Abstract

A new concept for invariant pattern recognition is presented that uses object contour information. First, an angular signature of the object contour is obtained by a nonlinear operation applied to two-dimensional directional convolutions with a long, narrow kernel. The angular signature function is normalized by either its area or its energy to achieve quasi-invariance to scale. The resulting signature is then compared with template signatures for the invariant recognition for which an angular similarity measure is obtained from a one-dimensional correlation between the two signatures. Numerical experiments demonstrate that the method discussed exhibits invariance to shift and angular orientation and quasi-invariance to scale.

© 1993 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 1.
  2. D. Casasent, D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15, 1795–1799 (1976).
    [CrossRef] [PubMed]
  3. Y. Sheng, C. Lejeune, H. H. Arsenault, “Frequency-domain Fourier–Mellin descriptors for invariant pattern recognition,” Opt. Eng. 27, 354–357 (1988).
  4. Y. Hsu, H. H. Arsenault, “Pattern discrimination by multiple circular harmonic components,” Appl. Opt. 23, 841–844 (1984).
    [CrossRef] [PubMed]
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    [CrossRef]
  8. J. Rosen, J. Shamir, “Circular harmonic phase filters for efficient rotation-invariant pattern recognition,” Appl. Opt. 27, 2895–2899 (1988).
    [CrossRef] [PubMed]
  9. R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Commun. ACM 15, 11–15 (1972).
    [CrossRef]
  10. D. Casasent, S. I. Chien, “Efficient (ϕ, s) string code symbolic feature generation,” Opt. Commun. 67, 103–106 (1988).
    [CrossRef]
  11. Y. Naor, J. Shamir, “Angular feature mapping: an optical method,” Appl. Opt. 29, 713–716 (1990).
    [CrossRef] [PubMed]
  12. Y.-K. Lee, W. T. Rhodes, “Scale- and rotation-invariant pattern recognition by a rotating kernel min-max transformation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 146–155 (1990).
  13. Y.-K. Lee, W. T. Rhodes, “Feature detection and enhancement by a rotating kernel min–max transformation,” in Hybrid Image and Signal Processing II, D. P. Casasent, A. G. Tescher, eds. Proc. Soc. Photo-Opt. Instrum. Eng.1297, 154–159 (1900).
  14. Y.-K. Lee, W. T. Rhodes, “Nonlinear image processing by a rotating kernel transformation,” Opt. Lett. 15, 1383–1385 (1990).
    [CrossRef] [PubMed]
  15. Y.-K. Lee, “Nonlinear image processing and pattern analysis by rotating kernel transformation and optical Fourier transform.” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Ga., 1990).
  16. W. T. Rhodes, A. A. Sawchuk, “Incoherent optical processing,” in Information Processing, S. H. Lee, ed. (Springer-Verlag, New York, 1987), pp. 69–110.
  17. I. Glaser, “Incoherent information processing,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 389–509.
    [CrossRef]

1990 (2)

1988 (3)

J. Rosen, J. Shamir, “Circular harmonic phase filters for efficient rotation-invariant pattern recognition,” Appl. Opt. 27, 2895–2899 (1988).
[CrossRef] [PubMed]

Y. Sheng, C. Lejeune, H. H. Arsenault, “Frequency-domain Fourier–Mellin descriptors for invariant pattern recognition,” Opt. Eng. 27, 354–357 (1988).

D. Casasent, S. I. Chien, “Efficient (ϕ, s) string code symbolic feature generation,” Opt. Commun. 67, 103–106 (1988).
[CrossRef]

1985 (2)

1984 (2)

1976 (1)

1972 (1)

R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Arsenault, H. H.

Y. Sheng, C. Lejeune, H. H. Arsenault, “Frequency-domain Fourier–Mellin descriptors for invariant pattern recognition,” Opt. Eng. 27, 354–357 (1988).

