Abstract

A novel recognition process is presented that is invariant under position, rotation, and scale changes. The recognition process is based on the Fang-Häusler transform [Appl. Opt. 29, 704 (1990)] and is applied to the autoconvolved image, rather than to the image itself. This makes the recognition process sensitive not only to the image histogram but also to its detailed pattern, resulting in a more reliable process that is also applicable to binary images. The proposed recognition process is demonstrated, by use of a fast algorithm, on several types of binary images with a real transform kernel, which contains amplitude, as well as phase, information. Good recognition is achieved for both synthetic and scanned images. In addition, it is shown that the Fang-Hausler transform is also invariant under a general affine transformation of the spatial coordinates.

© 1997 Optical Society of America

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  1. A. VanderLugt, “Signal detection by complex matched spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  2. Y. N. Hsu, H. H. Arsenault, G. April, “Rotation-invariant digital pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4012–4015 (1982).
    [CrossRef] [PubMed]
  3. O. Bryngdhal, “Geometrical transformations in optics,” J. Opt. Soc. Am. 64, 1092–1099 (1974).
    [CrossRef]
  4. J. Cederquist, A. M. Tai, “Computer-generated holograms for geometric transformations,” Appl. Opt. 23, 3099–3104 (1984).
    [CrossRef] [PubMed]
  5. D. Cassasent, D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15, 1795–1799 (1976).
    [CrossRef]
  6. D. Cassasent, D. Psaltis, “Deformation invariant, space-variant, optical pattern recognition,” Prog. Opt. 16, 298–302 (1978).
  7. D. Casassent, W.-T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343–2350 (1986).
    [CrossRef]
  8. B. V. K. Vijaya Kumar, E. Pochapsky, “Signal-to-noise ratio considerations in modified matched spatial filters,” J. Opt. Soc. Am. A 3, 777–786 (1986).
    [CrossRef]
  9. M. K. Hu, “Visual pattern recognition by moment invariance,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).
  10. D. Cassasent, L. Cheatham, D. Fetterly, “Optical system to compute intensity moments: design,” Appl. Opt. 21, 3292–3298 (1982).
    [CrossRef]
  11. J. Duvernoy, Y.-L. Sheng, “Effective optical processor for computing image moments at TV rate: use in handwriting recognition,” Appl. Opt. 26, 2320–2327 (1987).
    [CrossRef] [PubMed]
  12. M. Fang, G. Häusler, “Class of transforms invariant under shift, rotation, and scaling,” Appl. Opt. 29, 704–708 (1990).
    [CrossRef] [PubMed]
  13. E. Ghahramani, L. R. B. Patterson, “Scale translation, and rotation invariant orthonormalized optical/optoelectric neural networks,” Appl. Opt. 32, 7225–7232 (1993).
    [CrossRef] [PubMed]
  14. A. Oppenheim, J. Lin, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
    [CrossRef]
  15. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  16. L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation-invariant, phase-only, and binary phase-only correlation,” Appl. Opt. 28, 1251–1256 (1989).
    [CrossRef] [PubMed]
  17. B. Javidi, C.-J. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
    [CrossRef] [PubMed]
  18. B. Javidi, “Nonlinear joint transform,” Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef] [PubMed]
  19. C. J. Kuo, “Theoretical expression for the correlation signal of nonlinear joint-transform correlators,” Appl. Opt. 31, 6264–6271 (1992).
    [CrossRef] [PubMed]
  20. R. C. Gonzalez, R. D. Woods, Digital Image Processing (Addison-Wesley, 1993), Chap 7.

1993 (1)

E. Ghahramani, L. R. B. Patterson, “Scale translation, and rotation invariant orthonormalized optical/optoelectric neural networks,” Appl. Opt. 32, 7225–7232 (1993).
[CrossRef] [PubMed]

1992 (1)

C. J. Kuo, “Theoretical expression for the correlation signal of nonlinear joint-transform correlators,” Appl. Opt. 31, 6264–6271 (1992).
[CrossRef] [PubMed]

1990 (1)

M. Fang, G. Häusler, “Class of transforms invariant under shift, rotation, and scaling,” Appl. Opt. 29, 704–708 (1990).
[CrossRef] [PubMed]

1989 (2)

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation-invariant, phase-only, and binary phase-only correlation,” Appl. Opt. 28, 1251–1256 (1989).
[CrossRef] [PubMed]

B. Javidi, “Nonlinear joint transform,” Appl. Opt. 28, 2358–2367 (1989).
[CrossRef] [PubMed]

1988 (1)

