## Joint wavelet transform correlation with separated target and reference planes

Optics Express, Vol. 2, Issue 5, pp. 177-183 (1998)

http://dx.doi.org/10.1364/OE.2.000177

Acrobat PDF (286 KB)

### Abstract

In recent years, we realize the usefulness of feature extraction for optical correlator and hereby, we investigate the capability of Laplace operator in feature extraction of multiple targets. The first-order terms and the false alarm terms in the correlation output would be removed using electronic power spectrum subtraction technique. Most importantly, the entire magneto-optic SLM is completely utilized for displaying only targets in the input scene. A new cost efficient hardware implementation is proposed and aforementioned result of the proposed system is evaluated through computer simulation.

© Optical Society of America

## 1. Introduction

1. C. S. Weaver and J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. **5**, 1248–1249 (1966). [CrossRef] [PubMed]

2. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory **IT-10**139–145 (1964). [CrossRef]

3. F. T. S. Yu and D. A. Gregory, “Optical Pattern Recognition: Architectures and Techniques,” Proc. IEEE **84**, 733–752 (1996). [CrossRef]

4. B. Javidi and C. K. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. **27**, 663–665 (1988). [CrossRef] [PubMed]

7. M.S. Alam and M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. **32**, 4344–4350 (1993). [CrossRef] [PubMed]

11. X. J. Lu, A. Katz, E. G. Kanterakis, and N. P. Caviris, “Joint transform correlator that uses wavelet transforms,” Opt. Lett. **17**, 1700–1702 (1992). [CrossRef] [PubMed]

15. M. S. Alam, O. Perez, and M. A. Karim, “Preprocessed multiobject joint transform correlator,” Appl. Opt. **32**, 3102–3107 (1993). [CrossRef] [PubMed]

16. S. Zhong, J. Jiang, and C. Li, “Joint wavelet transform correlator with power spectrum subtraction for improved performance,” Opt. Eng. **36**, 2787–2792 (1997). [CrossRef]

17. X. Huang, H. Lai, and Z. Gao, “Multiple-Target detection with the use of a modified amplitude-modulated joint transform correlator,” Appl. Opt. **36**, 9198–9204 (1997). [CrossRef]

12. W. L. Wang, G. F. Jin, Y. B. Yan, and M. X. Wu, “Joint wavelet-transform correlator for image feature extraction,” Appl. Opt. **34**, 370–376 (1995). [CrossRef] [PubMed]

13. F. Ahmed, M. A. Karim, and M. S. Alam, “Wavelet transform-based correlatorfor the recognition of rotationally distorted images,” Opt. Eng. **34**, 3187–3192 (1995). [CrossRef]

18. Q. Tang and B. Javidi, “Multiple-object detection with chirp-encoded joint transform correlator,” Appl. Opt. **32**, 5079–5088 (1993). [CrossRef] [PubMed]

## 2. Theory

*x*

_{0},

*y*

_{0},

*x*, and

_{i}*y*are the spatial domain variables. The lens 3 will give the Fourier transform of the images that is projected by the collimated beam at a focal length away. The result of the Fourier transform is given by

_{i}*ϕ*,

_{ti}*ϕ*, and

_{tk}*ϕ*are the phase factors of the targets and the reference, respectively, and the

_{r}*x*and

_{k}*y*are the spatial domain variables. When the shutter is closed, the targets-only power spectrum is recorded and described by

_{k}*R*(

*u*,

*v*)|

^{2}. The refence-only power spectrum is known in regard to the Laplace operator used, and is precalculated and stored in the computer for further computation. It is given by

## 3. Computer simulation results

## 4. Conclusion

## References and links

1. | C. S. Weaver and J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. |

2. | A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory |

3. | F. T. S. Yu and D. A. Gregory, “Optical Pattern Recognition: Architectures and Techniques,” Proc. IEEE |

4. | B. Javidi and C. K. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. |

5. | F. T. S. Yu, F. Cheng, T. Nagata, and D. A. Gregory, “Effects of fringe binarization of multiobject joint transform correlation,” Appl. Opt. |

6. | W. B. Hahn Jr. and D. L. Flannery, “Design elements of binary joint transform correlation and selected optimization techniques,” Opt. Eng. |

7. | M.S. Alam and M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. |

8. | M. S. Alam and M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. |

9. | M. S. Alam, “Fractional power fringe-adjusted joint transform correlator,” Opt. Eng. |

10. | B. Javidi, F. Parchekani, and G. S. Zhang, “Minimum-mean-square-error filters for detecting a noisy target in background noise,” Appl. Opt. |

11. | X. J. Lu, A. Katz, E. G. Kanterakis, and N. P. Caviris, “Joint transform correlator that uses wavelet transforms,” Opt. Lett. |

12. | W. L. Wang, G. F. Jin, Y. B. Yan, and M. X. Wu, “Joint wavelet-transform correlator for image feature extraction,” Appl. Opt. |

13. | F. Ahmed, M. A. Karim, and M. S. Alam, “Wavelet transform-based correlatorfor the recognition of rotationally distorted images,” Opt. Eng. |

