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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2002

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

2000

1999

1998

1997

1989

1988

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

1983

1964

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.

IEEE Trans. Inf. Theory

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

J. Opt. Soc. Am. A

Opt. Commun.

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.

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.

Other

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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