## Three-dimensional object recognition using a quasi-correlator invariant to imaging distances

Optics Express, Vol. 16, Issue 22, pp. 17148-17153 (2008)

http://dx.doi.org/10.1364/OE.16.017148

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### Abstract

We present a new method for performing electro-optical three-dimensional (3-D) object recognition under incoherent white-light illumination. Perspective projections of the 3-D scene are acquired from multiple points of view and then processed into a single complex two-dimensional modified Fresnel hologram of the scene. This hologram is processed with a single filter which is matched to a single object, so that all identical objects in the scene yield similar correlation peaks in the 3-D space with almost no dependency on the distances of the objects from the acquisition plane. The new method is demonstrated by experiments.

© 2008 Optical Society of America

## 1. Introduction

1. R. Bamler and J. Hofer-Alfeis, “Three- and four dimensional filter operations by coherent optics,” Opt. Acta. **29**, 747–757 (1982). [CrossRef]

2. J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. **37**, 7538–7544 (1998). [CrossRef]

3. T. C. Poon and T. Kim, “Optical image recognition of three dimensional objects,” Appl. Opt. **38**, 370–381 (1999). [CrossRef]

4. J. J. Esteve-Taboada, D. Mas, and J. Garcia, “Three dimensional object recognition by Fourier transform profilometry,” Appl. Opt. **38**, 4760–4765 (1999). [CrossRef]

5. B. Javidi, R. Ponce-Díaz, and S. -H. Hong, “Three-dimensional recognition of occluded objects by using computational integral imaging,” Opt. Lett. **31**, 1106–1108 (2006). [CrossRef] [PubMed]

7. D.-H. Shin and H. Yoo, “Scale-variant magnification for computational integral imaging and its application to 3D object correlator,” Opt. Express **16**, 8855–8867 (2008). [CrossRef] [PubMed]

8. Y. Li and J. Rosen, “Object recognition using three-dimensional optical quasi-correlation,” J. Opt. Soc. Am. A **19**, 1755–1762 (2002). [CrossRef]

2. J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. **37**, 7538–7544 (1998). [CrossRef]

9. N. T. Shaked, J. Rosen, and A. Stern, “Integral holography: white-light single-shot hologram acquisition,” Opt. Express **15**, 5754–5760 (2007). [CrossRef] [PubMed]

10. N. T. Shaked, B. Katz, and J. Rosen, “Fluorescence multicolor hologram recorded by using a macrolens array,” Opt. Lett. **33**, 1461–1463 (2008). [CrossRef] [PubMed]

11. N. T. Shaked and J. Rosen, “Modified Fresnel computer-generated hologram directly recorded by multiple-viewpoint projections,” Appl. Opt. **47**, D21–D27 (2008). [CrossRef] [PubMed]

12. N. T. Shaked and J. Rosen, “Multiple-viewpoint projection holograms synthesized by spatially-incoherent correlation with broad functions,” J. Opt. Soc. Am. A **25**, 2129–2138 (2008). [CrossRef]

## 2. Description of the method

*P*(

_{m,n}*x*) be the (

_{p}, y_{p}*m*,

*n*)-th captured projection of the 3-D scene. The DIMFH of this scene is defined by [11

11. N. T. Shaked and J. Rosen, “Modified Fresnel computer-generated hologram directly recorded by multiple-viewpoint projections,” Appl. Opt. **47**, D21–D27 (2008). [CrossRef] [PubMed]

12. N. T. Shaked and J. Rosen, “Multiple-viewpoint projection holograms synthesized by spatially-incoherent correlation with broad functions,” J. Opt. Soc. Am. A **25**, 2129–2138 (2008). [CrossRef]

*b*is an adjustable parameter. To reconstruct the recorded 3-D scene, we can illuminate the DIMFH by a coherent plane wave, or alternatively, compute the Fresnel propagation along the optical axis in the computer. In the latter method, the reconstructed plane located at axial distance

*d*from the hologram is defined as follows:

_{D}convolution, and Qd is a quadratic phase function defined as follows:

*p*is the pixel size of the camera, and

*γ*=

*bf*(where

^{2}α^{2}/Δp^{2}*α*is the camera gap between two adjacent projections, and

*f*is the focal length of the imaging lens of the camera). The transverse magnification of the DIMFH is constant regardless of the object axial distance, and equal to Δ

*p*/

*α*[12

12. N. T. Shaked and J. Rosen, “Multiple-viewpoint projection holograms synthesized by spatially-incoherent correlation with broad functions,” J. Opt. Soc. Am. A **25**, 2129–2138 (2008). [CrossRef]

*d*is in a quadratic relation with the coinciding axial distance in the 3-D scene [11

11. N. T. Shaked and J. Rosen, “Modified Fresnel computer-generated hologram directly recorded by multiple-viewpoint projections,” Appl. Opt. **47**, D21–D27 (2008). [CrossRef] [PubMed]

**25**, 2129–2138 (2008). [CrossRef]

*f*(

*m, n*) of the correlator is generated beforehand by using the middle projection of the object to be recognized, magnified by Δ

*p*/

*α*. Alternatively, a DIMFH of the object to be recognized can be generated beforehand using Eq. (1) [but now each projection is a different perspective view of this single object, located at (0,0,

*d*), rather than of the entire 3-D scene], and then convolving this DIMFH with

*Q*to yield

_{d}*f*(

*m, n*). .In both methods, the correlation plane located at axial distance

*d*from the hologram plane is given by

*d*), as well as the in-focus objects (located at axial distance

*d*) that do not match the PSF

*f*(

*m, n*), do not yield distinct correlation peaks in correlation plane

*C*(

_{d}*m, n*). As explained above, since the transverse magnification of the hologram is constant,

*f*(

*m, n*) is matched to the object to be recognized in the 3-D scene, never mind whether this object is close to or far from the acquisition plane. Hence, the highest correlation peaks in the entire correlation space appear at all corresponding positions in which the object to be recognized is located at the 3-D scene.

*H*(

*m,n*) and

*f*(

*m, n*) can be performed optically by various optical correlators [13]. In addition,

*H*(

*m,n*)⊗

*f*(

*m,n*) itself is a hologram of correlation peaks that can be reconstructed optically by illuminating it with coherent plane wave to yield the 3-D correlation space, or alternatively, as suggested by Eq. (4), can be reconstructed digitally by convolving it with scaled quadratic phase functions.

## 3. Experimental results

*H*(

*m,n*) of the 3-D scene, shown in Figs. 3(a) and 3(b), was generated by Eq. (1). Then, the correlation space was obtained by calculating

*C*(

_{d}*m, n*) according to Eq. (4) for all axial distances in the range of the 3-D scene, where we used

*f*(

*m, n*), shown in Fig. 3(c), having phase-only spatial spectrum.

**25**, 2129–2138 (2008). [CrossRef]

8. Y. Li and J. Rosen, “Object recognition using three-dimensional optical quasi-correlation,” J. Opt. Soc. Am. A **19**, 1755–1762 (2002). [CrossRef]

## 4. Conclusions

## References and links

1. | R. Bamler and J. Hofer-Alfeis, “Three- and four dimensional filter operations by coherent optics,” Opt. Acta. |

2. | J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. |

3. | T. C. Poon and T. Kim, “Optical image recognition of three dimensional objects,” Appl. Opt. |

4. | J. J. Esteve-Taboada, D. Mas, and J. Garcia, “Three dimensional object recognition by Fourier transform profilometry,” Appl. Opt. |

5. | B. Javidi, R. Ponce-Díaz, and S. -H. Hong, “Three-dimensional recognition of occluded objects by using computational integral imaging,” Opt. Lett. |

6. | J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, “Resolution-enhanced three-dimensional image correlator using computationally reconstructed integral images,” Opt. Commun. |

7. | D.-H. Shin and H. Yoo, “Scale-variant magnification for computational integral imaging and its application to 3D object correlator,” Opt. Express |

