## Real-time image stabilization for arbitrary motion blurred image based on opto-electronic hybrid joint transform correlator |

Optics Express, Vol. 19, Issue 11, pp. 10762-10768 (2011)

http://dx.doi.org/10.1364/OE.19.010762

Acrobat PDF (911 KB)

### Abstract

An efficient approach was put forward to keep real-time image stabilization based on opto-electronic hybrid processing, by which image motion vector can be effectively detected and point spread function (PSF) was accurately modeled instantaneously, it will alleviate greatly the complexity of image restoration algorithm. The approach applies to arbitrary motion blurred images. We have also constructed an image stabilization measurement system. The experimental results show that the proposed method has advantages of real time and preferable effect.

© 2011 OSA

## 1. Introduction

1. Y. Yitzhaky, I. Mor, A. Lantzman, and N. S. Kopeika, “Direct method for restoration of motion-blurred images,” J. Opt. Soc. Am. A **15**(6), 1512–1519 (1998). [CrossRef]

3. B. Golik and D. Wueller, “Measurement method for image stabilizing systems,” Proc. SPIE **6502**, 65020O, 65020O–10 (2007). [CrossRef]

4. H. Choi, J.-P. Kim, M.-G. Song, W. C. Kim, N. C. Park, Y. P. Park, and K. S. Park, “Effects of motion of an imaging system and optical image stabilizer on the modulation transfer function,” Opt. Express **16**(25), 21132–21141 (2008). [CrossRef] [PubMed]

5. B. Likhterov and N. S. Kopeika, “Motion-blurred image restoration using modified inverse all-pole filters,” J. Electron. Imaging **13**(2), 257–263 (2004). [CrossRef]

7. Y. Tian, C. Rao, L. Zhu, and X. Rao, “Modified self-deconvolution restoration algorithm for adaptive-optics solar images,” Opt. Lett. **35**(15), 2541–2543 (2010). [CrossRef] [PubMed]

8. V. Loyev and Y. Yitzhaky, “Initialization of iterative parametric algorithms for blind deconvolution of motion-blurred images,” Appl. Opt. **45**(11), 2444–2452 (2006). [CrossRef] [PubMed]

9. J. Zhang, Q. Zhang, and G. He, “Blind deconvolution of a noisy degraded image,” Appl. Opt. **48**(12), 2350–2355 (2009). [CrossRef] [PubMed]

1. Y. Yitzhaky, I. Mor, A. Lantzman, and N. S. Kopeika, “Direct method for restoration of motion-blurred images,” J. Opt. Soc. Am. A **15**(6), 1512–1519 (1998). [CrossRef]

3. B. Golik and D. Wueller, “Measurement method for image stabilizing systems,” Proc. SPIE **6502**, 65020O, 65020O–10 (2007). [CrossRef]

10. C. W. Chiu, P. C.-P. Chao, and D. Y. Wu, “Optimal design of magnetically actuated optical image stabilizer mechanism for cameras in mobile phones via genetic algorithm,” IEEE Trans. Magn. **43**(6), 2582–2584 (2007). [CrossRef]

11. J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. **35**(21), 3553–3555 (2010). [CrossRef] [PubMed]

15. J. Widjaja, “Wavelet filter for improving detection performance of compression-based joint transform correlator,” Appl. Opt. **49**(30), 5768–5776 (2010). [CrossRef] [PubMed]

## 2. Theory

### 2.1 Principle of image stabilization

*g*(

*x,y*) can be represented aswhere * denotes two-dimensional convolution operation,

*h*(

*x*,

*y*) refers to the PSF of the degradation process,

*f*(

*x*,

*y*) represents the original object image, and

*n*(

*x*,

*y*) is additive noise. Then, the goal of image restoration is to model

*h*(

*x*,

*y*) accurately. Here supposing

*n*(

*x*,

*y*) is ignored, Eq. (1) can be rewritten asAccording to previous work by N. S. Kopeika

*et al*,

*h*(

*x,y*) can also be defined as [16

16. O. Hadar, I. Dror, and N. S. Kopeika, “Numerical calculation of image motion and vibration modulation transfer functions-a new method,” Proc. SPIE **1533**, 61–74 (1991). [CrossRef]

*T*denotes the integration period, represents velocity vector of images captured by high-speed CCD camera,

*n*is quantity of captured images during an integration period. So actually, the goal of image stabilization turns to how to detect velocity vector

### 2.2 Motion vector detection and Image restoration algorithms

*f*(

_{i}*x, y-a*) and

*f*(

_{i + 1}*x + ∆x, y + a + ∆y*) captured by a high-speed CCD camera are displayed side by side onto SLM1 placed in a front focal plane of a Fourier transforming lens2. Here assuming current frame image

*f*(

_{i}*x, y-a*) is reference image

*r*(

*x, y*), and next frame image

*f*(

_{i + 1}*x + ∆x, y + a + ∆y*) denotes object image

*t*(

*x, y*),

*a*denotes image displacement in the

*y*direction.

