Abstract

A novel scale and shift invariant pattern recognition method is proposed to improve the discrimination capability and noise robustness by combining the bidimensional empirical mode decomposition with the Mellin radial harmonic decomposition. The flatness of its peak intensity response versus scale change is improved. This property is important, since we can detect a large range of scaled patterns (from 0.2 to 1) using a global threshold. Within this range, the correlation peak intensity is relatively uniform with a variance below 20%. This proposed filter has been tested experimentally to confirm the result from numerical simulation for cases both with and without input white noise.

© 2009 Optical Society of America

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References

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  1. D. Mendlovic, E. Maron, and N. Konforti, "Shift and scale invariant pattern recognition using Mellin radial harmonics," Opt. Commun. 67, 172-176(1988).
    [CrossRef]
  2. A. Moya, J. J. Esteve-Taboada, J. Garcia, and C. Ferreira, "Shift- and scale-invariant recognition of contour objects with logarithmic radial harmonic filters," Appl. Opt. 39, 5347-5351(2000).
    [CrossRef]
  3. Y.-S. Cheng and H.-C. Chen, "Improved performance of scale-invariant pattern recognition using a combined Mellin radial harmonic function and wavelet transform," Opt. Eng. 46, 107204 (Oct. 29, 2007)
    [CrossRef]
  4. J. C. Nunes, Y. Bouaoune, E. Deléchelle, O. Niang, and Ph. Bunel, "Image analysis by bidimensional empirical mode decomposition," Image Vision Comput. 21, 1019-1026(2003).
    [CrossRef]
  5. C. Damerval, S. Meignen, and V. Perrier, "A fast algorithm for bidimensional EMD," IEEE Signal Process Lett. 12, 701-704 (2005).
    [CrossRef]
  6. C. Damerval, "BEMD Toolbox : Bidimensional Empirical Mode Decomposition," http://ljk.imag.fr/membres/Christophe.Damerval/software.html.

2007

Y.-S. Cheng and H.-C. Chen, "Improved performance of scale-invariant pattern recognition using a combined Mellin radial harmonic function and wavelet transform," Opt. Eng. 46, 107204 (Oct. 29, 2007)
[CrossRef]

2005

C. Damerval, S. Meignen, and V. Perrier, "A fast algorithm for bidimensional EMD," IEEE Signal Process Lett. 12, 701-704 (2005).
[CrossRef]

2003

J. C. Nunes, Y. Bouaoune, E. Deléchelle, O. Niang, and Ph. Bunel, "Image analysis by bidimensional empirical mode decomposition," Image Vision Comput. 21, 1019-1026(2003).
[CrossRef]

2000

1988

D. Mendlovic, E. Maron, and N. Konforti, "Shift and scale invariant pattern recognition using Mellin radial harmonics," Opt. Commun. 67, 172-176(1988).
[CrossRef]

Bouaoune, Y.

J. C. Nunes, Y. Bouaoune, E. Deléchelle, O. Niang, and Ph. Bunel, "Image analysis by bidimensional empirical mode decomposition," Image Vision Comput. 21, 1019-1026(2003).
[CrossRef]

Bunel, Ph.

J. C. Nunes, Y. Bouaoune, E. Deléchelle, O. Niang, and Ph. Bunel, "Image analysis by bidimensional empirical mode decomposition," Image Vision Comput. 21, 1019-1026(2003).
[CrossRef]

Chen, H.-C.

Y.-S. Cheng and H.-C. Chen, "Improved performance of scale-invariant pattern recognition using a combined Mellin radial harmonic function and wavelet transform," Opt. Eng. 46, 107204 (Oct. 29, 2007)
[CrossRef]

Cheng, Y.-S.

Y.-S. Cheng and H.-C. Chen, "Improved performance of scale-invariant pattern recognition using a combined Mellin radial harmonic function and wavelet transform," Opt. Eng. 46, 107204 (Oct. 29, 2007)
[CrossRef]

Damerval, C.

C. Damerval, S. Meignen, and V. Perrier, "A fast algorithm for bidimensional EMD," IEEE Signal Process Lett. 12, 701-704 (2005).
[CrossRef]

Deléchelle, E.

J. C. Nunes, Y. Bouaoune, E. Deléchelle, O. Niang, and Ph. Bunel, "Image analysis by bidimensional empirical mode decomposition," Image Vision Comput. 21, 1019-1026(2003).
[CrossRef]

Esteve-Taboada, J. J.

Ferreira, C.

Garcia, J.

Konforti, N.

D. Mendlovic, E. Maron, and N. Konforti, "Shift and scale invariant pattern recognition using Mellin radial harmonics," Opt. Commun. 67, 172-176(1988).
[CrossRef]

Maron, E.

D. Mendlovic, E. Maron, and N. Konforti, "Shift and scale invariant pattern recognition using Mellin radial harmonics," Opt. Commun. 67, 172-176(1988).
[CrossRef]

Meignen, S.

C. Damerval, S. Meignen, and V. Perrier, "A fast algorithm for bidimensional EMD," IEEE Signal Process Lett. 12, 701-704 (2005).
[CrossRef]

Mendlovic, D.

