing of bridge displacement,” NDT Int. 39(5), 425–431 (2006).
[Crossref]

Silverstein, A.

F. Xiao, A. Silverstein, and J. Farrell, “Camera-motion and effective spatial resolution,” in Proceedings of International Congress of Imaging Science (Society for Imaging Science and Technology, 2006), pp. 33–36.

Song, M.-G.

Stetson, K. A.

Szeliski, R.

N. Joshi, S. B. Kang, C. L. Zitnick, and R. Szeliski, “Image deblurring using inertial measurement sensors,” ACM Trans. Graphics 29(4), 30 (2010).

Tanaka, M.

K. Hayashi, M. Tanaka, H. Kusaka, and H. Hashi, “New approach on multi-axial analysis of camera shake,” in Proceedings of IEEE Conference on Consumer Electronics (IEEE, 2010), pp. 39–40.
[Crossref]

Tsuda, H.

Tsujiuchi, J.

S. Ueha, N. Magome, and J. Tsujiuchi, “Comments on speckle interferometry with regard to displacements of the camera during an exposure,” Opt. Commun. 27(3), 324–326 (1978).
[Crossref]

Tsuruta, T.

H. Kondo, H. Imazeki, and T. Tsuruta, “Measurement of image blur due to intrinsic vibration of the camera body by applying speckle photography,” J. Appl. Photogr. Eng. 9(5), 138–142 (1983).

Ueha, S.

S. Ueha, N. Magome, and J. Tsujiuchi, “Comments on speckle interferometry with regard to displacements of the camera during an exposure,” Opt. Commun. 27(3), 324–326 (1978).
[Crossref]

Wahbeh, A. M.

A. M. Wahbeh, J. P. Caffrey, and S. F. Masri, “A vision-based approach for the direct measurement of displacements in vibrating systems,” Smart Mater. Struct. 12(5), 785–794 (2003).
[Crossref]

Wang, J.

E. Kee, S. Paris, S. Chen, and J. Wang, “Modeling and removing spatially-varying optical blur,” in Proceedings of IEEE Conference on Computational Photography (IEEE, 2011), pp. 1–8.

Wang, Y.

P. Xu, Q. Hao, C. Huang, and Y. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35(7), 547–552 (2003).
[Crossref]

Wueller, D.

B. Golik and D. Wueller, “Measurement method for image stabilizing systems,” Proc. SPIE 6502, 65020O (2007).
[Crossref]

Xiao, F.

F. Xiao, A. Silverstein, and J. Farrell, “Camera-motion and effective spatial resolution,” in Proceedings of International Congress of Imaging Science (Society for Imaging Science and Technology, 2006), pp. 33–36.

Xu, P.

P. Xu, Q. Hao, C. Huang, and Y. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35(7), 547–552 (2003).
[Crossref]

Yeh, Y.

Y. Yeh and H. Z. Cummins, “Localized fluid flow measurements with an He–Ne laser spectrometer,” Appl. Phys. Lett. 4(10), 176–178 (1964).
[Crossref]

Yue, K.

Zhang, M.

Zitnick, C. L.

N. Joshi, S. B. Kang, C. L. Zitnick, and R. Szeliski, “Image deblurring using inertial measurement sensors,” ACM Trans. Graphics 29(4), 30 (2010).

ACM Trans. Graphics (1)

N. Joshi, S. B. Kang, C. L. Zitnick, and R. Szeliski, “Image deblurring using inertial measurement sensors,” ACM Trans. Graphics 29(4), 30 (2010).

Appl. Phys. Lett. (1)

Y. Yeh and H. Z. Cummins, “Localized fluid flow measurements with an He–Ne laser spectrometer,” Appl. Phys. Lett. 4(10), 176–178 (1964).
[Crossref]

IEEE Trans. Consum. Electron. (1)

K. Sato, S. Ishizuka, A. Nikami, and M. Sato, “Control techniques for optical image stabilizing system,” IEEE Trans. Consum. Electron. 39(3), 461–466 (1993).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

M. Ben-Ezra and S. K. Nayar, “Motion-based motion deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 689–698 (2004).
[Crossref] [PubMed]

Int. J. Precis. Eng. Manuf. (1)

S. C. Shin, W.-S. Ohm, S.-M. Kim, and S. Kang, “A method for evaluation of an optical image stabilizer in an image sensor module,” Int. J. Precis. Eng. Manuf. 12(2), 367–370 (2011).
[Crossref]

J. Appl. Photogr. Eng. (1)

H. Kondo, H. Imazeki, and T. Tsuruta, “Measurement of image blur due to intrinsic vibration of the camera body by applying speckle photography,” J. Appl. Photogr. Eng. 9(5), 138–142 (1983).

