Abstract

An automatic method for three-dimensional (3-D) shape recognition is proposed. It combines the Fourier transform profilometry technique with a real-time recognition setup such as the joint transform correlator (JTC). A grating is projected onto the object surface resulting in a distorted grating pattern. Since this pattern carries information about the depth and the shape of the object, their comparison provides a method for recognizing 3-D objects in real time. A two-cycle JTC is used for this purpose. Experimental results demonstrate the theory and show the utility of the new proposed method.

© 1999 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. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  3. A. Pu, R. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
    [CrossRef]
  4. E. Paquet, M. Rioux, H. H. Arsenault, “Invariant pattern recognition for range images using the phase Fourier transform and a neural network,” Opt. Eng. 34, 1178–1183 (1995).
    [CrossRef]
  5. J. Rosen, “Three-dimensional electro-optical correlation,” J. Opt. Soc. Am. A 15, 430–436 (1998).
    [CrossRef]
  6. J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. 37, 7538–7544 (1998).
    [CrossRef]
  7. O. Faugeras, Three-Dimensional Computer Vision. A Geometric Viewpoint (MIT Press, Cambridge, Mass., 1993).
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    [CrossRef] [PubMed]
  9. X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
    [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics, Physical and Quantum Electronics Series (McGraw-Hill, New York, 1968).
  11. T. Haist, M. Schönleber, H. J. Tiziani, “Positioning of noncooperative objects by use of joint transform correlation combined with fringe projection,” Appl. Opt. 37, 7553–7559 (1998).
    [CrossRef]
  12. M. Alam, Y. Gu, “Sobel operator based multiobject joint transform correlation,” Optik (Stuttgart) 100, 28–32 (1995).
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    [CrossRef] [PubMed]

1998 (3)

1997 (1)

A. Pu, R. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

1995 (2)

E. Paquet, M. Rioux, H. H. Arsenault, “Invariant pattern recognition for range images using the phase Fourier transform and a neural network,” Opt. Eng. 34, 1178–1183 (1995).
[CrossRef]

M. Alam, Y. Gu, “Sobel operator based multiobject joint transform correlation,” Optik (Stuttgart) 100, 28–32 (1995).

1990 (1)

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
[CrossRef]

1989 (1)

1983 (1)

1966 (1)

1964 (1)

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

Alam, M.

M. Alam, Y. Gu, “Sobel operator based multiobject joint transform correlation,” Optik (Stuttgart) 100, 28–32 (1995).

Arsenault, H. H.

E. Paquet, M. Rioux, H. H. Arsenault, “Invariant pattern recognition for range images using the phase Fourier transform and a neural network,” Opt. Eng. 34, 1178–1183 (1995).
[CrossRef]

Denkewalter, R.

A. Pu, R. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Faugeras, O.

O. Faugeras, Three-Dimensional Computer Vision. A Geometric Viewpoint (MIT Press, Cambridge, Mass., 1993).

Goodman, J. W.

C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef] [PubMed]

J. W. Goodman, Introduction to Fourier Optics, Physical and Quantum Electronics Series (McGraw-Hill, New York, 1968).

Gregory, D. A.

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
[CrossRef]

Gu, Y.

M. Alam, Y. Gu, “Sobel operator based multiobject joint transform correlation,” Optik (Stuttgart) 100, 28–32 (1995).

Haist, T.

Javidi, B.

Lu, X. J.

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
[CrossRef]

Mutoh, K.

Paquet, E.

E. Paquet, M. Rioux, H. H. Arsenault, “Invariant pattern recognition for range images using the phase Fourier transform and a neural network,” Opt. Eng. 34, 1178–1183 (1995).
[CrossRef]

Psaltis, D.

A. Pu, R. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Pu, A.

A. Pu, R. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

Rioux, M.

E. Paquet, M. Rioux, H. H. Arsenault, “Invariant pattern recognition for range images using the phase Fourier transform and a neural network,” Opt. Eng. 34, 1178–1183 (1995).
[CrossRef]

Rosen, J.

Schönleber, M.

Takeda, M.

Tiziani, H. J.

VanderLugt, A.

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

Weaver, C. S.

Yu, F. T. S.

