Abstract

A novel method of three-dimensional (3-D) object recognition is proposed. Several projections of a 3-D target are recorded under white-light illumination and fused into a single complex two-dimensional function. After proper filtering, the resulting function is coded into a computer-generated hologram. When this hologram is coherently illuminated, a correlation space is reconstructed such that light peaks indicate the existence and locations of true targets in the observed 3-D scene. Experimental results and comparisons with results of another 3-D object recognition technique are presented.

© 2002 Optical Society of America

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References

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  1. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  2. R. Bamler, J. Hofer-Alfeis, “Three- and four-dimensional filter operations by coherent optics,” Opt. Acta 29, 747–757 (1982).
    [CrossRef]
  3. J. Rosen, “Three-dimensional optical Fourier transform and correlation,” Opt. Lett. 22, 964–966 (1997).
    [CrossRef] [PubMed]
  4. J. Rosen, “Three-dimensional electro-optical correlator,” J. Opt. Soc. Am. A 15, 430–436 (1998).
    [CrossRef]
  5. J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. 37, 7538–7544 (1998).
    [CrossRef]
  6. Y. Li, J. Rosen, “Three-dimensional pattern recognition with a single two-dimensional synthetic reference function,” Appl. Opt. 39, 1251–1259 (2000).
    [CrossRef]
  7. Y. Li, J. Rosen, “Three-dimensional correlator with general complex filters,” Appl. Opt. 39, 6561–6572 (2000).
    [CrossRef]
  8. J. J. Esteve-Taboada, D. Mas, J. Garcia, “Three-dimensional object recognition by Fourier transform profilometry,” Appl. Opt. 38, 4760–4765 (1999).
    [CrossRef]
  9. M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [CrossRef] [PubMed]
  10. Y. Frauel, E. Tajahuerce, M.-A. Castro, B. Javidi, “Distortion-tolerant three-dimensional object recognition with digital holography,” Appl. Opt. 40, 3887–3893 (2001).
    [CrossRef]
  11. O. Matoba, E. Tajahuerce, B. Javidi, “Real-time three-dimensional object recognition with multiple perspectives imaging,” Appl. Opt. 40, 3318–3325 (2001).
    [CrossRef]
  12. Y. Li, D. Abookasis, J. Rosen, “Computer-generated holograms of three-dimensional realistic objects recorded without wave interference,” Appl. Opt. 40, 2864–2870 (2001).
    [CrossRef]
  13. J. Rosen, “Computer-generated holograms of images reconstructed on curved surfaces,” Appl. Opt. 38, 6136–6140 (1999).
    [CrossRef]
  14. O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.
  15. B. V. K. Vijaya-Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef]

2001 (3)

2000 (2)

1999 (2)

1998 (2)

1997 (1)

1990 (1)

1983 (1)

1982 (1)

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

1964 (1)

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

Abookasis, D.

Bamler, R.

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

Bryngdahl, O.

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.

Castro, M.-A.

Esteve-Taboada, J. J.

Frauel, Y.

Garcia, J.

Hassebrook, L.

Hofer-Alfeis, J.

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

Javidi, B.

Li, Y.

Mas, D.

Matoba, O.

Mutoh, K.

Rosen, J.

Tajahuerce, E.

Takeda, M.

VanderLugt, A.

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

Vijaya-Kumar, B. V. K.

Wyrowski, F.

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.

Appl. Opt. (10)

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

Y. Li, J. Rosen, “Three-dimensional pattern recognition with a single two-dimensional synthetic reference function,” Appl. Opt. 39, 1251–1259 (2000).
[CrossRef]

Y. Li, J. Rosen, “Three-dimensional correlator with general complex filters,” Appl. Opt. 39, 6561–6572 (2000).
[CrossRef]

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

M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
[CrossRef] [PubMed]

Y. Frauel, E. Tajahuerce, M.-A. Castro, B. Javidi, “Distortion-tolerant three-dimensional object recognition with digital holography,” Appl. Opt. 40, 3887–3893 (2001).
[CrossRef]

O. Matoba, E. Tajahuerce, B. Javidi, “Real-time three-dimensional object recognition with multiple perspectives imaging,” Appl. Opt. 40, 3318–3325 (2001).
[CrossRef]

