Abstract

A generalized approach leads to spatial filters that accept changes of scale by a factor of 4. The procedure employs phase filters with reduced tolerance requirements and achieves high discrimination capability and efficient light throughput. Computer simulations and laboratory experiments show the advantages of this novel approach.

© 1989 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. J. Rosen, J. Shamir, “Circular Harmonic Phase Filters for Efficient Rotation-Invariant Pattern Recognition,” Appl. Opt. 27, 2895 (1988).
    [CrossRef] [PubMed]
  4. D. Casasent, D. Psaltis, “Position, Rotation, and Scale Invariant Optical Correlation,” Appl. Opt. 15, 1795 (1976).
    [CrossRef] [PubMed]
  5. K. Mersereau, G. M. Morris, “Scale, Rotation, and Shift Invariant Image Recognition,” Appl. Opt. 25, 2338 (1986).
    [CrossRef] [PubMed]
  6. G. F. Schils, D. W. Sweeney, “Iterative Technique for the Synthesis of Distortion-Invariant Optical-Correlation Filters,” Opt. Lett. 12, 307 (1987).
    [CrossRef] [PubMed]
  7. T. Szoplik, “Shift and Scale-Invariant Anamorphic Fourier Correlator,” J. Opt. Soc. Am. A 2, 1419 (1985).
    [CrossRef]
  8. T. Szoplik, H. H. Arsenault, “Shift and Scale-Invariant Anamorphic Fourier Correlator Using Multiple Circular Harmonic Filters,” Appl. Opt. 24, 3179 (1985).
    [CrossRef] [PubMed]
  9. A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Spatial-Temporal Correlation Filter for In-Plane Distortion Invariance,” Appl. Opt. 25, 4466 (1986).
    [CrossRef] [PubMed]
  10. H. H. Arsenault, Y. Sheng, “Properties of Circular Harmonic Expansion for Rotation-Invariant Pattern Recognition,” Appl. Opt. 25, 3225 (1986).
    [CrossRef] [PubMed]
  11. G. F. Schils, D. W. Sweeney, “Rotationally Invariant Corrlation Filters for Multiple Images,” J. Opt. Soc. Am. A 3, 902 (1986).
    [CrossRef]

1988 (1)

1987 (3)

1986 (4)

1985 (2)

1976 (1)

Arsenault, H. H.

Casasent, D.

Caulfield, H. J.

Mahalanobis, A.

Mersereau, K.

Morris, G. M.

Psaltis, D.

Rosen, J.

Schils, G. F.

Shamir, J.

Sheng, Y.

Sweeney, D. W.

Szoplik, T.

Vijaya Kumar, B. V. K.

Appl. Opt. (8)

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

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Figures (9)

Fig. 1
Fig. 1

Input pattern for the computer experiments from which the letter F should be recognized. The x in the large F was the origin for the filter generation, and the scaling factors are as indicated.

Fig. 2
Fig. 2

Output distribution for (a) regular matched filter, (b) phase-only matched filter. The filters were matched to the largest F.

Fig. 3
Fig. 3

Correlation peak intensity as a function of the LRH frequency p.

Fig. 4
Fig. 4

Real (a) and imaginary (b) parts of the LRH filter represented by four gray levels.

Fig. 5
Fig. 5

Output pattern with LRH filter matched to the largest F of the input (Fig. 1).

Fig. 6
Fig. 6

Input pattern for laboratory experiment.

Fig. 7
Fig. 7

Holographic LRH filter.

Fig. 8
Fig. 8

Output distribution and intensity scan along correlation peaks. Cross-correlations with the P values are invisible due to the threshold chosen.

Fig. 9
Fig. 9

Scale dependence of correlation peaks normalized to unity. The relative intensities are compared in Table I. MF, matched filter; POF, phase-only matched filter; LRH and modified LRH with s = 0.05.

Tables (1)

Tables Icon

Table I Comparison of Performance for the Various Filters Matched to Recognize the Large F

Equations (14)

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C i j ( x 0 , y 0 ) = f i ( x , y ) m j * ( x - x 0 , y - y 0 ) d x d y ,
C i j ( 0 , 0 ) = f i ( x , y ) m j * ( x , y ) d x d y ,
C ( 0 ) = 0 0 2 π f ( r , θ ) m * ( r , θ ) r d θ d r .
C ( 0 ; a , α ) = 0 0 2 π f ( a r , θ + α ) m * ( r , θ ) r d θ d r .
C ( a ) = 0 2 π d R 1 a 2 F ( ρ a , ϕ ) M * ( ρ , ϕ ) ρ d ρ d ϕ ,
C ( a ) = 0 2 π d / a R / a F ( τ , ϕ ) M * ( a τ , ϕ ) τ d τ d ϕ .
C ( a ) = C 0 exp [ j σ ( a ) ] .
M p * ( ρ , ϕ ) = exp [ j Ω ( ϕ ) ] ( ρ / d ) j p / w ,
Ω ( ϕ ) = - arg [ d R F ( ρ , ϕ ) ( ρ d ) j p / w ρ d ρ ] .
w = 1 2 π ln ( R / d ) .
C p ( a ) = ( a d ) j p / w 0 2 π exp [ j Ω ( ϕ ) ] [ d / a R / a F ( τ , ϕ ) τ j p / w τ d τ ] d ϕ .
C p ( 1 ) = 0 2 π | d R F ( τ , ϕ ) τ j p / w τ d τ | d ϕ ,
= 1 a 0 C ( a ) - C ( 1 ) d a a 0 C ( 1 ) ,
M * ( ρ , ϕ ) = exp [ j Ω ( ϕ ) ] ( ρ / d ) s + j p / w .

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