14. | I. Ouzieli and D. Mendlovic, “Two-dimensional wavelet processor,” Appl. Opt. |

15. | M. S. Alam, O. Perez, and M. A. Karim, “Preprocessed multiobject joint transform correlator,” Appl. Opt. |

16. | S. Zhong, J. Jiang, and C. Li, “Joint wavelet transform correlator with power spectrum subtraction for improved performance,” Opt. Eng. |

17. | X. Huang, H. Lai, and Z. Gao, “Multiple-Target detection with the use of a modified amplitude-modulated joint transform correlator,” Appl. Opt. |

18. | Q. Tang and B. Javidi, “Multiple-object detection with chirp-encoded joint transform correlator,” Appl. Opt. |

19. | A. K. Jain, “Image Analysis and Computer Vision”, Chap. 9 in |

**OCIS Codes**

(100.4550) Image processing : Correlators

(100.5010) Image processing : Pattern recognition

**ToC Category:**

Research Papers

**History**

Original Manuscript: October 21, 1997

Revised Manuscript: October 9, 1997

Published: March 2, 1998

**Citation**

Boon Yi Soon, Mohammad Karim, Russell Hardie, and Mohammad Alam, "Joint wavelet transform correlation with separated target and reference planes," Opt. Express **2**, 177-183 (1998)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-2-5-177

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### References

- C. S. Weaver and J. W. Goodman, "Technique for optically convolving two functions," Appl. Opt. 5, 1248-1249 (1966).<br> [CrossRef] [PubMed]
- A. B. VanderLugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory IT-10 139-145 (1964).<br> [CrossRef]
- F. T. S. Yu and D. A. Gregory, "Optical Pattern Recognition: Architectures and Techniques," Proc. IEEE 84, 733-752 (1996).<br> [CrossRef]
- B. Javidi and C. K. Kuo, "Joint transform image correlation using a binary spatial light modulator at the Fourier plane," Appl. Opt. 27, 663-665 (1988).<br> [CrossRef] [PubMed]
- F. T. S. Yu, F. Cheng, T. Nagata, and D. A. Gregory, "Effects of fringe binarization of multiobject joint transform correlation," Appl. Opt. 28, 2988-2990 (1989).<br> [CrossRef] [PubMed]
- W. B. Hahn, Jr. and D. L. Flannery, "Design elements of binary joint transform correlation and selected optimization techniques," Opt. Eng. 31, 896-905 (1992).<br> [CrossRef]
- M.S. Alam and M. A. Karim, "Fringe-adjusted joint transform correlation," Appl. Opt. 32, 4344-4350 (1993).<br> [CrossRef] [PubMed]
- M. S. Alam and M. A. Karim, "Multiple target detection using a modified fringe-adjusted joint transform correlator," Opt. Eng. 33, 1610-1617 (1994).<br> [CrossRef]
- M. S. Alam, "Fractional power fringe-adjusted joint transform correlator," Opt. Eng. 43, 3208- 3216 (1995).<br> [CrossRef]
- B. Javidi, F. Parchekani, and G. S. Zhang, "Minimum-mean-square-error filters for detecting a noisy target in background noise," Appl. Opt. 35, 6964-6975 (1996).<br> [CrossRef] [PubMed]
- X. J. Lu, A. Katz, E. G. Kanterakis, and N. P. Caviris, "Joint transform correlator that uses wavelet transforms," Opt. Lett. 17, 1700-1702 (1992).<br> [CrossRef] [PubMed]
- W.L.Wang,G. F. Jin, Y. B. Yan, andM.X.Wu,"Jointwavelet-transformcorrelatorforimage feature extraction," Appl. Opt. 34, 370-376 (1995).<br> [CrossRef] [PubMed]
- F. Ahmed, M. A. Karim, and M. S. Alam, "Wavelet transform-based correlator for the recognition of rotationally distorted images," Opt. Eng. 34, 3187-3192 (1995).<br> [CrossRef]
- I. Ouzieli and D. Mendlovic, "Two-dimensional wavelet processor," Appl. Opt. 35, 5839-5846 (1996).<br> [CrossRef] [PubMed]
- M. S. Alam, O. Perez, and M. A. Karim, "Preprocessed multiobject joint transform correlator," Appl. Opt. 32, 3102-3107 (1993).<br> [CrossRef] [PubMed]
- S. Zhong, J. Jiang, and C. Li, "Joint wavelet transform correlator with power spectrum subtraction for improved performance," Opt. Eng. 36, 2787-2792 (1997). [CrossRef]
- X. Huang, H. Lai, and Z. Gao, "Multiple-Target detection with the use of a modified amplitude- modulated joint transform correlator," Appl. Opt. 36, 9198-9204 (1997).<br> [CrossRef]
- Q. Tang and B. Javidi, "Multiple-object detection with chirp-encodedjoint transform correlator," Appl. Opt. 32, 5079-5088 (1993).<br> [CrossRef] [PubMed]
- A. K. Jain, "Image Analysis and Computer Vision", Chap. 9 in Fundamentals of Digital Image Processing , T. Kailath, Ed., (Prentice Hall, Englewood Cliffs, 1989) pp. 351-353.

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