Abstract

We consider a new approach for enhancing the discrimination performance of the VanderLugt correlator. Instead of trying to optimize the correlation filter, or propose a new decision correlation peak detection criterion, we propose herein to denoise the correlation plane before applying the peak-to-correlation energy (PCE) criterion. For that purpose, we use a linear functional model to express a given correlation plane as a linear combination of the correlation peak, noise, and residual components. The correlation peak is modeled using an orthonormalized function and the singular value decomposition method. A set of training correlation planes is then selected to create the correlation noise components. Finally, an optimized correlation plane is reconstructed while discarding the noise components. Independently of the filter correlation used, this technique denoises the correlation plane by lowering the correlation noise magnitude in case of true correlation and decreases the false alarm rate when the target image does not belong to the desired class. Test results are presented, using a composite filter and a face recognition application, to verify the effectiveness of the proposed technique.

© 2012 Optical Society of America

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References

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  1. A. Alfalou and C. Brosseau, in Face Recognition, Milos Oravec, ed. (INTECH, 2010), pp. 354–380.
  2. F. T. S. Yu and S. Jutamulia, Optical Pattern Recognition (Cambridge University, 1998).
  3. A. A. S. Awwal, Appl. Opt. 49, B40 (2010).
    [CrossRef]
  4. P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and independent component analysis based approaches for biometric recognition,” in Face Recognition: Methods, Applications and Technology, (INTECH, to be published).
  5. A. Alfalou and C. Brosseau, Opt. Lett. 36, 645 (2011).
    [CrossRef]
  6. F. Dubois, Appl. Opt. 35, 4589 (1996).
    [CrossRef]
  7. R. D. Juday, J. Opt. Soc. Am. A 18, 1882 (2001).
    [CrossRef]
  8. H. Cardot, F. Ferraty, and P. Sarda, Statist. Probab. Lett. 45, 11 (1999).
    [CrossRef]
  9. A. Reynaud, S. Takerkart, G. S. Masson, and F. Chavane, NeuroImage 54, 1196 (2011).
    [CrossRef]
  10. M. Wall, A. Rechtsteiner, and L. Rocha, in A Practical Approach to Microarray Data Analysis, D. P. Berrar, W. Dubitzky, and M. Granzow, eds. (Springer, 2003), pp. 91–109.
  11. N. Gourier, D. Hall, and J. L. Crowley, in Proceedings of Pointing 2004, ICPR, International Workshop on Visual Observation of Deictic Gestures (2004).
  12. H. Zhou and T. H. Chao, Proc. SPIE 3715, 394 (1999).
    [CrossRef]

2011 (2)

A. Alfalou and C. Brosseau, Opt. Lett. 36, 645 (2011).
[CrossRef]

A. Reynaud, S. Takerkart, G. S. Masson, and F. Chavane, NeuroImage 54, 1196 (2011).
[CrossRef]

2010 (1)

2001 (1)

1999 (2)

H. Cardot, F. Ferraty, and P. Sarda, Statist. Probab. Lett. 45, 11 (1999).
[CrossRef]

H. Zhou and T. H. Chao, Proc. SPIE 3715, 394 (1999).
[CrossRef]

1996 (1)

Alam, M. S.

P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and independent component analysis based approaches for biometric recognition,” in Face Recognition: Methods, Applications and Technology, (INTECH, to be published).

Alfalou, A.

A. Alfalou and C. Brosseau, Opt. Lett. 36, 645 (2011).
[CrossRef]

A. Alfalou and C. Brosseau, in Face Recognition, Milos Oravec, ed. (INTECH, 2010), pp. 354–380.

P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and independent component analysis based approaches for biometric recognition,” in Face Recognition: Methods, Applications and Technology, (INTECH, to be published).

Awwal, A. A. S.

Brosseau, C.

A. Alfalou and C. Brosseau, Opt. Lett. 36, 645 (2011).
[CrossRef]

A. Alfalou and C. Brosseau, in Face Recognition, Milos Oravec, ed. (INTECH, 2010), pp. 354–380.

P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and independent component analysis based approaches for biometric recognition,” in Face Recognition: Methods, Applications and Technology, (INTECH, to be published).

Cardot, H.

H. Cardot, F. Ferraty, and P. Sarda, Statist. Probab. Lett. 45, 11 (1999).
[CrossRef]

Chao, T. H.

H. Zhou and T. H. Chao, Proc. SPIE 3715, 394 (1999).
[CrossRef]

Chavane, F.

A. Reynaud, S. Takerkart, G. S. Masson, and F. Chavane, NeuroImage 54, 1196 (2011).
[CrossRef]

Crowley, J. L.

N. Gourier, D. Hall, and J. L. Crowley, in Proceedings of Pointing 2004, ICPR, International Workshop on Visual Observation of Deictic Gestures (2004).