B. Javidi, C.-J. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
[CrossRef] [PubMed]

1987 (1)

J. Duvernoy, Y.-L. Sheng, “Effective optical processor for computing image moments at TV rate: use in handwriting recognition,” Appl. Opt. 26, 2320–2327 (1987).
[CrossRef] [PubMed]

1986 (2)

D. Casassent, W.-T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343–2350 (1986).
[CrossRef]

B. V. K. Vijaya Kumar, E. Pochapsky, “Signal-to-noise ratio considerations in modified matched spatial filters,” J. Opt. Soc. Am. A 3, 777–786 (1986).
[CrossRef]

1984 (2)

J. Cederquist, A. M. Tai, “Computer-generated holograms for geometric transformations,” Appl. Opt. 23, 3099–3104 (1984).
[CrossRef] [PubMed]

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

1982 (2)

D. Cassasent, L. Cheatham, D. Fetterly, “Optical system to compute intensity moments: design,” Appl. Opt. 21, 3292–3298 (1982).
[CrossRef]

Y. N. Hsu, H. H. Arsenault, G. April, “Rotation-invariant digital pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4012–4015 (1982).
[CrossRef] [PubMed]

1981 (1)

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

1978 (1)

D. Cassasent, D. Psaltis, “Deformation invariant, space-variant, optical pattern recognition,” Prog. Opt. 16, 298–302 (1978).

1976 (1)

D. Cassasent, D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15, 1795–1799 (1976).
[CrossRef]

1974 (1)

O. Bryngdhal, “Geometrical transformations in optics,” J. Opt. Soc. Am. 64, 1092–1099 (1974).
[CrossRef]

1964 (1)

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

1962 (1)

M. K. Hu, “Visual pattern recognition by moment invariance,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).

April, G.

Y. N. Hsu, H. H. Arsenault, G. April, “Rotation-invariant digital pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4012–4015 (1982).
[CrossRef] [PubMed]

Arsenault, H. H.

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation-invariant, phase-only, and binary phase-only correlation,” Appl. Opt. 28, 1251–1256 (1989).
[CrossRef] [PubMed]

Y. N. Hsu, H. H. Arsenault, G. April, “Rotation-invariant digital pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4012–4015 (1982).
[CrossRef] [PubMed]

Bryngdhal, O.

O. Bryngdhal, “Geometrical transformations in optics,” J. Opt. Soc. Am. 64, 1092–1099 (1974).
[CrossRef]

Casassent, D.

D. Casassent, W.-T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343–2350 (1986).
[CrossRef]

Cassasent, D.

D. Cassasent, L. Cheatham, D. Fetterly, “Optical system to compute intensity moments: design,” Appl. Opt. 21, 3292–3298 (1982).
[CrossRef]

D. Cassasent, D. Psaltis, “Deformation invariant, space-variant, optical pattern recognition,” Prog. Opt. 16, 298–302 (1978).

D. Cassasent, D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15, 1795–1799 (1976).
[CrossRef]

Cederquist, J.

J. Cederquist, A. M. Tai, “Computer-generated holograms for geometric transformations,” Appl. Opt. 23, 3099–3104 (1984).
[CrossRef] [PubMed]

Chang, W.-T.

D. Casassent, W.-T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343–2350 (1986).
[CrossRef]

Cheatham, L.

D. Cassasent, L. Cheatham, D. Fetterly, “Optical system to compute intensity moments: design,” Appl. Opt. 21, 3292–3298 (1982).
[CrossRef]

Duvernoy, J.

J. Duvernoy, Y.-L. Sheng, “Effective optical processor for computing image moments at TV rate: use in handwriting recognition,” Appl. Opt. 26, 2320–2327 (1987).
[CrossRef] [PubMed]

Fang, M.

M. Fang, G. Häusler, “Class of transforms invariant under shift, rotation, and scaling,” Appl. Opt. 29, 704–708 (1990).
[CrossRef] [PubMed]

Fetterly, D.

D. Cassasent, L. Cheatham, D. Fetterly, “Optical system to compute intensity moments: design,” Appl. Opt. 21, 3292–3298 (1982).
[CrossRef]

Ghahramani, E.

E. Ghahramani, L. R. B. Patterson, “Scale translation, and rotation invariant orthonormalized optical/optoelectric neural networks,” Appl. Opt. 32, 7225–7232 (1993).
[CrossRef] [PubMed]

Gianino, P. D.

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

Gonzalez, R. C.

R. C. Gonzalez, R. D. Woods, Digital Image Processing (Addison-Wesley, 1993), Chap 7.

Häusler, G.

