Abstract

Matching of three-dimensional (3-D) objects is achieved by Wigner analysis of the correlation pattern between the phase-only holographic information of a reference object and that of a target object. First, holographic information on the reference object and on the target object is extracted by use of optical scanning holography as a form of electrical signal. This electrical information is then stored in a computer for digital processing. In the digital computer, the correlation between the phase-only information of the hologram of the reference object and that of the target object is calculated and analyzed by use of a Wigner distribution. The Wigner distribution yields a space-frequency map of the correlation pattern that indicates whether the 3-D image of the target object matches that of the reference object. When the 3-D image of the target object matches that of the reference object, the Wigner distribution gives a well-defined line that directly indicates the 3-D location of the matched target object. Optical experiments with digital processing are described to demonstrate the proposed matching technique.

© 2000 Optical Society of America

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References

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  1. A. K. Jain, P. J. Flynn, Three-Dimensional Object Recognition Systems (Elsevier, Amsterdam, 1993).
  2. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  3. N. Collings, Optical Pattern Recognition Using Holographic Techniques (Addison-Wesley, Reading, Mass., 1998).
  4. G. I. Vasilenko, L. M. Tsibul’kin, Image Recognition by Holography (Plenum, New York, 1989).
  5. E. C. Tam, F. T. S. Yu, D. A. Gregory, R. D. Juday, “Autonomous real-time object tracking with an adaptive joint transform correlator,” Opt. Eng. 29, 314–320 (1990).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. T. Kim, T.-C. 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]
  10. T. Kim, T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional image matching using two-dimensional optical heterodyne scanning,” Opt. Mem. Neural Network 8, 139–145 (1999).
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    [CrossRef]
  12. T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 521–527 (1985).
    [CrossRef]
  13. L. Onural, M. T. Ozgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A 9, 252–260 (1992).
    [CrossRef]
  14. H. J. Caulfield, “Automated analysis of particle holograms,” Opt. Eng. 24, 462–463 (1985).
    [CrossRef]
  15. C. S. Vikram, M. L. Billet, “Far-field holography at non-image planes for size analysis of small particles,” Appl. Phys. B 33, 149–153 (1984).
    [CrossRef]
  16. C. S. Vikram, M. L. Billet, “On the problem of automated analysis of particle holograms: proposal for direct diffraction measurements without holography,” Optik 73, 160–162 (1986).
  17. A. V. Oppengheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
    [CrossRef]
  18. D. Kermisch, “Image reconstruction from phase information only,” J. Opt. Soc. Am. A 60, 15–17 (1970).
    [CrossRef]
  19. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  20. P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Irwin, Boston, Mass., 1991).
  21. T. A. C. M. Classen, W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis. 1. Continuous-time signals,” Philips J. Res. 35, 217–250 (1980).
  22. T. A. C. M. Classen, W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis. 2. Discrete-time signals,” Philips J. Res. 35, 276–300 (1980).

1999 (3)

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

T. Kim, T.-C. 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]

T. Kim, T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional image matching using two-dimensional optical heterodyne scanning,” Opt. Mem. Neural Network 8, 139–145 (1999).

1998 (1)

1996 (1)

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

1992 (1)

1990 (1)

E. C. Tam, F. T. S. Yu, D. A. Gregory, R. D. Juday, “Autonomous real-time object tracking with an adaptive joint transform correlator,” Opt. Eng. 29, 314–320 (1990).
[CrossRef]

1986 (1)

C. S. Vikram, M. L. Billet, “On the problem of automated analysis of particle holograms: proposal for direct diffraction measurements without holography,” Optik 73, 160–162 (1986).

1985 (2)

1984 (2)

C. S. Vikram, M. L. Billet, “Far-field holography at non-image planes for size analysis of small particles,” Appl. Phys. B 33, 149–153 (1984).
[CrossRef]

J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

1981 (1)

A. V. Oppengheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

1980 (2)

T. A. C. M. Classen, W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis. 1. Continuous-time signals,” Philips J. Res. 35, 217–250 (1980).

T. A. C. M. Classen, W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis. 2. Discrete-time signals,” Philips J. Res. 35, 276–300 (1980).

1970 (1)

D. Kermisch, “Image reconstruction from phase information only,” J. Opt. Soc. Am. A 60, 15–17 (1970).
[CrossRef]

1964 (1)

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

Bamler, R.

