Abstract

Multiple circular harmonic components of the same target can be used jointly to discriminate between the target and other objects. Two methods are considered: Coherent superposition and decision making in multidimensional space. Experimental results for the discrimination between a tank and a truck are given.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. M. Cormack, J. Appl. Phys. 34, 2722 (1963).
    [CrossRef]
  2. A. M. Cormack, J. Appl. Phys. 35, 2908 (1964).
    [CrossRef]
  3. E. W. Hansen, J. W. Goodman, Opt. Commun. 24, 268 (1978).
    [CrossRef]
  4. E. W. Hansen, Appl. Opt. 20, 2266 (1981).
    [CrossRef] [PubMed]
  5. Y.-N. Hsu, H. H. Arsenault, G. April, Appl. Opt. 21, 4012 (1982).
    [CrossRef] [PubMed]
  6. Y.-N. Hsu, H. H. Arsenault, Appl. Opt. 21, 4016 (1982).
    [CrossRef] [PubMed]
  7. H. H. Arsenault, Y.-N. Hsu, Appl. Opt. 22, 130 (1983).
    [CrossRef] [PubMed]
  8. Y.-N. Hsu, H. H. Arsenault, “Statistical Performance of Circular Harmonic Filters for Rotation-Invariant Pattern Recognition,” submitted for publication.

1983 (1)

1982 (2)

1981 (1)

1978 (1)

E. W. Hansen, J. W. Goodman, Opt. Commun. 24, 268 (1978).
[CrossRef]

1964 (1)

A. M. Cormack, J. Appl. Phys. 35, 2908 (1964).
[CrossRef]

1963 (1)

A. M. Cormack, J. Appl. Phys. 34, 2722 (1963).
[CrossRef]

April, G.

Arsenault, H. H.

H. H. Arsenault, Y.-N. Hsu, Appl. Opt. 22, 130 (1983).
[CrossRef] [PubMed]

Y.-N. Hsu, H. H. Arsenault, Appl. Opt. 21, 4016 (1982).
[CrossRef] [PubMed]

Y.-N. Hsu, H. H. Arsenault, G. April, Appl. Opt. 21, 4012 (1982).
[CrossRef] [PubMed]

Y.-N. Hsu, H. H. Arsenault, “Statistical Performance of Circular Harmonic Filters for Rotation-Invariant Pattern Recognition,” submitted for publication.

Cormack, A. M.

A. M. Cormack, J. Appl. Phys. 35, 2908 (1964).
[CrossRef]

A. M. Cormack, J. Appl. Phys. 34, 2722 (1963).
[CrossRef]

Goodman, J. W.

E. W. Hansen, J. W. Goodman, Opt. Commun. 24, 268 (1978).
[CrossRef]

Hansen, E. W.

E. W. Hansen, Appl. Opt. 20, 2266 (1981).
[CrossRef] [PubMed]

E. W. Hansen, J. W. Goodman, Opt. Commun. 24, 268 (1978).
[CrossRef]

Hsu, Y.-N.

H. H. Arsenault, Y.-N. Hsu, Appl. Opt. 22, 130 (1983).
[CrossRef] [PubMed]

Y.-N. Hsu, H. H. Arsenault, Appl. Opt. 21, 4016 (1982).
[CrossRef] [PubMed]

Y.-N. Hsu, H. H. Arsenault, G. April, Appl. Opt. 21, 4012 (1982).
[CrossRef] [PubMed]

Y.-N. Hsu, H. H. Arsenault, “Statistical Performance of Circular Harmonic Filters for Rotation-Invariant Pattern Recognition,” submitted for publication.

Appl. Opt. (4)

J. Appl. Phys. (2)

A. M. Cormack, J. Appl. Phys. 34, 2722 (1963).
[CrossRef]

A. M. Cormack, J. Appl. Phys. 35, 2908 (1964).
[CrossRef]

Opt. Commun. (1)

E. W. Hansen, J. W. Goodman, Opt. Commun. 24, 268 (1978).
[CrossRef]

Other (1)

Y.-N. Hsu, H. H. Arsenault, “Statistical Performance of Circular Harmonic Filters for Rotation-Invariant Pattern Recognition,” submitted for publication.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Target orientation measured by the angle α.

Fig. 2
Fig. 2

Output phasors due to different circular harmonic orders.

Fig. 3
Fig. 3

Systems of coherent superposition.

Fig. 4
Fig. 4

Patterns used in the experiment: (a) target: a tank; (b) object: a truck.

Tables (4)

Tables Icon

Table I Circular Harmonic Coefficients of the Tank Pattern in Fig. 4(a) About the Geometrical Center

Tables Icon

Table II Circular Harmonic Coefficients of the Tank Pattern in Fig. 4(a) About the Proper Centers

Tables Icon

Table III Output Peak Signal Moduli of Filters for Different Circular Harmonic Orders

Tables Icon

Table IV Statistical Discrimination Between the Image of a Tank and the Image of a Truck in the Presence of Noise

Equations (18)

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

f ( r , θ ) = m = - f m ( r ) exp ( j m θ ) .
k f M k ( r ) exp ( j M k θ )
C ( α ) = k A ( M k ) exp ( j M k α ) ,
C 0 h ( α ) 2 = [ k A ( M k ) ] 2 ,
W ( f x , f y ) = N in 4 rect ( 2 F x ) rect ( 2 F y )
P t ( i ) = ( SNR ) exp [ - ( SNR ) ( i + 1 ) ] I 0 [ 2 ( SNR ) i ] ,
P b ( i ) = ( SNR ) exp { - ( SNR ) [ i + B 2 ( M ) A 2 ( M ) ] } × I 0 [ 2 ( SNR ) B ( M ) A ( M ) i ] ,
i = I A 2 ( M ) .
SNR = 4 A ( M ) N in .
P t ( i ) = k P t ( i k ) ,
P b ( i ) = k P b ( i k ) .
P t ( i ) P b ( i ) = P b ( C t b - C b b ) P t ( C b t - C t t ) = C ,
f ( i ) = k I 0 [ 2 ( SNR k ) i k ] I 0 [ 2 ( SNR k ) B ( M k ) A ( M k ) i k ] = C ,
C = C k exp { ( SNR k ) [ 1 - B 2 ( M k ) A 2 ( M k ) ] } .
P n . d . = f ( i ) C P t ( i ) d i ,
P f . a . = f ( i ) C P b ( i ) d i .
SNR in = 4 S max 2 N in .
SNR k = S N R i n A ( M ) k S max 2 .

Metrics