Abstract

A new concept for on-line tracking and recognition in robot vision is presented. It uses the high speed Fourier transform properties of coherent optical systems but replaces the holographic filtering (hardware) by electronic processing (software) of amplitude and phase in the Fourier plane. The phase information is extracted by heterodyne detection. The 2-D moments of optical patterns can be determined by the same method.

© 1983 Optical Society of America

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References

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  1. M. R. Teague, Appl. Opt. 19, 1353 (1980).
    [CrossRef] [PubMed]
  2. D. Casasent, D. Psaltis, Proc. Soc. Photo-Opt. Instrum. Eng. 201, 107 (1979).
  3. A. D. Gara, Appl. Opt. 18, 172 (1979).
    [CrossRef] [PubMed]
  4. A. D. Gara, “Optical Computing for Image Processing,” in Computer Vision and Sensor-Based Robots, G. G. Dodd, L. Rossol, Eds. (Plenum, New York, 1979), pp. 207–234.
    [CrossRef]
  5. R. Dändliker, K. Hess, T. Sidler, “Hybrid Optoelectronic Object Recognition,” in Technical Digest, Conference on Lasers and Electrooptic Systems (Optical Society of America, Washington, D.C., 1982), paper THF3.
  6. C. B. Johnson, S. Nevin, J. Bebris, J. B. Abshire, Appl. Opt. 19, 3491 (1980).
    [CrossRef] [PubMed]
  7. R. Dändliker, Prog. Opt. 17, 40 (1980).
  8. J. C. Wyant, Laser Focus, 65 (May1982).
  9. M. R. Teague, J. Opt. Soc. Am. 70, 920 (1980).
    [CrossRef]

1982

J. C. Wyant, Laser Focus, 65 (May1982).

1980

1979

D. Casasent, D. Psaltis, Proc. Soc. Photo-Opt. Instrum. Eng. 201, 107 (1979).

A. D. Gara, Appl. Opt. 18, 172 (1979).
[CrossRef] [PubMed]

Abshire, J. B.

Bebris, J.

Casasent, D.

D. Casasent, D. Psaltis, Proc. Soc. Photo-Opt. Instrum. Eng. 201, 107 (1979).

Dändliker, R.

R. Dändliker, Prog. Opt. 17, 40 (1980).

R. Dändliker, K. Hess, T. Sidler, “Hybrid Optoelectronic Object Recognition,” in Technical Digest, Conference on Lasers and Electrooptic Systems (Optical Society of America, Washington, D.C., 1982), paper THF3.

Gara, A. D.

A. D. Gara, Appl. Opt. 18, 172 (1979).
[CrossRef] [PubMed]

A. D. Gara, “Optical Computing for Image Processing,” in Computer Vision and Sensor-Based Robots, G. G. Dodd, L. Rossol, Eds. (Plenum, New York, 1979), pp. 207–234.
[CrossRef]

Hess, K.

R. Dändliker, K. Hess, T. Sidler, “Hybrid Optoelectronic Object Recognition,” in Technical Digest, Conference on Lasers and Electrooptic Systems (Optical Society of America, Washington, D.C., 1982), paper THF3.

Johnson, C. B.

Nevin, S.

Psaltis, D.

D. Casasent, D. Psaltis, Proc. Soc. Photo-Opt. Instrum. Eng. 201, 107 (1979).

Sidler, T.

R. Dändliker, K. Hess, T. Sidler, “Hybrid Optoelectronic Object Recognition,” in Technical Digest, Conference on Lasers and Electrooptic Systems (Optical Society of America, Washington, D.C., 1982), paper THF3.

Teague, M. R.

Wyant, J. C.

J. C. Wyant, Laser Focus, 65 (May1982).

Appl. Opt.

J. Opt. Soc. Am.

Laser Focus

J. C. Wyant, Laser Focus, 65 (May1982).

Proc. Soc. Photo-Opt. Instrum. Eng.

D. Casasent, D. Psaltis, Proc. Soc. Photo-Opt. Instrum. Eng. 201, 107 (1979).

Prog. Opt.

