Abstract

A method of scale-invariant recognition of three-dimensional (3-D) objects is presented. Several images of the observed scene are recorded under white-light illumination from several different points of view and compressed into a single complex two-dimensional matrix. After filtering with a single scale-invariant filter, the resultant function is then coded into a computer-generated hologram (CGH). When this CGH is coherently illuminated, a correlation space is reconstructed in which light peaks indicate the existence and location of true targets in the tested 3-D scene. The light peaks are detectable for different sizes of the true objects, as long as they are within the invariance range of the filter. Experimental results in a complete electro-optical system are presented, and comparisons with other systems are investigated by use of computer simulation.

© 2003 Optical Society of America

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References

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    [CrossRef]
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2002 (2)

J. J. Esteve-Taboada, J. Garcia, C. Ferreira, “Optical recognition of three-dimensional objects with scale invariance using a classical convergent correlator,” Opt. Eng. 41, 1324–1330 (2002).
[CrossRef]

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

2001 (1)

2000 (4)

1999 (1)

1998 (2)

1997 (1)

1989 (1)

1988 (1)

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonic,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

1983 (1)

1964 (1)

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

Abookasis, D.

Esteve-Taboada, J. J.

Ferreira, C.

J. J. Esteve-Taboada, J. Garcia, C. Ferreira, “Optical recognition of three-dimensional objects with scale invariance using a classical convergent correlator,” Opt. Eng. 41, 1324–1330 (2002).
[CrossRef]

J. J. Esteve-Taboada, J. Garcia, C. Ferreira, “Rotation-invariant optical recognition of three-dimensional objects,” Appl. Opt. 39, 5998–6005 (2000).
[CrossRef]

Garcia, J.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, New York, 1996) Chap. 8.

Javidi, B.

Konforti, N.

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonic,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Li, Y.

Marom, E.

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonic,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Mas, D.

Mendlovic, D.

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonic,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Mutoh, K.

Rosen, J.

Shamir, J.

Tajahuerce, E.

Takeda, M.

Vander Lugt, A.

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

Appl. Opt. (8)

IEEE Trans. Inf. Theory (1)

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

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonic,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Opt. Eng. (1)

J. J. Esteve-Taboada, J. Garcia, C. Ferreira, “Optical recognition of three-dimensional objects with scale invariance using a classical convergent correlator,” Opt. Eng. 41, 1324–1330 (2002).
[CrossRef]

Opt. Lett. (2)

Other (1)

J. Goodman, Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, New York, 1996) Chap. 8.

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Figures (7)

Fig. 1
Fig. 1

Schematic of the proposed system.

Fig. 2
Fig. 2

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

Fig. 3
Fig. 3

(a) Phase angle of the LRH filter when OSA is on the reference object, (b) amplitude and (c) the phase angle of the generated spatial spectrum of the correlation space.

Fig. 4
Fig. 4

Central part of the CGH generated from T(u, v) by use of the holographic coding method. The reference is the object with OSA on its face.

Fig. 5
Fig. 5

Optically reconstructed correlation results when the OSA is on the reference object. (a) The pattern recorded at z 0 = 7.1 cm, (b) at z 0 = -3.7 cm, where the back focal point is at z 0 = 0, (c) and (d) are the 3-D plots of (a) and (b), respectively.

Fig. 6
Fig. 6

Same as Fig. 5, but for the reference object with BGU on its face.

Fig. 7
Fig. 7

(a) Scale dependence of correlation peaks normalized to unity. MF, matched filter; POF, phase-only matched filter; LRH, logarithmic radial harmonic filter. (b) Scale dependence of the discrimination ability measured by SNR for different filters.

Tables (1)

Tables Icon

Table 1 SNR Performances of the Proposed System when Matched Filter, Phase-Only Filter, and the LRH Filter Were Employed

Equations (17)

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ξ, η=Mzx cos θ+z sin θ, y,
ξ, ηMzx+zθ, y.
o3u, v   o2ξ, η, auexp-i2πuξ +vη/λfdξdη.
o3u, v  o1x, y, zexp-i2πuξ +vη/λfΔxΔyΔz.
o3u, v  o1x, y, zexp-i2πMzux+vy +au2z/λfΔxΔyΔz.
o3u, v   o1x, y, zexp-i2πMzux+vy +au2z/λfdxdydz.
Hu, v   fx, y, zexp-i2πM0ux+vy +au2z/λfdxdydz.
Tu, v=o3u, vH*u, v   o1x, y, z×exp-i2πMzux+vy+au2z/λfdxdydz× f*-x, -y, -z×exp-i2πM0ux+vy+au2z/λfdxdydz=  o1x, y, zf*-x, -y, -z×exp-i 2πM0λfuMzM0 x+x+vMzM0 y+y+au2MzM0 z+z ×dxdydzdxdydz=  o1x, y, zf*MzM0 x-xc, MzM0 y-yc, MzM0 z-zc×exp-i 2πM0λfuxc+vyc+au2zcdxdydzdxcdycdzc= gxc, yc, zc-i 2πM0λfuxc+vyc+au2zcdxcdycdzc,
xc=MzM0 x+x, yc=MzM0 y+y, zc=MzM0 z+z
gxc, yc, zc= o1x, y, zf*×MzM0 x-xc, MzM0 y-yc, MzM0 z-zcdxdydz.
c0αc01 expiσα,
c0α=02πdR o3ρα, ϕH˜*ρ, ϕρdϕdρ=02πd/αR/α o3τ, ϕH˜*ατ, ϕτdϕdτ.
H˜ρ, ϕ=expiΩϕρdipw,
w=12πlnRd.
Ωϕ=argdR Hρ, ϕρd-ipwρdρ.
Tru, v=0.51+ReTu, vexp-i2πλfdxu+dyv,
SNR=maximum correlation peak intensity of the true targetmaximum noise intensity.

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