J. Hofer-Alfeis, R. Bamler, “Three- and four-dimensional convolution by coherent optical filtering,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fienup, B. E. A. Saleh, eds., Proc. SPIE373, 77–87 (1981).
[CrossRef]

Banerjee, P. P.

P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Irwin, Boston, Mass., 1991).

Billet, M. L.

C. S. Vikram, M. L. Billet, “On the problem of automated analysis of particle holograms: proposal for direct diffraction measurements without holography,” Optik 73, 160–162 (1986).

C. S. Vikram, M. L. Billet, “Far-field holography at non-image planes for size analysis of small particles,” Appl. Phys. B 33, 149–153 (1984).
[CrossRef]

Caulfield, H. J.

H. J. Caulfield, “Automated analysis of particle holograms,” Opt. Eng. 24, 462–463 (1985).
[CrossRef]

Classen, T. A. C. M.

T. A. C. M. Classen, W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis. 1. Continuous-time signals,” Philips J. Res. 35, 217–250 (1980).

T. A. C. M. Classen, W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis. 2. Discrete-time signals,” Philips J. Res. 35, 276–300 (1980).

Collings, N.

N. Collings, Optical Pattern Recognition Using Holographic Techniques (Addison-Wesley, Reading, Mass., 1998).

Flynn, P. J.

A. K. Jain, P. J. Flynn, Three-Dimensional Object Recognition Systems (Elsevier, Amsterdam, 1993).

Gianino, P. D.

Gregory, D. A.

E. C. Tam, F. T. S. Yu, D. A. Gregory, R. D. Juday, “Autonomous real-time object tracking with an adaptive joint transform correlator,” Opt. Eng. 29, 314–320 (1990).
[CrossRef]

Hofer-Alfeis, J.

J. Hofer-Alfeis, R. Bamler, “Three- and four-dimensional convolution by coherent optical filtering,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fienup, B. E. A. Saleh, eds., Proc. SPIE373, 77–87 (1981).
[CrossRef]

Horner, J. L.

Jain, A. K.

A. K. Jain, P. J. Flynn, Three-Dimensional Object Recognition Systems (Elsevier, Amsterdam, 1993).

Juday, R. D.

E. C. Tam, F. T. S. Yu, D. A. Gregory, R. D. Juday, “Autonomous real-time object tracking with an adaptive joint transform correlator,” Opt. Eng. 29, 314–320 (1990).
[CrossRef]

Kermisch, D.

D. Kermisch, “Image reconstruction from phase information only,” J. Opt. Soc. Am. A 60, 15–17 (1970).
[CrossRef]

Kim, T.

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

T. Kim, T.-C. 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]

T. Kim, T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional image matching using two-dimensional optical heterodyne scanning,” Opt. Mem. Neural Network 8, 139–145 (1999).

Lim, J. S.

A. V. Oppengheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Mecklenbrauker, W. F. G.

T. A. C. M. Classen, W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis. 1. Continuous-time signals,” Philips J. Res. 35, 217–250 (1980).

T. A. C. M. Classen, W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis. 2. Discrete-time signals,” Philips J. Res. 35, 276–300 (1980).

Onural, L.

Oppengheim, A. V.

A. V. Oppengheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Ozgen, M. T.

Poon, T.-C.

T. Kim, T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional image matching using two-dimensional optical heterodyne scanning,” Opt. Mem. Neural Network 8, 139–145 (1999).

T. Kim, T.-C. 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]

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

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 521–527 (1985).
[CrossRef]

P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Irwin, Boston, Mass., 1991).

Rosen, J.

Shinoda, K.

T. Kim, T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional image matching using two-dimensional optical heterodyne scanning,” Opt. Mem. Neural Network 8, 139–145 (1999).

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

Suzuki, Y.

T. Kim, T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional image matching using two-dimensional optical heterodyne scanning,” Opt. Mem. Neural Network 8, 139–145 (1999).

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

Tam, E. C.

E. C. Tam, F. T. S. Yu, D. A. Gregory, R. D. Juday, “Autonomous real-time object tracking with an adaptive joint transform correlator,” Opt. Eng. 29, 314–320 (1990).
[CrossRef]

Tsibul’kin, L. M.

G. I. Vasilenko, L. M. Tsibul’kin, Image Recognition by Holography (Plenum, New York, 1989).

VanderLugt, A. B.