M. Fang, G. Häusler, “Class of transforms invariant under shift, rotation, and scaling,” Appl. Opt. 29, 704–708 (1990).
[CrossRef] [PubMed]

Horner, J. L.

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

Hsu, Y. N.

Y. N. Hsu, H. H. Arsenault, G. April, “Rotation-invariant digital pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4012–4015 (1982).
[CrossRef] [PubMed]

Hu, M. K.

M. K. Hu, “Visual pattern recognition by moment invariance,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).

Javidi, B.

B. Javidi, “Nonlinear joint transform,” Appl. Opt. 28, 2358–2367 (1989).
[CrossRef] [PubMed]

B. Javidi, C.-J. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
[CrossRef] [PubMed]

Kuo, C. J.

C. J. Kuo, “Theoretical expression for the correlation signal of nonlinear joint-transform correlators,” Appl. Opt. 31, 6264–6271 (1992).
[CrossRef] [PubMed]

Kuo, C.-J.

B. Javidi, C.-J. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
[CrossRef] [PubMed]

Leclerc, L.

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation-invariant, phase-only, and binary phase-only correlation,” Appl. Opt. 28, 1251–1256 (1989).
[CrossRef] [PubMed]

Lin, J.

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

Oppenheim, A.

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

Patterson, L. R. B.

E. Ghahramani, L. R. B. Patterson, “Scale translation, and rotation invariant orthonormalized optical/optoelectric neural networks,” Appl. Opt. 32, 7225–7232 (1993).
[CrossRef] [PubMed]

Pochapsky, E.

B. V. K. Vijaya Kumar, E. Pochapsky, “Signal-to-noise ratio considerations in modified matched spatial filters,” J. Opt. Soc. Am. A 3, 777–786 (1986).
[CrossRef]

Psaltis, D.

D. Cassasent, D. Psaltis, “Deformation invariant, space-variant, optical pattern recognition,” Prog. Opt. 16, 298–302 (1978).

D. Cassasent, D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15, 1795–1799 (1976).
[CrossRef]

Sheng, Y.

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation-invariant, phase-only, and binary phase-only correlation,” Appl. Opt. 28, 1251–1256 (1989).
[CrossRef] [PubMed]

Sheng, Y.-L.

J. Duvernoy, Y.-L. Sheng, “Effective optical processor for computing image moments at TV rate: use in handwriting recognition,” Appl. Opt. 26, 2320–2327 (1987).
[CrossRef] [PubMed]

Tai, A. M.

J. Cederquist, A. M. Tai, “Computer-generated holograms for geometric transformations,” Appl. Opt. 23, 3099–3104 (1984).
[CrossRef] [PubMed]

VanderLugt, A.

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

Vijaya Kumar, B. V. K.

B. V. K. Vijaya Kumar, E. Pochapsky, “Signal-to-noise ratio considerations in modified matched spatial filters,” J. Opt. Soc. Am. A 3, 777–786 (1986).
[CrossRef]

Woods, R. D.

R. C. Gonzalez, R. D. Woods, Digital Image Processing (Addison-Wesley, 1993), Chap 7.

Appl. Opt. (13)

Y. N. Hsu, H. H. Arsenault, G. April, “Rotation-invariant digital pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4012–4015 (1982).
[CrossRef] [PubMed]

J. Cederquist, A. M. Tai, “Computer-generated holograms for geometric transformations,” Appl. Opt. 23, 3099–3104 (1984).
[CrossRef] [PubMed]

D. Cassasent, D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15, 1795–1799 (1976).
[CrossRef]

D. Casassent, W.-T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343–2350 (1986).
[CrossRef]

D. Cassasent, L. Cheatham, D. Fetterly, “Optical system to compute intensity moments: design,” Appl. Opt. 21, 3292–3298 (1982).
[CrossRef]

J. Duvernoy, Y.-L. Sheng, “Effective optical processor for computing image moments at TV rate: use in handwriting recognition,” Appl. Opt. 26, 2320–2327 (1987).
[CrossRef] [PubMed]

M. Fang, G. Häusler, “Class of transforms invariant under shift, rotation, and scaling,” Appl. Opt. 29, 704–708 (1990).
[CrossRef] [PubMed]

E. Ghahramani, L. R. B. Patterson, “Scale translation, and rotation invariant orthonormalized optical/optoelectric neural networks,” Appl. Opt. 32, 7225–7232 (1993).
[CrossRef] [PubMed]