Y. Li, D. Abookasis, J. Rosen, “Computer-generated holograms of three-dimensional realistic objects recorded without wave interference,” Appl. Opt. 40, 2864–2870 (2001).
[CrossRef]

J. Rosen, “Computer-generated holograms of images reconstructed on curved surfaces,” Appl. Opt. 38, 6136–6140 (1999).
[CrossRef]

B. V. K. Vijaya-Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
[CrossRef]

IEEE Trans. Inf. Theory (1)

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

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

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

Opt. Lett. (1)

Other (1)

O. Bryngdahl, F. Wyrowski, “Digital holography—computer-generated holograms,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.

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Figures (8)

Fig. 1
Fig. 1

Schematic of the proposed system.

Fig. 2
Fig. 2

Schematic of the computational process from capturing the projections to displaying the hologram.

Fig. 3
Fig. 3

Sixteen out of sixty-five projections of the tested scene, imaged from -16° to 16°.

Fig. 4
Fig. 4

(a) Amplitude and (b) phase function of the compressed spatial spectrum of the scene; (c) phase function of the 3-D POF.

Fig. 5
Fig. 5

Central part of the CGH generated from T(u, v) by use of the holographic coding method.

Fig. 6
Fig. 6

Simulated correlation results recorded at (a) z=12.5 pixels, (b) z=-12 pixels; (c) and (d) are the 3-D plots of (a) and (b), respectively.

Fig. 7
Fig. 7

Experimental correlation results recorded at (a) 2.6 cm and (b) -2.5 cm along the z axis; their 3-D plots are shown in (c) and (d), respectively.

Fig. 8
Fig. 8

Simulated correlation plots along the z0 axis. Dotted–dashed curve, case of the back true object, the asterisk curve, false object; and solid curve, front true object.

Tables (1)

Tables Icon

Table 1 Summary of SNR and PCE between the Hybrid BGU Correlator and the 3-D OQC for Two Kinds of Filters

Equations (13)

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(xi, yi)=M(x cos θi+z sin θi, y),
o3(u, v)o2(xi, yi, au)exp[-j2π×(uxi+vyi)/λf]dxidyi.
o3(u, v)o2(xi, yi, au)exp[-j2πM×(ux+vy+au2z)/λf]dxidyi.
o3(u, v)o1(x, y, z)exp[-j2πM×(ux+vy+au2z)/λf]ΔxΔyΔz.
o3(u, v)o1(x, y, z)exp[-j2πM×(ux+vy+au2z)/λf]dxdydz.
F(u, v)f*(-x,-y,-z)exp[-j2πM×(ux+vy+au2z)/λf]dxdydz,
T(u, v)=o3(u, v)F(u, v)o1(x, y, z)exp[-j2πM×(ux+vy+au2z)/λf]dxdydz×f*(-ξ,-η,-ζ)exp[-j2πM×(uξ+vη+au2ζ)/λf]dξdηdζ= o1(x, y, z)f*(-ξ,-η,-ζ)×exp-{j2πM[u(x+ξ)+v(y+η)+au2(z+ζ)/λf]}dxdydzdξdηdζ=o1(x, y, z)f*(x-xˆ, y-yˆ, z-zˆ)dxdydz×exp[-j2πM(uxˆ+vyˆ+au2zˆ)/λf]dxˆdyˆdzˆ=g(xˆ, yˆ, zˆ)exp[-j2πM(uxˆ+vyˆ+au2zˆ)/λf]dxˆdyˆdzˆ,
g(xˆ, yˆ, zˆ)=o1(x, y, z)f*(x-xˆ, y-yˆ, z-zˆ)dxdydz,
xˆ=x+ξ,yˆ=y+η,zˆ=z+ζ.
T˜(u, v)=g(xˆ, yˆ, zˆ)exp{-j2πM×[uxˆ+vyˆ+a(u2+v2)zˆ]/λf}dxˆdyˆdzˆ.
Tr(u, v)=0.51+ReT(u, v)expj2πλf(dxu+dyv),
SNR=maximumcorrelationpeakintensityofthetruetargetmaximumnoiseintensity.
PCE=maximumcorrelationpeakintensityofthetruetargetaveragecorrelationplaneenergy,

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