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

Vasilenko, G. I.

G. I. Vasilenko, L. M. Tsibul’kin, Image Recognition by Holography (Plenum, New York, 1989).

Vikram, C. S.

C. S. Vikram, M. L. Billet, “On the problem of automated analysis of particle holograms: proposal for direct diffraction measurements without holography,” Optik 73, 160–162 (1986).

C. S. Vikram, M. L. Billet, “Far-field holography at non-image planes for size analysis of small particles,” Appl. Phys. B 33, 149–153 (1984).
[CrossRef]

Wu, M.

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

Wu, M. H.

T. Kim, T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional image matching using two-dimensional optical heterodyne scanning,” Opt. Mem. Neural Network 8, 139–145 (1999).

Yu, F. T. S.

E. C. Tam, F. T. S. Yu, D. A. Gregory, R. D. Juday, “Autonomous real-time object tracking with an adaptive joint transform correlator,” Opt. Eng. 29, 314–320 (1990).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

C. S. Vikram, M. L. Billet, “Far-field holography at non-image planes for size analysis of small particles,” Appl. Phys. B 33, 149–153 (1984).
[CrossRef]

IEEE Trans. Inf. Theory (1)

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

J. Opt. Soc. Am. A (4)

Opt. Eng. (3)

H. J. Caulfield, “Automated analysis of particle holograms,” Opt. Eng. 24, 462–463 (1985).
[CrossRef]

E. C. Tam, F. T. S. Yu, D. A. Gregory, R. D. Juday, “Autonomous real-time object tracking with an adaptive joint transform correlator,” Opt. Eng. 29, 314–320 (1990).
[CrossRef]

T. Kim, T.-C. 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. Mem. Neural Network (1)

T. Kim, T.-C. Poon, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional image matching using two-dimensional optical heterodyne scanning,” Opt. Mem. Neural Network 8, 139–145 (1999).

Optik (1)

C. S. Vikram, M. L. Billet, “On the problem of automated analysis of particle holograms: proposal for direct diffraction measurements without holography,” Optik 73, 160–162 (1986).

Philips J. Res. (2)

T. A. C. M. Classen, W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis. 1. Continuous-time signals,” Philips J. Res. 35, 217–250 (1980).

T. A. C. M. Classen, W. F. G. Mecklenbrauker, “The Wigner distribution—a tool for time-frequency signal analysis. 2. Discrete-time signals,” Philips J. Res. 35, 276–300 (1980).

Proc. IEEE (2)

A. V. Oppengheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Optical scanning holography,” Proc. IEEE 84, 753–764 (1996).
[CrossRef]

Other (5)

J. Hofer-Alfeis, R. Bamler, “Three- and four-dimensional convolution by coherent optical filtering,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fienup, B. E. A. Saleh, eds., Proc. SPIE373, 77–87 (1981).
[CrossRef]

N. Collings, Optical Pattern Recognition Using Holographic Techniques (Addison-Wesley, Reading, Mass., 1998).

G. I. Vasilenko, L. M. Tsibul’kin, Image Recognition by Holography (Plenum, New York, 1989).

P. P. Banerjee, T.-C. Poon, Principles of Applied Optics (Irwin, Boston, Mass., 1991).

A. K. Jain, P. J. Flynn, Three-Dimensional Object Recognition Systems (Elsevier, Amsterdam, 1993).

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Figures (12)

Fig. 1
Fig. 1

Experimental setup for optical scanning holography: M’s, mirrors; -(d/dt), electronic differentiator; ⊗’s, electronic multipliers; LPF’s, low-pass filters; other abbreviations defined in text.

Fig. 2
Fig. 2

Flow chart for 3-D image matching by use of phase-only holographic information on the target and on the reference objects and the Wigner distribution.

Fig. 3
Fig. 3

3-D reference object R with Lx=Ly=1 cm and δz=5 cm.

Fig. 4
Fig. 4

(a) Cosine hologram of the reference object; (b) sine hologram of the reference object.

Fig. 5
Fig. 5

(a) Cosine hologram of the 3-D target object with different depth and transverse locations (Δx=0 mm, Δy=2.5 mm, and Δz=25 cm) but otherwise the same as the 3-D reference object. (b) As in (a) but for a sine hologram of the 3-D target object.

Fig. 6
Fig. 6

Wigner distribution of the correlation output when the 3-D target object and the 3-D reference object are displaced along the depth and transverse locations but are otherwise identical.

