Abstract

A novel, to our knowledge, method of distortion-invariant three-dimensional (3-D) pattern recognition is proposed. A single two-dimensional synthetic discriminant function is employed as a reference function in the 3-D correlator. Thus the proposed system is able to identify and locate any true-class object in the 3-D scene. Preliminary simulation and experimental results are presented.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Rosen, “Three-dimensional electro-optical correlation,” J. Opt. Soc. Am. A 15, 430–436 (1998).
    [CrossRef]
  2. J. Rosen, “Three-dimensional joint transform correlator,” Appl. Opt. 37, 7538–7544 (1998).
    [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 8, p. 251.
  4. D. F. Hester, D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
    [CrossRef] [PubMed]
  5. B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
    [CrossRef]
  6. A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987).
    [CrossRef] [PubMed]
  7. D. Mendlovic, E. Marom, N. Konforti, “Complex reference-invariant joint-transform correlator,” Opt. Lett. 15, 1224–1226 (1990); U. Mahlab, J. Rosen, J. Shamir, “Iterative generation of complex reference functions in a joint-transform correlator,” Opt. Lett. 16, 330–332 (1991).
    [CrossRef] [PubMed]
  8. R. Piestun, J. Rosen, J. Shamir, “Generation of continuous complex-valued functions for a joint transform correlator,” Appl. Opt. 20, 4398–4405 (1994).
    [CrossRef]
  9. J. Rosen, T. Kotzer, J. Shamir, “Optical implementation of phase extraction pattern recognition,” Opt. Commun. 83, 10–14 (1991).
    [CrossRef]

1998 (2)

1994 (1)

R. Piestun, J. Rosen, J. Shamir, “Generation of continuous complex-valued functions for a joint transform correlator,” Appl. Opt. 20, 4398–4405 (1994).
[CrossRef]

1992 (1)

1991 (1)

J. Rosen, T. Kotzer, J. Shamir, “Optical implementation of phase extraction pattern recognition,” Opt. Commun. 83, 10–14 (1991).
[CrossRef]

1990 (1)

1987 (1)

1980 (1)

Casasent, D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 8, p. 251.

Hester, D. F.

Konforti, N.

Kotzer, T.

J. Rosen, T. Kotzer, J. Shamir, “Optical implementation of phase extraction pattern recognition,” Opt. Commun. 83, 10–14 (1991).
[CrossRef]

Mahalanobis, A.

Marom, E.

Mendlovic, D.

Piestun, R.

R. Piestun, J. Rosen, J. Shamir, “Generation of continuous complex-valued functions for a joint transform correlator,” Appl. Opt. 20, 4398–4405 (1994).
[CrossRef]

Rosen, J.

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

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

R. Piestun, J. Rosen, J. Shamir, “Generation of continuous complex-valued functions for a joint transform correlator,” Appl. Opt. 20, 4398–4405 (1994).
[CrossRef]

J. Rosen, T. Kotzer, J. Shamir, “Optical implementation of phase extraction pattern recognition,” Opt. Commun. 83, 10–14 (1991).
[CrossRef]

Shamir, J.

R. Piestun, J. Rosen, J. Shamir, “Generation of continuous complex-valued functions for a joint transform correlator,” Appl. Opt. 20, 4398–4405 (1994).
[CrossRef]

J. Rosen, T. Kotzer, J. Shamir, “Optical implementation of phase extraction pattern recognition,” Opt. Commun. 83, 10–14 (1991).
[CrossRef]

Vijaya Kumar, B. V. K.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Schematic of the 3-D joint transform correlator equipped with the SDF.

Fig. 2
Fig. 2

Three images of plane P 3 out of 19 as observed from different points of view.

Fig. 3
Fig. 3

Intensity of the correlation results of the 3-D joint transform correlator.

Fig. 4
Fig. 4

Correlation peak of one true-class object versus the object’s rotation angle for the conventional reference function (rectangles) and for the SDF reference function (triangles).

Fig. 5
Fig. 5

Schematic of the experimental setup of the 3-D correlator.

Fig. 6
Fig. 6

Three images of the input scene out of 23, as observed from different points of view by the CCD camera on plane P 2.

Fig. 7
Fig. 7

(a) Magnitude and (b) phase angle of the MACE-SDF filter used in the experiment.

Fig. 8
Fig. 8

Intensity of the correlation plane resulting from the experiment of the 3-D correlation. The values of z 0 are given in centimeters.

Equations (12)

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

xi, yi=M0x cos θ+z sin θ, y,
g1x, y, z=o1x-x˜, y, z-z˜+r1x, y, z.
I4u, v, θ   g3xi, yi; θ×expi 2πλfuxi+vyidxidyi2,
I4u, v, θ  g1x, y, zexpi 2πλfuxi+vyiΔxΔyΔz2=g1x, y, zexpi 2πM0λfux cos θ+vy+uz sin θΔxΔyΔz2,
I4u, v, θ   g1x, y, zexpi 2πM0λfux cos θ+vy+uz sin θdxdydz2.
cx0, y0, z0   Ĩ4u cos θ, v, u sin θ×exp-i 2πM0λfx0u cos θ+y0v+z0u sin θdu cos θdvdu sin θ= g1x, y, zg1*x-x0, y-y0,× z-z0dxdydz.
 Fiu, v; θjR*u, vdudv=ci,j,  i=1, 2, j=1,, M,
Ei,j= |Fiu, v; θj|2|R*u, v|2dudv.
Eav=1/MR+DR,
Dk, k=i=12j=1M |Fi,jk|2.
F¯+R=c.
R=D-1F¯F¯+D-1F¯-1c.

Metrics