Y. Hsu, H. H. Arsenault, “Pattern discrimination by multiple circular harmonic components,” Appl. Opt. 23, 841–844 (1984).
[CrossRef] [PubMed]

Casasent, D.

D. Casasent, S. I. Chien, “Efficient (ϕ, s) string code symbolic feature generation,” Opt. Commun. 67, 103–106 (1988).
[CrossRef]

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

Chien, S. I.

D. Casasent, S. I. Chien, “Efficient (ϕ, s) string code symbolic feature generation,” Opt. Commun. 67, 103–106 (1988).
[CrossRef]

Duda, R. O.

R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Glaser, I.

I. Glaser, “Incoherent information processing,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 389–509.
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 1.

Hart, P. E.

R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Hsu, Y.

Lee, Y.-K.

Y.-K. Lee, W. T. Rhodes, “Nonlinear image processing by a rotating kernel transformation,” Opt. Lett. 15, 1383–1385 (1990).
[CrossRef] [PubMed]

Y.-K. Lee, “Nonlinear image processing and pattern analysis by rotating kernel transformation and optical Fourier transform.” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Ga., 1990).

Y.-K. Lee, W. T. Rhodes, “Feature detection and enhancement by a rotating kernel min–max transformation,” in Hybrid Image and Signal Processing II, D. P. Casasent, A. G. Tescher, eds. Proc. Soc. Photo-Opt. Instrum. Eng.1297, 154–159 (1900).

Y.-K. Lee, W. T. Rhodes, “Scale- and rotation-invariant pattern recognition by a rotating kernel min-max transformation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 146–155 (1990).

Lejeune, C.

Y. Sheng, C. Lejeune, H. H. Arsenault, “Frequency-domain Fourier–Mellin descriptors for invariant pattern recognition,” Opt. Eng. 27, 354–357 (1988).

Naor, Y.

Psaltis, D.

Rhodes, W. T.

Y.-K. Lee, W. T. Rhodes, “Nonlinear image processing by a rotating kernel transformation,” Opt. Lett. 15, 1383–1385 (1990).
[CrossRef] [PubMed]

W. T. Rhodes, A. A. Sawchuk, “Incoherent optical processing,” in Information Processing, S. H. Lee, ed. (Springer-Verlag, New York, 1987), pp. 69–110.

Y.-K. Lee, W. T. Rhodes, “Scale- and rotation-invariant pattern recognition by a rotating kernel min-max transformation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 146–155 (1990).

Y.-K. Lee, W. T. Rhodes, “Feature detection and enhancement by a rotating kernel min–max transformation,” in Hybrid Image and Signal Processing II, D. P. Casasent, A. G. Tescher, eds. Proc. Soc. Photo-Opt. Instrum. Eng.1297, 154–159 (1900).

Rosen, J.

Sawchuk, A. A.

W. T. Rhodes, A. A. Sawchuk, “Incoherent optical processing,” in Information Processing, S. H. Lee, ed. (Springer-Verlag, New York, 1987), pp. 69–110.

Schils, G. F.

Shamir, J.

Sheng, Y.

Y. Sheng, C. Lejeune, H. H. Arsenault, “Frequency-domain Fourier–Mellin descriptors for invariant pattern recognition,” Opt. Eng. 27, 354–357 (1988).

Stark, H.

Sweeney, D. W.

Wu, R.

Appl. Opt. (5)

Commun. ACM (1)

R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

D. Casasent, S. I. Chien, “Efficient (ϕ, s) string code symbolic feature generation,” Opt. Commun. 67, 103–106 (1988).
[CrossRef]

Opt. Eng. (1)

Y. Sheng, C. Lejeune, H. H. Arsenault, “Frequency-domain Fourier–Mellin descriptors for invariant pattern recognition,” Opt. Eng. 27, 354–357 (1988).

Opt. Lett. (1)

Other (6)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 1.