8. | Y. Li and J. Rosen, “Object recognition using three-dimensional optical quasi-correlation,” J. Opt. Soc. Am. A |

9. | N. T. Shaked, J. Rosen, and A. Stern, “Integral holography: white-light single-shot hologram acquisition,” Opt. Express |

10. | N. T. Shaked, B. Katz, and J. Rosen, “Fluorescence multicolor hologram recorded by using a macrolens array,” Opt. Lett. |

11. | N. T. Shaked and J. Rosen, “Modified Fresnel computer-generated hologram directly recorded by multiple-viewpoint projections,” Appl. Opt. |

12. | N. T. Shaked and J. Rosen, “Multiple-viewpoint projection holograms synthesized by spatially-incoherent correlation with broad functions,” J. Opt. Soc. Am. A |

13. | J. Goodman, |

**OCIS Codes**

(070.4550) Fourier optics and signal processing : Correlators

(070.5010) Fourier optics and signal processing : Pattern recognition

(070.6110) Fourier optics and signal processing : Spatial filtering

(100.6890) Image processing : Three-dimensional image processing

(100.3005) Image processing : Image recognition devices

(100.3008) Image processing : Image recognition, algorithms and filters

**ToC Category:**

Fourier optics and signal processing

**History**

Original Manuscript: July 8, 2008

Revised Manuscript: August 31, 2008

Manuscript Accepted: August 31, 2008

Published: October 13, 2008

**Citation**

Natan T. Shaked, Gideon Segev, and Joseph Rosen, "Three-dimensional object recognition using a quasi-correlator invariant to imaging distances," Opt. Express **16**, 17148-17153 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-22-17148

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### References

- R. Bamler and J. Hofer-Alfeis, "Three- and four dimensional filter operations by coherent optics," Opt. Acta. 29, 747-757 (1982). [CrossRef]
- J. Rosen, "Three-dimensional joint transform correlator," Appl. Opt. 37, 7538-7544 (1998). [CrossRef]
- T. C. Poon and T. Kim, "Optical image recognition of three dimensional objects," Appl. Opt. 38, 370-381 (1999). [CrossRef]
- J. J. Esteve-Taboada, D. Mas, and J. Garcia, "Three dimensional object recognition by Fourier transform profilometry," Appl. Opt. 38, 4760-4765 (1999). [CrossRef]
- B. Javidi, R. Ponce-Díaz, and S. -H. Hong, "Three-dimensional recognition of occluded objects by using computational integral imaging," Opt. Lett. 31, 1106-1108 (2006). [CrossRef] [PubMed]
- J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, "Resolution-enhanced three-dimensional image correlator using computationally reconstructed integral images," Opt. Commun. 26, 72-79 (2007). [CrossRef]
- D.-H. Shin and H. Yoo, "Scale-variant magnification for computational integral imaging and its application to 3D object correlator," Opt. Express 16, 8855-8867 (2008). [CrossRef] [PubMed]
- Y. Li and J. Rosen, "Object recognition using three-dimensional optical quasi-correlation," J. Opt. Soc. Am. A 19, 1755-1762 (2002). [CrossRef]
- N. T. Shaked, J. Rosen, and A. Stern, "Integral holography: white-light single-shot hologram acquisition," Opt. Express 15, 5754-5760 (2007). [CrossRef] [PubMed]
- N. T. Shaked, B. Katz, and J. Rosen, "Fluorescence multicolor hologram recorded by using a macrolens array," Opt. Lett. 33, 1461-1463 (2008). [CrossRef] [PubMed]
- N. T. Shaked and J. Rosen, "Modified Fresnel computer-generated hologram directly recorded by multiple-viewpoint projections," Appl. Opt. 47, D21-D27 (2008). [CrossRef] [PubMed]
- N. T. Shaked and J. Rosen, "Multiple-viewpoint projection holograms synthesized by spatially-incoherent correlation with broad functions," J. Opt. Soc. Am. A 25, 2129-2138 (2008). [CrossRef]
- J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 8.

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