*∆x*and

*∆y*is motion displacement of image

*f*(

_{i + 1}*x + ∆x, y + a + ∆y*) compared image

*f*(

_{i}*x, y-a*) in the

*x*and

*y*direction, respectively.

6. S. Prasad, “Statistical-information-based performance criteria for Richardson-Lucy image deblurring,” J. Opt. Soc. Am. A **19**(7), 1286–1296 (2002). [CrossRef]

*f*(

^{i}*x, y*) is the restored image after

*i*iterations,* is the convolution operation, and ⊗ is the correlation operation.

## 3. Experimental results and discussions

14. J. A. Butt and T. D. Wilkinson, “Binary phase only filters for rotation and scale invariant pattern recognition with the joint transform correlator,” Opt. Commun. **262**(1), 17–26 (2006). [CrossRef]

15. J. Widjaja, “Wavelet filter for improving detection performance of compression-based joint transform correlator,” Appl. Opt. **49**(30), 5768–5776 (2010). [CrossRef] [PubMed]

*Ф*(

*x*,

*y*) is a finite-duration window function that can generate a daughter wavelets by varying dilation (

*a*,

_{x}*a*) and shift (

_{y}*b*,

_{x}*b*) and is given asThe mother wavelet must satisfy the admissibility conditions that it must be oscillatory, have fast decay to zero, and integrate to zero. WT is defined as an inner product between an analyzed signal

_{y}*f*(

*x*,

*y*) and daughter wavelets

*ω*,

_{x}*ω*) are the spatial frequency coordinates in the

_{y}*x*and

*y*directions, respectively.

*h*(

*x*,

*y*). Secondly, the single blurred image captured by prime CCD camera is conveyed to DSP and restored by the R-L algorithm. Lastly, real-time and high-resolution images are acquired without delay. Figure 6 shows the real-time image stabilization results at different moving velocity, respectively.

## 4. Conclusions

## Acknowledgments

## References and links

1. | Y. Yitzhaky, I. Mor, A. Lantzman, and N. S. Kopeika, “Direct method for restoration of motion-blurred images,” J. Opt. Soc. Am. A |

2. | G. Hochman, Y. Yitzhaky, N. S. Kopeika, Y. Lauber, M. Citroen, and A. Stern, “Restoration of images captured by a staggered time delay and integration camera in the presence of mechanical vibrations,” Appl. Opt. |

3. | B. Golik and D. Wueller, “Measurement method for image stabilizing systems,” Proc. SPIE |

4. | H. Choi, J.-P. Kim, M.-G. Song, W. C. Kim, N. C. Park, Y. P. Park, and K. S. Park, “Effects of motion of an imaging system and optical image stabilizer on the modulation transfer function,” Opt. Express |

5. | B. Likhterov and N. S. Kopeika, “Motion-blurred image restoration using modified inverse all-pole filters,” J. Electron. Imaging |

6. | S. Prasad, “Statistical-information-based performance criteria for Richardson-Lucy image deblurring,” J. Opt. Soc. Am. A |

7. | Y. Tian, C. Rao, L. Zhu, and X. Rao, “Modified self-deconvolution restoration algorithm for adaptive-optics solar images,” Opt. Lett. |

8. | V. Loyev and Y. Yitzhaky, “Initialization of iterative parametric algorithms for blind deconvolution of motion-blurred images,” Appl. Opt. |

9. | J. Zhang, Q. Zhang, and G. He, “Blind deconvolution of a noisy degraded image,” Appl. Opt. |

10. | C. W. Chiu, P. C.-P. Chao, and D. Y. Wu, “Optimal design of magnetically actuated optical image stabilizer mechanism for cameras in mobile phones via genetic algorithm,” IEEE Trans. Magn. |

11. | J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. |

12. | H. T. Chang and C. T. T. Chen, “Enhanced optical image verification based on Joint Transform Correlator adopting Fourier hologram,” Opt. Rev. |

13. | A. R. Alsamman, “Spatially efficient reference phase-encrypted joint transform correlator,” Appl. Opt. |

