Abstract

A generalized approach for pattern recognition using spatial filters with reduced tolerance requirements was described in some recent publications. This approach leads to various possible implementations such as the composite matched filter, the circular harmonic matched filter, or the composite circular harmonic matched filter. The present work describes new examples leading to very high selectivity filters retaining rotation invariance and reduced requirements on device resolution. Computer simulations and laboratory experiments show the advantages of this approach.

© 1988 Optical Society of America

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References

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  1. J. Shamir, H. J. Caulfield, J. Rosen, “Pattern Recognition Using Reduced Information Content Filters,” Appl. Opt. 26, 2311 (1987).
    [CrossRef] [PubMed]
  2. J. Rosen, J. Shamir, “Distortion Invariant Pattern Recognition with Phase Filters,” Appl. Opt. 26, 2315 (1987).
    [CrossRef] [PubMed]
  3. H. H. Arsenault, Y. Sheng, “Properties of the Circular Harmonic Expansion for Rotation-Invariant Pattern Recognition,” Appl. Opt. 25, 3225 (1986), and references therein.
    [CrossRef] [PubMed]
  4. J. L. Horner, P. D. Gianino, “Applying the Phase-Only Filter Concept to the Synthetic Discriminant Function Correlation Filter,” Appl. Opt. 24, 851 (1985).
    [CrossRef] [PubMed]
  5. J. L. Horner, J. R. Leger, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. 24, 609 (1985).
    [CrossRef] [PubMed]
  6. H. J. Caulfield, W. T. Maloney, “Improved Discrimination in Optical Character Recognition,” Appl. Opt. 8, 2354 (1969).
    [CrossRef] [PubMed]
  7. G. F. Schils, D. W. Sweeney, “Iterative Technique for the Synthesis of Distortion-Invariant Optical Correlation Filters,” Opt. Lett. 12, 307 (1987).
    [CrossRef] [PubMed]

1987 (3)

1986 (1)

1985 (2)

1969 (1)

Arsenault, H. H.

Caulfield, H. J.

Gianino, P. D.

Horner, J. L.

Leger, J. R.

Maloney, W. T.

Rosen, J.

Schils, G. F.

Shamir, J.

Sheng, Y.

Sweeney, D. W.

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Figures (6)

Fig. 1
Fig. 1

Input pattern for the computer experiments from which the letter P should be recognized.

Fig. 2
Fig. 2

Output distribution for (a) regular matched filter; (b) phase-only matched filter; (c) harmonic component (n = 0) filter; and (d) harmonic component (n = 0) phase-only filter.

Fig. 3
Fig. 3

Output distribution with a harmonic component composite filter.

Fig. 4
Fig. 4

Bipolar amplitude scan along one diameter of a phase amplitude harmonic component filter.

Fig. 5
Fig. 5

Output pattern for the filter of Fig. 4.

Fig. 6
Fig. 6

(a) Input pattern for laboratory experiment; (b) filter made for recognizing P; (c) output pattern with phase-only harmonic component filter superposed by a line along which the intensity scan of (d) was taken; (e) output for a phase-amplitude harmonic component composite filter of Fig. 4 with intensity scan (f).

Tables (1)

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Table I Performance Comparison for the Various Filters (See Text for Details); Parameters ν1 and ν2 Define the Weight of Each Component of the Composite Filters

Equations (12)

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C ( x 0 , y 0 ) = f ( x , y ) g * ( x - x 0 , y - y 0 ) d x d y ,
C ( 0 ) = 0 0 2 π f ( r , θ ) g * ( r , θ ) r d θ d r ,
C ( 0 ; α ) = 0 0 2 π f ( r , θ + α ) g * ( r , θ ) r d θ d r .
C ( 0 ; α ) = K exp ( j n α ) ,
C ( 0 , α ) = n = - c n exp ( j n α ) .
F ( ρ , ϕ ) = n = - F n ( ρ ) exp ( j n ϕ ) ,
G ( ρ , ϕ ) = n = - G n ( ρ ) exp ( j n ϕ ) ,
C ( 0 ; α ) = 0 0 2 π F ( ρ , ϕ + α ) G * ( ρ , ϕ ) p d p d ϕ .
n = - c n exp ( j n α ) = n = - 0 F n ( ρ ) G n * ( ρ ) exp ( j n α ) ρ d ρ ,
c n = 0 F n ( ρ ) G n * ( ρ ) ρ d ρ .
G n ( ρ ) = 0 2 π F ( ρ , ϕ ) exp ( j n ϕ ) d ϕ | 0 2 π F ( ρ , ϕ ) exp ( j n ϕ ) d ϕ | ;             ρ 1 < ρ < ρ h ,
G F ( ρ ) = 0 2 π F F ( ρ , ϕ ) d ϕ ,

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