J. Opt. Soc. Am. (1)

NDT Int. (2)

H. S. Choi, J. H. Cheung, S. H. Kim, and J. H. Ahn, “Structural dynamic displacement vision system using digital image processing,” NDT Int. 44(7), 597–608 (2011).
[Crossref]

J. J. Lee and M. Shinozuka, “A vision-based system for remote sensing of bridge displacement,” NDT Int. 39(5), 425–431 (2006).
[Crossref]

Nucl. Eng. Technol. (1)

H.-S. Jeon, Y.-C. Choi, J.-H. Park, and J. W. Park, “Multi-point measurement of structural vibration using pattern recognition from camera image,” Nucl. Eng. Technol. 42(6), 704–711 (2010).
[Crossref]

Opt. Commun. (1)

S. Ueha, N. Magome, and J. Tsujiuchi, “Comments on speckle interferometry with regard to displacements of the camera during an exposure,” Opt. Commun. 27(3), 324–326 (1978).
[Crossref]

Opt. Express (4)

Opt. Laser Technol. (1)

P. Xu, Q. Hao, C. Huang, and Y. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35(7), 547–552 (2003).
[Crossref]

Proc. SPIE (3)

B. Golik and D. Wueller, “Measurement method for image stabilizing systems,” Proc. SPIE 6502, 65020O (2007).
[Crossref]

R. Safaee-Rad and M. Aleksic, “Handshake characterization and image stabilization for cell-phone cameras,” Proc. SPIE 7241, 72410V (2009).
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[Crossref]

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E. Kee, S. Paris, S. Chen, and J. Wang, “Modeling and removing spatially-varying optical blur,” in Proceedings of IEEE Conference on Computational Photography (IEEE, 2011), pp. 1–8.

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[Crossref]

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[Crossref]

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Figures (20)

Fig. 1
Fig. 1 Blurring process due to camera vibrations. A lattice pattern is used as an example test chart. For simplicity, the camera image is assumed to have the same scale as the test chart.
Fig. 2
Fig. 2 Geometric relationship between test chart and camera. (a) Front position. (b) Skewed position. For simplicity, horizontal and vertical displacements are omitted.
Fig. 3
Fig. 3 Relationship between test chart and camera image. (a) Case of time-varying pattern (N = 4, M = 3). For simplicity, each frame is color-coded. (b) Case of conventional static pattern. A closely aligned lattice pattern is used for the test chart.
Fig. 4
Fig. 4 Detection of rotational and translational displacements caused by camera vibrations. Each frame can be separated from the camera image, and the displacements can be estimated by comparison with the corresponding frame of the original test chart (N = 4, M = 3).
Fig. 5
Fig. 5 Acquisition of the reference pattern. The lattice pattern including all partial lattices is displayed simultaneously just for a moment when any vibration diminishes sufficiently after the shutter opens. The reference pattern can be cropped from the camera image.
Fig. 6
Fig. 6 Determination of lattice point positions and grouping. (a) Accumulated lattice pattern (N = 4, M = 3). (b) One of lattice points in the actual camera image. The exact circle with smooth contour (green circles) is fitted into the rough-edged circle (gray scale image) and the center point (red cross line) is aligned on it. (c) Extracted exact circles. (d) Estimated lattice point positions. (e) Grouping into partial lattices. Each partial lattice is color-coded. The displacements of lattice points are smaller than distances with the neighboring points and have no impact on grouping.
Fig. 7
Fig. 7 Geometric relationship between the displaced partial lattice pattern and the reference one at the n-th frame (M = 3). The displacement d x,n , d y,n , θ r,n can be calculated from the displaced lattice points and the reference ones by the least-square estimation.
Fig. 8
Fig. 8 (a) Customized light-emitting diode (LED) display developed in association with Tani Electronics Corporation. (b) Example of the captured image without being subject to vibrations. Each green circle indicates one partial lattice comprising a 3×3 LED array. Red circles indicate blank spaces. The shutter closing and opening time can be determined from the fore-and-aft position of the blank space. In this example, the blank space is equivalent to two partial lattices.
Fig. 9
Fig. 9 (a) Vibration exciter (Kohzu Precision Co., Ltd.) for verification of large motions. (b) Vibration exciter (Sigmakoki Co., Ltd.) for verification of small motions.
Fig. 10
Fig. 10 Verification using large vibrations. (a) Example of the captured image under circular motion applied along the yaw and pitch axes. (b) Applied circular motion and path detected by the previous method. (c) Path detected by the current method. (d) Applied sinusoidal motion along the roll axis and path detected by the current method.
Fig. 11
Fig. 11 Limitation on vibration amplitude. (a) Relationship between vibration amplitudes and detection success rates. (b) Captured image of the LED display in the case of detection failure.
Fig. 12
Fig. 12 Verification using small vibrations. (a) Comparison of applied sinusoidal vertical vibration with amplitude of 0.68 pixels and frequency of 5 Hz and detected vibration. (b) Spectrum distribution of vibrations depicted in (a). (c) Comparison of applied sinusoidal vertical vibration with amplitude of 0.14 pixels and frequency of 5 Hz and detected vibration. (d) Spectrum distribution of (c).
Fig. 13
Fig. 13 Comparison of estimation error in various vibration amplitudes. The estimation error means the root-mean-square deviation between the true displacement and the detected one. The blue crosses and red circles indicate the calculated results by the previous method and the current one, respectively.
Fig. 14
Fig. 14 Relationship between pattern contrast and estimation error. When the pattern contrast is lower than about 9, the detection fails.
Fig. 15
Fig. 15 Portions of LED array images cropped out from camera images. (a) One of the detection failure cases. (b) One of the high contrast images that leads to a lower estimation error. Each value of pattern contrasts is indicated in Fig. 14.
Fig. 16
Fig. 16 Detection of camera shakes. (a) Example of the detected trajectory. (b) Cumulative distribution of 10 trajectories plotted together in the same graph. Each starting point is located at the origin. The red-dotted sequence corresponds to the trajectory in (a).
Fig. 17
Fig. 17 Detection of residual vibrations from image stabilizer. (a) Example of the detected trajectory. It is to be noted that the scale of each axis is reduced by a factor of 1/5 when compared to the axes values indicated in Fig. 16(a). (b) Cumulative distribution of 10 trajectories plotted together in the same graph. The red sections correspond to the result shown in (a).
Fig. 18
Fig. 18 Detection of mirror slaps. (a) Vibration waveform along the vertical axis. (b) Spectrum distribution of (a). (c) Vibration waveform along the horizontal axis. (b) Spectrum distribution of (c).
Fig. 19
Fig. 19 Detection of shutter shocks. (a) Vibration waveform along the vertical axis. (b) Spectrum distribution of (a). (c) Vibration waveform along the horizontal axis. (d) Spectrum distribution of (c).
Fig. 20
Fig. 20 Comparison of estimation error for the case of the slanted test chart. The test chart is slanted by about 2° toward the image sensor.

