Abstract

A new method for pattern recognition that is invariant under changes of position, orientation, intensity, and scale is presented. The centroids of objects provide unique points that are related to the energy distribution. For obtaining more such unique points a conformal transform can be used to rearrange the energy distribution of the object. By means of the conformal transform many different centroids can be produced from the same object. A useful pattern-recognition and object-registration method that yields a position-, rotation-, intensity-, and scale-invariant feature vector based on these centroids can be created.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans. Inf. Theory. IT-8, 179–187 (1962).
  2. Y. S. Abu-Mostafa, D. Psaltis, “Recognition aspect of moment invariants,” IEEE Trans. Pattern Anal. Mach. Intel. PAMI-6, 698–706 (1984).
    [CrossRef]
  3. Y. Sheng, J. Duvernoy, “Circular Fourier–radial Mellin descriptors (FMDS) for pattern recognition,” J. Opt. Soc. Am. A 3, 885–888 (1986).
    [CrossRef] [PubMed]
  4. Y. Sheng, H. H. Arsenault, “Experiments on pattern recognition using invariant Fourier–Mellin descriptors,” J. Opt. Soc. Am. A 3, 771–776 (1986).
    [CrossRef] [PubMed]
  5. Y. Sheng, “Fourier–Mellin spatial filters for invariant pattern recognition,” Opt. Eng. 28, 494–499 (1989).
    [CrossRef]
  6. M. Fang, G. Hansler, “Class of transforms for invariant pattern recognition,” Appl. Opt. 29, 704–708 (1990).
    [CrossRef] [PubMed]
  7. R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992), p. 497.
  8. J. Duvernoy, “Optical–digital processing of directional terrain textures invariant under translation, rotation, and change of scale,” Appl. Opt. 23, 828–837 (1984).
    [CrossRef]
  9. T. Minemoto, K. Hara, “Hybrid pattern recognition by features extracted from object patterns and Fraunhofer diffraction patterns: development of a more useful method,” Appl. Opt. 25, 4065–4070 (1986).
    [CrossRef] [PubMed]
  10. V. Divijakovic, S. D. Ristov, B. Vojnovic, “Application of circular scanning of images to invariant pattern recognition,” Opt. Eng. 31, 1032–1037 (1992).
    [CrossRef]
  11. G. M. Morris, N. George, “Space and wavelength dependence of a dispersion-compensated matched filter,” Appl. Opt. 19, 3843–3850 (1980).
    [CrossRef] [PubMed]
  12. S. P. Almeida, S. K. Case, W. J. Dallas, “Multispectral size-averaged incoherent spatial filtering,” Appl. Opt. 18, 4025–4029 (1979).
    [CrossRef] [PubMed]
  13. K. Mersereau, G. M. Morris, “Scale-, rotation-, and shift-invariant image recognition,” Appl. Opt. 25, 2338–2342 (1986).
    [CrossRef]
  14. S. Chang, H. H. Arsenault, “Invariant optical-pattern recognition based on a contour bank,” Appl. Opt. 33, 3076–3085 (1994).
    [CrossRef] [PubMed]
  15. S. Chang, H. H. Arsenault, “Invariant pattern recognition using a calculus descriptor,” Opt. Eng. 33, 4045–4050 (1994).
    [CrossRef]
  16. S. Chang, C. P. Grover are preparing a paper entitled, “Optical centroid detection” for submission to Applied Optics.

1994

S. Chang, H. H. Arsenault, “Invariant optical-pattern recognition based on a contour bank,” Appl. Opt. 33, 3076–3085 (1994).
[CrossRef] [PubMed]

S. Chang, H. H. Arsenault, “Invariant pattern recognition using a calculus descriptor,” Opt. Eng. 33, 4045–4050 (1994).
[CrossRef]

1992

V. Divijakovic, S. D. Ristov, B. Vojnovic, “Application of circular scanning of images to invariant pattern recognition,” Opt. Eng. 31, 1032–1037 (1992).
[CrossRef]

1990

1989

Y. Sheng, “Fourier–Mellin spatial filters for invariant pattern recognition,” Opt. Eng. 28, 494–499 (1989).
[CrossRef]

1986

1984

Y. S. Abu-Mostafa, D. Psaltis, “Recognition aspect of moment invariants,” IEEE Trans. Pattern Anal. Mach. Intel. PAMI-6, 698–706 (1984).
[CrossRef]

J. Duvernoy, “Optical–digital processing of directional terrain textures invariant under translation, rotation, and change of scale,” Appl. Opt. 23, 828–837 (1984).
[CrossRef]

1980

1979

1962

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

Abu-Mostafa, Y. S.

Y. S. Abu-Mostafa, D. Psaltis, “Recognition aspect of moment invariants,” IEEE Trans. Pattern Anal. Mach. Intel. PAMI-6, 698–706 (1984).
[CrossRef]

Almeida, S. P.

Arsenault, H. H.

Case, S. K.

Chang, S.

S. Chang, H. H. Arsenault, “Invariant optical-pattern recognition based on a contour bank,” Appl. Opt. 33, 3076–3085 (1994).
[CrossRef] [PubMed]

S. Chang, H. H. Arsenault, “Invariant pattern recognition using a calculus descriptor,” Opt. Eng. 33, 4045–4050 (1994).
[CrossRef]

S. Chang, C. P. Grover are preparing a paper entitled, “Optical centroid detection” for submission to Applied Optics.

Dallas, W. J.

Divijakovic, V.