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

L. Leclerc, Y. Sheng, H. H. Arsenault, “Rotation-invariant, phase-only, and binary phase-only correlation,” Appl. Opt. 28, 1251–1256 (1989).
[CrossRef] [PubMed]

B. Javidi, C.-J. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
[CrossRef] [PubMed]

B. Javidi, “Nonlinear joint transform,” Appl. Opt. 28, 2358–2367 (1989).
[CrossRef] [PubMed]

C. J. Kuo, “Theoretical expression for the correlation signal of nonlinear joint-transform correlators,” Appl. Opt. 31, 6264–6271 (1992).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

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

IRE Trans. Inf. Theory (1)

M. K. Hu, “Visual pattern recognition by moment invariance,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).

J. Opt. Soc. Am. (1)

O. Bryngdhal, “Geometrical transformations in optics,” J. Opt. Soc. Am. 64, 1092–1099 (1974).
[CrossRef]

J. Opt. Soc. Am. A (1)

B. V. K. Vijaya Kumar, E. Pochapsky, “Signal-to-noise ratio considerations in modified matched spatial filters,” J. Opt. Soc. Am. A 3, 777–786 (1986).
[CrossRef]

Proc. IEEE (1)

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

Prog. Opt. (1)

D. Cassasent, D. Psaltis, “Deformation invariant, space-variant, optical pattern recognition,” Prog. Opt. 16, 298–302 (1978).

Other (1)

R. C. Gonzalez, R. D. Woods, Digital Image Processing (Addison-Wesley, 1993), Chap 7.

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Figures (9)

Fig. 1
Fig. 1

Block diagram of the recognition process.

Fig. 2
Fig. 2

(a) Test images A, B, and C and (b) their autoconvolutions, (c) their histograms, and (d) their FHT’s.

Fig. 3
Fig. 3

Comparison of the three synthetic images (76 dpi) that underwent a 0°–90° rotation. Correlation coefficients (a) ρ AA , ρ AB , and ρ AC , (b), ρ BB , ρ BA , and ρ BC , and (c) ρ CA , ρ CB , and ρ CC .

Fig. 4
Fig. 4

Improvement in ρ BB as the resolution increases to 288 dpi.

Fig. 5
Fig. 5

Comparison of the three synthetic images that underwent scale changes. The RP achieves better results than in the case of rotation. Correlation coefficients (a) ρ AA , ρ AB , and ρ AC , (b) ρ BB , ρ BA , and ρ BC , and (c) ρ CC , ρ CA , and ρ CB .

Fig. 6
Fig. 6

Correlation coefficients ρ ij for images A, B, and C after a combination of rotation, position (in pixels), and scaling (up to ×2) changes. The numbers on the x coordinate describe the rotation angle (upper row), the amount of translation (middle row), and the scaling factor (lower row).

Fig. 7
Fig. 7

Correlation coefficients ρ QQ and ρ QC after rotation, translation, and scaling for similar images. The vertical coordinate describes the scaling factor (upper row), the translation (middle row), and the rotation angle (bottom row).

Fig. 8
Fig. 8

Low-resolution (36 dpi) real images scanned by a CCD camera. (a) Lamed 1. (b) Lamed 2. (c) Gimel 1. (d) Gimel 2.

Fig. 9
Fig. 9

Matrix of the correlation coefficients calculated for the images of Fig. 8.

Equations (11)

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Fω=Ωf1xhω; f2xdx=Ω 1fxhω; 2fxdx,
x=A1x+B1y+C1, y=A2x+B2y+C2,
FTω=Ωf1xhω;f2xdx=Ωf1xhω;f2x1Jdx=1J=Ω f1xhω; f2xdx=1JFω,
f1x=f2x=fx,hω;f2x=exp-2πjωfx.
f1x=f2x=fx, hω;f2x=sin2πωfx.
Fω=Ω 1fxhω; 2fxdxαΔxΔy xi,jΩ 1fxi,jhω; 2fxi,j,
FωΔxΔyxi,jΩ 1fxi,jhω; 2fxi,jΔxΔy m 1fmhω; 2fmHm =ΔxΔy mf1,mhω;f2,mHm,
ρF1F2=RF1ω, F2ωRF1ω, F1ωRF2ω, F2ω1/2.
RF1ω, F2ω= F1ω-μF1F2ω-μF2dω, μF=Fωdωdω.
Fω=Ω1 f1xhω;f2xdx+Ω2g1xhω; g2xdx=Fω+Gω,
FAω=Ωfx+Aexp-2πjωfx+Adx=exp-2πjωAFω+A exp×-2πjωAΩexp-2πjωfxdx=k1Fω+Ak2ω.

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