Abstract

A method of constructing optimal multicriteria filters for optical pattern recognition is presented. In the particular case of synthetic discriminant function filters, this method is illustrated for double-optimization criteria, and filters that are not overspecialized are obtained, in contrast with traditional techniques. Furthermore, a rigorous comparison between different filters, with respect to the considered criteria, is provided with this approach.

© 1990 Optical Society of America

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References

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1989

1987

1986

1985

1982

1976

1933

J. Neyman, E. S. Pearson, Philos. Trans. R. Soc. London 231, 35 (1933).
[CrossRef]

Arsenault, H. H.

Cassasent, D.

Ennis, D. J.

Farn, M. W.

Gianino, P. D.

Goodman, J. W.

Horner, J. L.

Hsu, Y. N.

Jared, D. A.

Kumar, B. V. K.

Mahalanobis, A.

Neyman, J.

J. Neyman, E. S. Pearson, Philos. Trans. R. Soc. London 231, 35 (1933).
[CrossRef]

Pearson, E. S.

J. Neyman, E. S. Pearson, Philos. Trans. R. Soc. London 231, 35 (1933).
[CrossRef]

Psaltis, D.

Therrien, C. W.

C. W. Therrien, Decision Estimation and Classification (Wiley, New York, 1989).

Vijaya Kumar, B. V. K.

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Figures (2)

Fig. 1
Fig. 1

Plot of an OCC, which divides the plane into regions of more-efficient and less-efficient filters with respect to the criteria. The lower part of the diagram could be reached only if weaker constraints than those for the OCC are used.

Fig. 2
Fig. 2

OCC for a SDF filter synthesis with 40 training images. Inset: a representation in logarithmic coordinates and with the POF filter and the amplitude-only coding filter (AOF).

Equations (8)

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h x l = d l , l = 1 , , P , X h = d ,
v ̃ = F v , v = F v ̃ , and A ̃ = F A F ,
h = A 1 X ( X A 1 X ) 1 d ,
E 1 = l = 1 P d l ( x l + n ) h 2 = h C h ,
E 2 = l = 1 P k = 1 N x ̃ k l h ̃ k 2 = h ̃ D ̃ H ̃ ,
E ( η ) = E 2 η E 1 h ̃ X ϒ .
E ( μ ) = μ E 2 + ( 1 μ ) E 1 h X Γ , with μ [ 0 , 1 ] ,
h ̃ = B ̃ ( μ ) 1 X ̃ [ X B ̃ ( μ ) 1 X ] 1 d , with B ̃ ( μ ) = μ D ̃ + ( 1 μ ) C ̃ .

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