Fig. 7
Fig. 7

3-D target object T, which is composed of two slices that are identical to the reference object but located at different depths within the 3-D volume.

Fig. 8
Fig. 8

(a) Cosine hologram of target object, T shown in Fig. 7. (b) Sine hologram of target object T shown in Fig. 7.

Fig. 9
Fig. 9

Wigner distribution of the correlation: the 3-D target object is shown in Fig. 7, and the reference object is shown in Fig. 3.

Fig. 10
Fig. 10

3-D target object T, which is composed of two slices, the depths of whose 2-D patterns are the same as those of the reference object but different from those of the reference object.

Fig. 11
Fig. 11

(a) Cosine hologram of the target object shown in Fig. 10, (b) sine-hologram of the target object shown in Fig. 10.

Fig. 12
Fig. 12

Wigner distribution of the correlation output for a 3-D target object composed of two slices, the depths of whose 2-D patterns are the same as those of the reference object but different from those of the reference object.

Equations (25)

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Is(x, y; z)=|m1z(x, y)exp[j(ω0+Ω1)t]+m2z(x, y)exp[j(ω0+Ω2)t]|2,
miz(x, y)=mi(x, y)h(x, y; z),i=1, 2.
h(x, y; z)=jk02πzexp-jk02z(x2+y2),
g1(x, y)g2(x, y)= g1(x, y)g2(x-x, y-y)dxdy.
i(x, y; z)= Is(x, y; z)Io(x+x, y+y; z)dxdy=Is(x, y; z)  Io(x, y; z),
g(x, y)  h(x, y)= g*(x, y)h(x+x, y+y)dxdy.
Re[m1z(x, y)m2z*(x, y)]  Io(x, y; z),
Im[m1z(x, y)m2z*(x, y)]  Io(x, y; z),
iR(x, y)= Re[m1z(x, y)m2z*(x, y)  Io(x, y; z)]dz,
iI(x, y)= Im[m1z(x, y)m2z*(x, y)  Io(x, y; z)]dz,
Hsin(x, y)=k02πzsink02z(x2+y2)  Io(x, y; z)dz,
Hcos(x, y)=k02πzcosk02z(x2+y2)  Io(x, y; z)dz.
HIo(x, y)=Hcos(x, y; z)+jHsin(x, y; z)=k02πzexpjk02z(x2+y2)  Io(x, y; z)dz.
F{HR(x, y)}=Fk02πzexpjk02z(x2+y2)  R(x, y; z)dz=F*k02πzexpjk02z(x2+y2)F{R(x, y; z)}dzexpjz2k0(kx2+ky2)F{R(x, y; z)}dz,
F{R(x, y; z)}=A(kx, ky; z)exp[jϕ(kx, ky; z)].
F{HR(x, y)}=expjz2k0(kx2+ky2)A(kx, ky; z)×exp[jϕ(kx, ky; z)]dz=A(kx, ky; z)expjϕ(kx, ky; z)+z2k0(kx2+ky2)dz.
F{HR(x, y)}ϕ=exp{j arg[F{HR}]},
c(x, y)=F-1{exp[-j arg(F{HR})]exp[j arg(F{HT})]}=F-1{exp{-j[arg(F{HR})-arg(F{HT})]}},
F{HT}=|F{HT}|exp{j[arg(F{HT})]}=|F{HR}|expjarg(F{HR})+(Δxkx+Δyky)-Δz2k0(kx2+ky2).
arg(F{HT})=arg(F{HR})+(Δxkx+Δyky)-Δz2k0(kx2+ky2),
c(x, y)=F-1{C(kx, ky)}=F-1{exp{-j[arg(F{HR})-arg(F{HT})]}}=F-1exp-jarg(F{HR})-arg(F{HR})+(Δxkx+Δyky)-Δz2k0(kx2+ky2)=F-1expj(Δxkx+Δyky)-Δz2k0(kx2+ky2)expjk02Δz[(x-Δx)2+(y-Δy)2].
Wf(t, w)=-ft+τ2f*t-τ2exp(-jwτ)dτ,
Wf(t, ω)=2πδ(ω-αt).
|Wc(y, ky; x)|δky-k0Δz(y-Δy)×expjk02Δz(x-Δx)2=δky-k0Δz(y-Δy),
δky-k0Δz(y-Δy),

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