Equations (15)

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x= 0 ( R x 0 d ),whereR=[ 1 θ r θ r 1 ],d=[ d x d y ]=[ t x + 0 θ y t y + 0 θ p ].
f( x 0 )=f( R 1 (t)( 0 x+d(t) ) ), where R 1 (t)=[ 1 θ r (t) θ r (t) 1 ],d(t)=[ d x (t) d y (t) ]=[ t x (t)+ 0 θ y (t) t y (t)+ 0 θ p (t) ]
g(x)= 0 T s f( R 1 (t)( 0 x+d(t) ) )dt .
f( x 0 ,t)= n=1 N f( x 0 ,nΔT )δ(tnΔT) .
g(x)= 0 T s n=1 N f( R 1 (t)( 0 x+d(t) ),nΔT )δ(tnΔT) dt = n=1 N f( R 1 (nΔT)( 0 x+d(nΔT) ),nΔT ) .
[ x m,n y m,n ]=[ 1 θ r,n θ r,n 1 ][ x m,n r y m,n r ][ d x,n d y,n ],
v=Au,wherev=[ x 1,n x 1,n r y 1,n y 1,n r x M 2 ,n x M 2 ,n r y M 2 ,n y M 2 ,n r ],A=[ 1 0 y 1,n r 0 1 x 1,n r 1 0 y M 2 ,n r 0 1 x M 2 ,n r ],u=[ d x,n d y,n θ r,n ].
u ^ = argmin u R 3 vAu 2
u ^ = ( A T A) 1 A T v.
s R θys R θps R θrs [ x t xs y t ys ]= R θy R θp R θr [ x 0 t x y 0 t y 0 ]
x= 0 ( R s x 0 d s ), where R s =[ 1 θ r + θ rs θ r θ rs 1 ], d s =[ d xs d ys ]=[ t x 0 t xs + 0 ( θ y θ ys ) t y 0 t ys + 0 ( θ p θ ps ) ].
s[ x y ]=[ x 0 y 0 0 ],
s[ x y ]= R θy R θp R θr [ x 0 t x y 0 t y 0 ],
s[ x y ]=[ 1 θ r θ y θ r 1 θ p θ y θ p 1 ][ x 0 t x y 0 t y 0 ]
x= 0 ( R x 0 d 1 0 x 0 [ θ y θ p ] x 0 ), wherex=[ x y ], x 0 =[ x 0 y 0 ],R=[ 1 θ r θ r 1 ],d=[ d x d y ]=[ t x + 0 θ y t y + 0 θ p ].

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