R. Dändliker, Prog. Opt. 17, 40 (1980).

Other

A. D. Gara, “Optical Computing for Image Processing,” in Computer Vision and Sensor-Based Robots, G. G. Dodd, L. Rossol, Eds. (Plenum, New York, 1979), pp. 207–234.
[CrossRef]

R. Dändliker, K. Hess, T. Sidler, “Hybrid Optoelectronic Object Recognition,” in Technical Digest, Conference on Lasers and Electrooptic Systems (Optical Society of America, Washington, D.C., 1982), paper THF3.

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Figures (10)

Fig. 1
Fig. 1

Angular orientation α0 and lateral position xs,ys of the 2-D image of an object.

Fig. 2
Fig. 2

Hybrid optical–electronic system for robot vision.

Fig. 3
Fig. 3

Power spectrum (intensity): (a) circular scan, (b) signature P0(ϕ).

Fig. 4
Fig. 4

Digital correlation of signatures: (a) digitized signature P0(ϕ), (b) autocorrelation of P0(ϕ), (c) crosscorrelation C(α) of two scans.

Fig. 5
Fig. 5

Displacement fringes and phase: (a) detectors in the zero-order spot, (b) heterodyne signals for phase measurement.

Fig. 6
Fig. 6

Experimental verification of the shift theorem by heterodyne measurement of the phase ψ. Detector separation is a = 1/2R. Maximum displacement for ψ = ±180° is dmax = ±R. The accuracy of the phase measurement is Δψ = 1°, the corresponding resolution of the displacement is Δd/R = 0.6%.

Fig. 7
Fig. 7

Radial phase variations ψ(ρ) without (d = 0) and with (d = 0.03) object shift. Exact values (solid lines) and third-order approximations (dashed lines) are given.

Fig. 8
Fig. 8

Calculated angular phase variations ψ(ψ) for the same triangle as in Fig. 7.

Fig. 9
Fig. 9

Comparison of calculated (dashed) and measured angular phase variations ψ(ϕ) for the same object as in Figs. 7 and 8.

Fig. 10
Fig. 10

Detector array for simultaneous detection of linear and third-order phase terms.

Equations (15)

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O ^ ( p ) = d x 2 O ( x ) exp ( - i 2 π p · x ) ,
P ( ρ , ϕ ) = O ^ ( p ) 2 ,             ρ = p ,
P 0 ( ϕ ) = P ( ρ 0 , ϕ ) ,
C n ( α ) = d ϕ P 0 ( ϕ ) P n ( ϕ - α ) / p 0 p n ,
C r C n ( α max ) 1 ,
Q ^ ( p ) = O ^ ( p ) exp ( - i 2 π x s · p ) ,
ψ x = 2 π Δ p x s ,             ψ y = 2 π Δ q y s .
Q ^ ( p ) = O ^ exp ( - i 2 π x s · p ) = O ^ exp { i [ ψ ( p ) - 2 π x s · p ] } .
O ^ ( p , q ) = m , n 1 m ! n ! [ m + n p m q n O ^ ] 0 p m q n = m , n ( - i 2 π ) m + n m ! n ! M m n p m q n ,
M m n = d x d y O ( x , y ) x m y n = A m n + i B m n .
ψ ( p = 0 ) = 0 = B 00 ,             ( A 00 0 ) ,
ψ / p p = 0 = 0 = A 10 ,             ψ / q p = 0 = 0 = A 01 .
ψ ( p , q ) ( 2 π ) 3 m + n = 3 1 m ! n ! A m n c A 00 p m q n ,
ψ ( ρ , ϕ ) π 3 ρ 3 [ ( μ 30 + μ 12 ) cos ϕ + ( μ 21 + μ 03 ) sin ϕ + ( 1 3 μ 30 - μ 12 ) cos 3 ϕ + ( μ 21 - 1 3 μ 03 ) sin 3 ϕ ] ,
ψ s ( ρ , ϕ ) = - 2 π x s · p = - 2 π ρ ( x s cos ϕ + y s sin ϕ ) ,

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