D. Mendlovic, E. Maron, and N. Konforti, "Shift and scale invariant pattern recognition using Mellin radial harmonics," Opt. Commun. 67, 172-176(1988).
[CrossRef]

Moya, A.

Niang, O.

J. C. Nunes, Y. Bouaoune, E. Deléchelle, O. Niang, and Ph. Bunel, "Image analysis by bidimensional empirical mode decomposition," Image Vision Comput. 21, 1019-1026(2003).
[CrossRef]

Nunes, J. C.

J. C. Nunes, Y. Bouaoune, E. Deléchelle, O. Niang, and Ph. Bunel, "Image analysis by bidimensional empirical mode decomposition," Image Vision Comput. 21, 1019-1026(2003).
[CrossRef]

Perrier, V.

C. Damerval, S. Meignen, and V. Perrier, "A fast algorithm for bidimensional EMD," IEEE Signal Process Lett. 12, 701-704 (2005).
[CrossRef]

Appl. Opt.

IEEE Signal Process Lett.

C. Damerval, S. Meignen, and V. Perrier, "A fast algorithm for bidimensional EMD," IEEE Signal Process Lett. 12, 701-704 (2005).
[CrossRef]

Image Vision Comput.

J. C. Nunes, Y. Bouaoune, E. Deléchelle, O. Niang, and Ph. Bunel, "Image analysis by bidimensional empirical mode decomposition," Image Vision Comput. 21, 1019-1026(2003).
[CrossRef]

Opt. Commun.

D. Mendlovic, E. Maron, and N. Konforti, "Shift and scale invariant pattern recognition using Mellin radial harmonics," Opt. Commun. 67, 172-176(1988).
[CrossRef]

Opt. Eng.

Y.-S. Cheng and H.-C. Chen, "Improved performance of scale-invariant pattern recognition using a combined Mellin radial harmonic function and wavelet transform," Opt. Eng. 46, 107204 (Oct. 29, 2007)
[CrossRef]

Other

C. Damerval, "BEMD Toolbox : Bidimensional Empirical Mode Decomposition," http://ljk.imag.fr/membres/Christophe.Damerval/software.html.

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Figures (5)

Fig. 1.
Fig. 1.

The reference object and the BEMD components. (a) F16 fighter as the reference object. (b) to (g): the corresponding BIMFs of the F16 (from BIMF1 to BIMF6).(h) the residue of BEMD decomposition.

Fig. 2.
Fig. 2.

Shift and scale invariance test. (a) Four scaled versions of the F16 fighter with scale factors β=1,0.8,0.5,0.2. (b) to (g): The correlation intensity distribution and the corresponding cross-sectional intensity distribution when using (b) and (c) the RHF, (d) and (e) the PORHF, (f) and (g) the BEMD_RHF.

Fig. 3.
Fig. 3.

Distinguishing the scaled versions of the reference pattern from the false target. (a) The input image with 4 scaled F16 and 1 Mig25. (b) The correlation intensity distribution. (c) The corresponding cross-sectional intensity distribution.

Fig. 4.
Fig. 4.

Comparing the normalized correlation peak intensity of BEMD_RHF with that of the MRHW when the scale factor changes from 0.1 to 1.

Fig. 5.
Fig. 5.

Noise robustness test. (a),(d),(g),(j), (m) and (p) The input images with SNR=25, 15, 5, 0, -2, and -5; (b), (e), (h), (k), (n), (q) and (c), (f), (i), (l), (o), (r) The corresponding correlation intensity distribution planes and the corresponding cross-sectional intensity distributions through the correlation peaks

Equations (17)

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f(r,θ)=m=fm(θ)ri2πm1
fm(θ;x0,y0)=L1 r0R0f(r,θ;x0,y0)ri2πm1rdr
fM(r,θ;x0,y0)=fM (θ;x0,y0) ri2πM1
Cgf(x1,y1;x0,y0)2=02πr0R0g(r,θ;x1,y1)fM*(r,θ;x0,y0)rdrdθ2
=02πr0R0[m=gm(θ;x1,y1)ri2πm1][fM*(θ;x0,y0)ri2πM1]rdrdθ2
=02πr0R0m=[gm(θ;x1,y1)fM*(θ;x0,y0)ri2π(mM)1]drdθ2
={0mM02πr0R0gM(θ;x1,y1)fM*(θ;x0,y0)r1drdθ2m=M
=L02πgM(θ;x1,y1)fM*(θ;x0,y0)dθ2
Cgβf(x1,y1;x0,y0)2=02πr0R0g(rβ,θ;x1,y1)fM*(r,θ;x0,y0)rdrdθ2
=02πr0R0[m=gm(θ;x1,y1)ri2πm1β1i2πm]×
[fM*(θ;x0,y0)ri2πM1]rdrdθ2
=β2 L02πgM(θ;x1,y1)fM*(θ;x0,y0)dθ2
=β2 Cgf(x1,y1;x0,y0)2
I=i=1n(Fi)+R
Cgf(x1,y1;x0,y0)=radial{F1(f)}F1(g)
Resid(g4)=gF1(g)F2(g)F3(g)
Cgf(x1,y1;x0,y0)=radial{F1(f)}Edge(Resid(g4))

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