Y.-K. Lee, W. T. Rhodes, “Scale- and rotation-invariant pattern recognition by a rotating kernel min-max transformation,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 146–155 (1990).

Y.-K. Lee, W. T. Rhodes, “Feature detection and enhancement by a rotating kernel min–max transformation,” in Hybrid Image and Signal Processing II, D. P. Casasent, A. G. Tescher, eds. Proc. Soc. Photo-Opt. Instrum. Eng.1297, 154–159 (1900).

Y.-K. Lee, “Nonlinear image processing and pattern analysis by rotating kernel transformation and optical Fourier transform.” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Ga., 1990).

W. T. Rhodes, A. A. Sawchuk, “Incoherent optical processing,” in Information Processing, S. H. Lee, ed. (Springer-Verlag, New York, 1987), pp. 69–110.

I. Glaser, “Incoherent information processing,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 389–509.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Illustration of the angular signature function P(θ) obtained by using f[Max, Min] = Max2(x, y), where ** represents 2-D convolution: (a) object, (b) four kernel orientations with a long, narrow 2-D kernel that is symmetric, (c) P(θ).

Fig. 2
Fig. 2

Approximate scale invariance obtained by normalizing the angular signature function P(θ) by its area to produce p(θ): (a) scale of ~ 2.8, (b) scale of ~ 1.4, (c) scale of 1.0.

Fig. 3
Fig. 3

Plots of the peak ratios rS [= B/(B + D′)] versus B, in which E is used as the template and the objects used are those shown in Fig. 4.

Fig. 4
Fig. 4

Results of recognizing (a) four different objects and (b) the letter E with four different scales (approximately) 1.0, 0.7, 1.3, and 2.0).

Fig. 5
Fig. 5

Numerical results of recognizing (a) similar and distorted objects and (b) rotated and noisy versions of the character E. The RKMT function and kernel used are the same as those used for Fig. 3.

Tables (2)

Tables Icon

Table 1 Numerical Results of P(θ) and p′(θ) for the Objects Shown In Fig. 3a

Tables Icon

Table 2 Results of Calculating Peak Ratioa rS with B = 0.5

Equations (11)

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P ( θ ) = - - f [ Max ( x , y ) , Min ( x , y ) ] × δ [ θ - θ max ( x , y ) ] d x d y ,
P ( θ i ) = m n f [ Max ( m , n ) , Min ( m , n ) ] × δ ( 0 ) [ θ i - θ Max ( m , n ) ] ,
δ ( 0 ) [ θ i - θ Max ( m , n ) ] = { 1 for θ i = θ Max 0 otherwise .
p ( θ ) = P ( θ ) 0 2 π P ( θ ) d θ .
D i j ( θ 0 ) = { 0 2 π [ p i ( θ ) - p j ( θ + θ 0 ) ] 2 d θ } 1 / 2
D i j ( θ 0 ) = [ 0 2 π p i 2 ( θ ) d θ + 0 2 π p j 2 ( θ ) d θ - 2 0 2 π p i ( θ ) p j ( θ + θ 0 ) d θ ] 1 / 2 ,
D i j ( θ ) 0 = 1 2 { 0 2 π [ p i ( θ ) - p j ( θ + θ 0 ) ] 2 d θ } 1 / 2 = 1 2 [ 0 2 π p i 2 ( θ ) d θ + 0 2 π p j 2 ( θ ) d θ - 2 0 2 π p i ( θ ) p j ( θ + θ 0 ) d θ ] 1 / 2 ,
p ( θ ) = P ( θ ) [ 0 2 π P 2 ( θ ) d θ ] 1 / 2 .
D i j ( θ 0 ) = [ 1 - 0 2 π p i ( θ ) p j ( θ + θ 0 ) d θ ] 1 / 2 = [ 1 - C i j ( θ 0 ) ] 1 / 2 ,
S = 1 B + D ( θ R ) ,
r s = B B + D ( θ R ) ,

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