Dubois, F.

Ferraty, F.

H. Cardot, F. Ferraty, and P. Sarda, Statist. Probab. Lett. 45, 11 (1999).
[CrossRef]

Gourier, N.

N. Gourier, D. Hall, and J. L. Crowley, in Proceedings of Pointing 2004, ICPR, International Workshop on Visual Observation of Deictic Gestures (2004).

Hall, D.

N. Gourier, D. Hall, and J. L. Crowley, in Proceedings of Pointing 2004, ICPR, International Workshop on Visual Observation of Deictic Gestures (2004).

Juday, R. D.

Jutamulia, S.

F. T. S. Yu and S. Jutamulia, Optical Pattern Recognition (Cambridge University, 1998).

Katz, P.

P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and independent component analysis based approaches for biometric recognition,” in Face Recognition: Methods, Applications and Technology, (INTECH, to be published).

Masson, G. S.

A. Reynaud, S. Takerkart, G. S. Masson, and F. Chavane, NeuroImage 54, 1196 (2011).
[CrossRef]

Rechtsteiner, A.

M. Wall, A. Rechtsteiner, and L. Rocha, in A Practical Approach to Microarray Data Analysis, D. P. Berrar, W. Dubitzky, and M. Granzow, eds. (Springer, 2003), pp. 91–109.

Reynaud, A.

A. Reynaud, S. Takerkart, G. S. Masson, and F. Chavane, NeuroImage 54, 1196 (2011).
[CrossRef]

Rocha, L.

M. Wall, A. Rechtsteiner, and L. Rocha, in A Practical Approach to Microarray Data Analysis, D. P. Berrar, W. Dubitzky, and M. Granzow, eds. (Springer, 2003), pp. 91–109.

Sarda, P.

H. Cardot, F. Ferraty, and P. Sarda, Statist. Probab. Lett. 45, 11 (1999).
[CrossRef]

Takerkart, S.

A. Reynaud, S. Takerkart, G. S. Masson, and F. Chavane, NeuroImage 54, 1196 (2011).
[CrossRef]

Wall, M.

M. Wall, A. Rechtsteiner, and L. Rocha, in A Practical Approach to Microarray Data Analysis, D. P. Berrar, W. Dubitzky, and M. Granzow, eds. (Springer, 2003), pp. 91–109.

Yu, F. T. S.

F. T. S. Yu and S. Jutamulia, Optical Pattern Recognition (Cambridge University, 1998).

Zhou, H.

H. Zhou and T. H. Chao, Proc. SPIE 3715, 394 (1999).
[CrossRef]

Appl. Opt. (2)

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

NeuroImage (1)

A. Reynaud, S. Takerkart, G. S. Masson, and F. Chavane, NeuroImage 54, 1196 (2011).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

H. Zhou and T. H. Chao, Proc. SPIE 3715, 394 (1999).
[CrossRef]

Statist. Probab. Lett. (1)

H. Cardot, F. Ferraty, and P. Sarda, Statist. Probab. Lett. 45, 11 (1999).
[CrossRef]

Other (5)

M. Wall, A. Rechtsteiner, and L. Rocha, in A Practical Approach to Microarray Data Analysis, D. P. Berrar, W. Dubitzky, and M. Granzow, eds. (Springer, 2003), pp. 91–109.

N. Gourier, D. Hall, and J. L. Crowley, in Proceedings of Pointing 2004, ICPR, International Workshop on Visual Observation of Deictic Gestures (2004).

P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and independent component analysis based approaches for biometric recognition,” in Face Recognition: Methods, Applications and Technology, (INTECH, to be published).

A. Alfalou and C. Brosseau, in Face Recognition, Milos Oravec, ed. (INTECH, 2010), pp. 354–380.

F. T. S. Yu and S. Jutamulia, Optical Pattern Recognition (Cambridge University, 1998).

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Figures (3)

Fig. 1.
Fig. 1.

Illustrating the principle of correlation.

Fig. 2.
Fig. 2.

Synoptic diagram of the correlation plane denoising process.

Fig. 3.
Fig. 3.

The results obtained using different kinds of filters. The first row shows the ROC curves using a 3-reference segmented filter: (a) without optimization, (b) with our optimized method and using 12 correlation plane noise models. The second row shows the corresponding results using 5-references filters: (c) using a segmented composite filter, (d) using a OT MACH filter.

Equations (5)

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

Pc=i=1MβiYi+R,
Peak(i,j)=|sinc((ii0)22σi2)+sinc((jj0)22σj2)|,
Ypeak=[thin_SVD(Peak1)thin_SVD(Peakk)]=[V1tVkt].
Ynoise=[noise1noisen].
Y=[YpeakYnoise].

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