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. B (1)

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (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. Eng. (2)

A. Pu, R. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

E. Paquet, M. Rioux, H. H. Arsenault, “Invariant pattern recognition for range images using the phase Fourier transform and a neural network,” Opt. Eng. 34, 1178–1183 (1995).
[CrossRef]

Optik (Stuttgart) (1)

M. Alam, Y. Gu, “Sobel operator based multiobject joint transform correlation,” Optik (Stuttgart) 100, 28–32 (1995).

Other (2)

J. W. Goodman, Introduction to Fourier Optics, Physical and Quantum Electronics Series (McGraw-Hill, New York, 1968).

O. Faugeras, Three-Dimensional Computer Vision. A Geometric Viewpoint (MIT Press, Cambridge, Mass., 1993).

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Figures (6)

Fig. 1
Fig. 1

Optical arrangement for projecting the grating and grabbing the input image.

Fig. 2
Fig. 2

Experimental setup including the acquisition part and the JTC process.

Fig. 3
Fig. 3

Scheme of the procedure for obtaining object-height information by fringe projection. For simplicity a linear phase factor has been removed in (e), and the objects are assumed to have uniform reflectivity.

Fig. 4
Fig. 4

(a) Input scene. (b) Reference object. Both images are displayed side by side on the SLM. Note that, despite the 3-D shapes of the two pawns being the same, the deformed grating pattern is different, owing to the different location of the grating.

Fig. 5
Fig. 5

(a) Input plane arrangement for the input scene f and the reference object s. (b) Output plane of the JTC. The asterisk indicates the cross-correlation operation.

Fig. 6
Fig. 6

Experimental optical correlation. The zero order in the lowest part of the image has been clipped for graphic purposes.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

g0x, y=n=- An exp2πinf0x,
f0=1p
gx, y=rx, yn=- An exp2πinf0x+sx, y,
gx, y=rx, yn=- An expi2πnf0x+nϕx, y,
ϕx, y=2πf0sx, y=2πf0CD¯.
gx, y=rx, yn=- qnx, yexp2πinf0x,
qnx, y=An expinϕx, y.
CD¯=-dhx, yL-hx, y,
ϕx, y=-2πf0dhx, yL-hx, y.
rx, yqnx, yrx, yAn expinkhx, y,
U0x0, y0=sx0, y0-Y/2+sx0, y0+Y/2,
sx0, y0=rx0, y0n=- qnx0, y0exp2πinf0x0,
sx0, y0=rx0, y0n=- qnx0, y0exp2πinf0x0.
U1x1, y1=Sx1λz, y1λzexp-iπy1Y/λz+Sx1λz, y1λzexpiπy1Y/λz,
Sx1λz, y1λz=Su, v=n=- Qnu-nf0, vrx0, y0,
U1u, v=n=- Qnu-nf0, vrx0, y0× exp-iπvY+n=- Qnu-nf0, vrx0, y0expiπvY.
U1u, v=Q1u-f0, vrx0, y0×exp-iπvY+Q1u-f0, vrx0, y0expiπvY.
-1U1u, v=A1rx1, y1exp{iϕx1, y1+2πf0x1}δx1, y1-Y/2+A1rx1, y1expiϕx1, y1+2πf0x1δx1, y1+Y/2.
Iu, v=|Q1u-f0, vrx0, y0|2+|Q1u-f0, vrx0, y0|2+Q1u-f0, vrx0, y0(Q1*u-f0, vrx0, y0*)exp-i2πvY+(Q1*u-f0, vrx0, y0*)Q1u-f0, vrx0, y0expi2πvY,
U2x1, y1=s˜x1, y1  s˜x1, y1+s˜x1, y1  s˜x1, y1+s˜x1, y1  s˜x1, y1δx1, y1-Y+s˜x1, y1  s˜x1, y1δx1, y1+Y,
s˜x1, y1=r-x1, -y1q1-x1, -y1exp-2πif0x1=r-x1, -y1A1 expiϕ-x1, -y1-2πf0x1,
s˜x1, y1=r-x1, -y1A1 expiϕ-x1, -y1-2πf0x1.
s˜x1, y1  s˜x1, y1=- s˜α, βs˜*α-x1, β-y1dαdβ=A1A1* exp-2πif0x1rx1, y1×expiϕx1, y1  rx1, y1×expiϕx1, y1,

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