Abstract

An automatic method for rotation-invariant three-dimensional (3-D) object recognition is proposed. The method is based on the use of 3-D information contained in the deformed fringe pattern obtained when a grating is projected onto an object’s surface. The proposed method was optically implemented by means of a two-cycle joint transform correlator. The rotation invariance is achieved by means of encoding with the fringe pattern a single component of the circular-harmonic expansion derived from the target. Thus the method is invariant for rotations around the line of sight. The whole experimental setup can be constructed with simple equipment. Experimental results show the utility of the proposed method.

© 2000 Optical Society of America

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  1. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
    [CrossRef]
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    [CrossRef] [PubMed]
  6. D. Mendlovic, N. Konforti, E. Marom, “Shift and projection invariant pattern recognition using logarithmic harmonics,” Appl. Opt. 29, 4784–4789 (1990).
    [CrossRef] [PubMed]
  7. E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
    [CrossRef]
  8. O. Faugeras, Three-Dimensional Computer Vision. A Geometric Viewpoint (MIT Press, Cambridge, Mass., 1993).
  9. A. Pu, R. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
    [CrossRef]
  10. 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]
  11. E. Paquet, P. García-Martínez, J. García, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. T. Poon, T. Kim, “Optical image recognition of three-dimensional objects,” Appl. Opt. 38, 370–381 (1999).
    [CrossRef]
  15. T. Kim, T. Poon, “Extraction of 3-D location of matched 3-D object using power fringe-adjusted filtering and Wigner analysis,” Opt. Eng. 38, 2176–2183 (1999).
    [CrossRef]
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    [CrossRef]
  17. J. J. Esteve-Taboada, D. Mas, J. García, “Three-dimensional object recognition by Fourier transform profilometry,” Appl. Opt. 38, 4760–4765 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  23. P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
    [CrossRef]
  24. F. T. S. Yu, X. Li, E. Tam, S. Jutamulia, D. A. Gregory, “Rotation invariant pattern recognition with a programmable joint transform correlator,” Appl. Opt. 28, 4725–4727 (1989).
    [CrossRef] [PubMed]
  25. D. Mendlovic, E. Marom, N. Konforti, “Complex reference-invariant joint-transform correlator,” Opt. Lett. 15, 1224–1226 (1990).
    [CrossRef] [PubMed]
  26. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef] [PubMed]
  27. M. Alam, Y. Gu, “Sobel operator based multiobject joint transform correlation,” Optik (Stuttgart) 100, 28–32 (1995).
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    [CrossRef] [PubMed]

2000 (1)

1999 (3)

1998 (3)

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

E. Paquet, P. García-Martínez, J. García, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[CrossRef]

J. Rosen, “Three-dimensional electro-optical correlation,” J. Opt. Soc. Am. A 15, 430–436 (1998).
[CrossRef]

1997 (1)

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

1995 (3)

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]

P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

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

1994 (1)

1993 (1)

1990 (3)

1989 (3)

1988 (1)

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

1987 (1)

1983 (1)

1982 (2)

1967 (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.

Denkewalter, R.

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

Esteve-Taboada, J. J.

Faugeras, O.

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

Ferreira, C.

P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

García, J.

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

E. Paquet, P. García-Martínez, J. García, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[CrossRef]

P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

García-Martínez, P.

E. Paquet, P. García-Martínez, J. García, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[CrossRef]

P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

Ghiglia, D. C.

Goodman, J. W.

Gregory, D. A.

Gu, Y.

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

Hsu, Y. N.

Ina, H.

Javidi, B.

Jutamulia, S.

Kim, T.

T. Poon, T. Kim, “Optical image recognition of three-dimensional objects,” Appl. Opt. 38, 370–381 (1999).
[CrossRef]

T. Kim, T. Poon, “Extraction of 3-D location of matched 3-D object using power fringe-adjusted filtering and Wigner analysis,” Opt. Eng. 38, 2176–2183 (1999).
[CrossRef]

Kobayashi, S.

Konforti, N.

D. Mendlovic, N. Konforti, E. Marom, “Shift and projection invariant pattern recognition using logarithmic harmonics,” Appl. Opt. 29, 4784–4789 (1990).
[CrossRef] [PubMed]

D. Mendlovic, E. Marom, N. Konforti, “Complex reference-invariant joint-transform correlator,” Opt. Lett. 15, 1224–1226 (1990).
[CrossRef] [PubMed]

E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
[CrossRef]

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

Li, X.

Lohmann, A. W.

Marom, E.

D. Mendlovic, E. Marom, N. Konforti, “Complex reference-invariant joint-transform correlator,” Opt. Lett. 15, 1224–1226 (1990).
[CrossRef] [PubMed]

D. Mendlovic, N. Konforti, E. Marom, “Shift and projection invariant pattern recognition using logarithmic harmonics,” Appl. Opt. 29, 4784–4789 (1990).
[CrossRef] [PubMed]

E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
[CrossRef]

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

Mas, D.

Mendlovic, D.