14. | J. A. Butt and T. D. Wilkinson, “Binary phase only filters for rotation and scale invariant pattern recognition with the joint transform correlator,” Opt. Commun. |

15. | J. Widjaja, “Wavelet filter for improving detection performance of compression-based joint transform correlator,” Appl. Opt. |

16. | O. Hadar, I. Dror, and N. S. Kopeika, “Numerical calculation of image motion and vibration modulation transfer functions-a new method,” Proc. SPIE |

**OCIS Codes**

(100.0100) Image processing : Image processing

(300.0300) Spectroscopy : Spectroscopy

**ToC Category:**

Image Processing

**History**

Original Manuscript: February 8, 2011

Revised Manuscript: March 25, 2011

Manuscript Accepted: May 1, 2011

Published: May 18, 2011

**Citation**

Yixian Qian, Yong Li, Jie Shao, and Hua Miao, "Real-time image stabilization for arbitrary motion blurred image based on opto-electronic hybrid joint transform correlator," Opt. Express **19**, 10762-10768 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10762

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### References

- Y. Yitzhaky, I. Mor, A. Lantzman, and N. S. Kopeika, “Direct method for restoration of motion-blurred images,” J. Opt. Soc. Am. A 15(6), 1512–1519 (1998). [CrossRef]
- G. Hochman, Y. Yitzhaky, N. S. Kopeika, Y. Lauber, M. Citroen, and A. Stern, “Restoration of images captured by a staggered time delay and integration camera in the presence of mechanical vibrations,” Appl. Opt. 43(22), 4345–4354 (2004). [CrossRef] [PubMed]
- B. Golik and D. Wueller, “Measurement method for image stabilizing systems,” Proc. SPIE 6502, 65020O, 65020O–10 (2007). [CrossRef]
- H. Choi, J.-P. Kim, M.-G. Song, W. C. Kim, N. C. Park, Y. P. Park, and K. S. Park, “Effects of motion of an imaging system and optical image stabilizer on the modulation transfer function,” Opt. Express 16(25), 21132–21141 (2008). [CrossRef] [PubMed]
- B. Likhterov and N. S. Kopeika, “Motion-blurred image restoration using modified inverse all-pole filters,” J. Electron. Imaging 13(2), 257–263 (2004). [CrossRef]
- S. Prasad, “Statistical-information-based performance criteria for Richardson-Lucy image deblurring,” J. Opt. Soc. Am. A 19(7), 1286–1296 (2002). [CrossRef]
- Y. Tian, C. Rao, L. Zhu, and X. Rao, “Modified self-deconvolution restoration algorithm for adaptive-optics solar images,” Opt. Lett. 35(15), 2541–2543 (2010). [CrossRef] [PubMed]
- V. Loyev and Y. Yitzhaky, “Initialization of iterative parametric algorithms for blind deconvolution of motion-blurred images,” Appl. Opt. 45(11), 2444–2452 (2006). [CrossRef] [PubMed]
- J. Zhang, Q. Zhang, and G. He, “Blind deconvolution of a noisy degraded image,” Appl. Opt. 48(12), 2350–2355 (2009). [CrossRef] [PubMed]
- C. W. Chiu, P. C.-P. Chao, and D. Y. Wu, “Optimal design of magnetically actuated optical image stabilizer mechanism for cameras in mobile phones via genetic algorithm,” IEEE Trans. Magn. 43(6), 2582–2584 (2007). [CrossRef]
- J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. 35(21), 3553–3555 (2010). [CrossRef] [PubMed]
- H. T. Chang and C. T. T. Chen, “Enhanced optical image verification based on Joint Transform Correlator adopting Fourier hologram,” Opt. Rev. 11(3), 165–169 (2004). [CrossRef]
- A. R. Alsamman, “Spatially efficient reference phase-encrypted joint transform correlator,” Appl. Opt. 49(10), B104–B110 (2010). [CrossRef] [PubMed]
- J. A. Butt and T. D. Wilkinson, “Binary phase only filters for rotation and scale invariant pattern recognition with the joint transform correlator,” Opt. Commun. 262(1), 17–26 (2006). [CrossRef]
- J. Widjaja, “Wavelet filter for improving detection performance of compression-based joint transform correlator,” Appl. Opt. 49(30), 5768–5776 (2010). [CrossRef] [PubMed]
- O. Hadar, I. Dror, and N. S. Kopeika, “Numerical calculation of image motion and vibration modulation transfer functions-a new method,” Proc. SPIE 1533, 61–74 (1991). [CrossRef]

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