V. Divijakovic, S. D. Ristov, B. Vojnovic, “Application of circular scanning of images to invariant pattern recognition,” Opt. Eng. 31, 1032–1037 (1992).
[CrossRef]

Duvernoy, J.

Fang, M.

George, N.

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992), p. 497.

Grover, C. P.

S. Chang, C. P. Grover are preparing a paper entitled, “Optical centroid detection” for submission to Applied Optics.

Hansler, G.

Hara, K.

Hu, M. K.

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

Mersereau, K.

Minemoto, T.

Morris, G. M.

Psaltis, D.

Y. S. Abu-Mostafa, D. Psaltis, “Recognition aspect of moment invariants,” IEEE Trans. Pattern Anal. Mach. Intel. PAMI-6, 698–706 (1984).
[CrossRef]

Ristov, S. D.

V. Divijakovic, S. D. Ristov, B. Vojnovic, “Application of circular scanning of images to invariant pattern recognition,” Opt. Eng. 31, 1032–1037 (1992).
[CrossRef]

Sheng, Y.

Vojnovic, B.

V. Divijakovic, S. D. Ristov, B. Vojnovic, “Application of circular scanning of images to invariant pattern recognition,” Opt. Eng. 31, 1032–1037 (1992).
[CrossRef]

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992), p. 497.

Appl. Opt.

IEEE Trans. Pattern Anal. Mach. Intel.

Y. S. Abu-Mostafa, D. Psaltis, “Recognition aspect of moment invariants,” IEEE Trans. Pattern Anal. Mach. Intel. PAMI-6, 698–706 (1984).
[CrossRef]

IRE Trans. Inf. Theory.

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

J. Opt. Soc. Am. A

Opt. Eng.

Y. Sheng, “Fourier–Mellin spatial filters for invariant pattern recognition,” Opt. Eng. 28, 494–499 (1989).
[CrossRef]

V. Divijakovic, S. D. Ristov, B. Vojnovic, “Application of circular scanning of images to invariant pattern recognition,” Opt. Eng. 31, 1032–1037 (1992).
[CrossRef]

S. Chang, H. H. Arsenault, “Invariant pattern recognition using a calculus descriptor,” Opt. Eng. 33, 4045–4050 (1994).
[CrossRef]

Other

S. Chang, C. P. Grover are preparing a paper entitled, “Optical centroid detection” for submission to Applied Optics.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992), p. 497.

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 (7)

Fig. 1
Fig. 1

Diagram of a pattern-recognition system with image transforms.

Fig. 2
Fig. 2

Diagram of a pattern-recognition system with conformal transforms.

Fig. 3
Fig. 3

Schematic of a hybrid pattern-recognition system for producing centroid invariants.

Fig. 4
Fig. 4

Aircraft images used in the simulations (from left to right and top to bottom): N128, Nj128, Mig25, N64, N256, F102, Jaguar, F18.

Fig. 5
Fig. 5

(a) The input aircraft image. (b) The centroid peaks of the input aircraft image. (c) The mass peaks of the input aircraft image.

Fig. 6
Fig. 6

Four centroids and their six centroid phasors.

Fig. 7
Fig. 7

Three-dimensional plot of the recognition results from the eight aircraft images: Serial 6 (S6) is the result from a six-component vector. Serial 5 (S5) is the result from a five-component vector. Serial 4 (S4) is the result from a four-component vector. Serial 3 (S3) is the result from a three-component vector. Serial 2 (S2) is the result from a two-component vector. Serial 1 (S1) is the result from a one-component vector.

Tables (3)

Tables Icon

Table 1 Centroid Invariants of Eight Aircrafta

Tables Icon

Table 2 Centroid Invariants of Eight Aircraft

Tables Icon

Table 3 Distances of Vectorsa

Equations (23)

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

Cfx, y= xfx, ydxdy fx, ydxdy,  yfx, ydxdy fx, ydxdy.
Cλfx, y= xλfx, ydxdy λfx, ydxdy,  yλfx, ydxdy λfx, ydxdy=λ  xfx, ydxdyλ  fx, ydxdy, λ  yfx, ydxdyλ  fx, ydxdy=Cfx, y.
Hλf=HλfH=λHf,
Pij=Pixi, yi-Pjxj, yj=pij expjΦ.
pij=xi-xj2-yi-yj21/2,
Φ=arctanyi-yjxi-xj.
m=1M0 pij2,
M0= fx, ydxdy.
mk=pijk2M0k=1kxi-xj2+1kyi-yj2 fxk, ykdxdy=1k2 pij21k2 M0,
m=m1, m2,, mi, mn.
Hfx, y=fx, yb.
CHλfx, y=Cλbfbx, y=λbxfbx, ydxdyλbfbx, ydxdy, λbyfbx, ydxdyλbfbx, ydxdy=CHfx, y.
M0=R2 fx, ydxdy=fx, y  Dx, y|x=0, y=0,
Dx, y=1x2+y2r20otherwise.
lx, y=C |mxr, yr-mxi, yi|ma,
ma=mxr, yr+mxi, yi2.
fx, y=True objectlx, ydFalse objectotherwise,
Lx, y=jn Cj|mjxr, yr-mjxi, yi|maj,
fx, y=True objectLx, ydFalse objectotherwise,
Hfx, y=f2x, y.
Hfx, y=f2x, y.
Hfx, y=fx, yfx, y1300otherwise.
Hfx, y=1fx, y1450otherwise.

Metrics