D. Mendlovic, N. Konforti, E. Marom, “Shift and projection invariant pattern recognition using logarithmic harmonics,” Appl. Opt. 29, 4784–4789 (1990).
[CrossRef] [PubMed]

D. Mendlovic, E. Marom, N. Konforti, “Complex reference-invariant joint-transform correlator,” Opt. Lett. 15, 1224–1226 (1990).
[CrossRef] [PubMed]

E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
[CrossRef]

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

Mutoh, K.

Paquet, E.

E. Paquet, P. García-Martínez, J. García, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[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]

Paris, D. P.

Poon, T.

T. Poon, T. Kim, “Optical image recognition of three-dimensional objects,” Appl. Opt. 38, 370–381 (1999).
[CrossRef]

T. Kim, T. Poon, “Extraction of 3-D location of matched 3-D object using power fringe-adjusted filtering and Wigner analysis,” Opt. Eng. 38, 2176–2183 (1999).
[CrossRef]

Prémont, G.

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]

Romero, L. A.

Rosen, J.

Shamir, J.

Sheng, Y.

Tajahuerce, E.

Takeda, M.

Tam, E.

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.

Appl. Opt. (12)

A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
[CrossRef] [PubMed]

Y. N. Hsu, H. H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
[CrossRef] [PubMed]

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

J. Rosen, J. Shamir, “Scale invariant pattern recognition with logarithmic radial harmonic filters,” Appl. Opt. 28, 240–244 (1989).
[CrossRef] [PubMed]

B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
[CrossRef] [PubMed]

F. T. S. Yu, X. Li, E. Tam, S. Jutamulia, D. A. Gregory, “Rotation invariant pattern recognition with a programmable joint transform correlator,” Appl. Opt. 28, 4725–4727 (1989).
[CrossRef] [PubMed]

D. Mendlovic, N. Konforti, E. Marom, “Shift and projection invariant pattern recognition using logarithmic harmonics,” Appl. Opt. 29, 4784–4789 (1990).
[CrossRef] [PubMed]

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

T. Poon, T. Kim, “Optical image recognition of three-dimensional objects,” Appl. Opt. 38, 370–381 (1999).
[CrossRef]

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

G. Prémont, Y. Sheng, “Fast design of circular harmonic filters using simulated annealing,” Appl. Opt. 32, 3116–3121 (1993).
[CrossRef]

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

IEEE Trans. Inf. Theory (1)

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

J. Opt. (1)

E. Paquet, P. García-Martínez, J. García, “Tridimensional invariant correlation based on phase-coded and sine-coded range images,” J. Opt. 29, 35–39 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Commun. (3)

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

P. García-Martínez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
[CrossRef]

Opt. Eng. (3)

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]

T. Kim, T. Poon, “Extraction of 3-D location of matched 3-D object using power fringe-adjusted filtering and Wigner analysis,” Opt. Eng. 38, 2176–2183 (1999).
[CrossRef]

Opt. Lett. (2)

Optik (Stuttgart) (1)

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

Other (1)

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

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Figures (8)

Fig. 1
Fig. 1

Optical arrangement for projecting the grating and grabbing the 2-D images.

Fig. 2
Fig. 2

Scheme of the procedure for obtaining the object-height information by fringe projection.

Fig. 3
Fig. 3

Experimental setup including the acquisition part and the JTC process.

Fig. 4
Fig. 4

Three-dimensional profile of the test objects.

Fig. 5
Fig. 5

Whole experimental process using the two-cycle modified JTC.

Fig. 6
Fig. 6

Experimental optical correlation for the scene shown in the upper left-hand image of Fig. 5. This image shows only the upper part of the JTC output and the zero order. A horizontal profile along the position marked with the narrow white lines is shown.

Fig. 7
Fig. 7

Input scene used to test the discrimination capability of the system. It is composed of the target (rotated this time 90° with respect to the object on the left in the upper left-hand image of Fig. 5) and of another object that, while having the same 2-D contour as the target, has a different 3-D shape.

Fig. 8
Fig. 8

Experimental optical correlation for the scene shown in Fig. 7. This image shows only the upper part of the JTC output and the zero order. A horizontal profile along the position marked with the narrow white lines is shown.

Equations (11)

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

sx, y=rx, yn=- qnx, yexp2πinf0x,
qnx, y=An expinϕx, y,
ϕx, y=-2πf0dhx, yL-hx, y.
s˜u, v=n=- Qnu-nf0, v  rx, y,
s˜u, v=Q1u, v  rx, y.
-1s˜u, v=A1rx, yexpiϕx, y.
fr, θ=M=- fMrexpiMθ,
fMr=12π02π fr, θexp-iMθdθ,
fr, θ+α=M=- fMrexpiMαexpiMθ.
CMα=2π expiMα0 |fMr|2rdr.
|gcx, y+A exp-i2πy/p|2=|gcx, y|2+A2+2A|gcx, y| cosφx, y-2πy/p=|gcx, y|2+A2+gc*x, yA exp-i2πy/p+gcx, yA expi2πy/p,

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