Abstract

As Danielsson says in his comment on the paper by Arsenault, the phase information is not used and the same signature vectors can have different shapes. However, in practice the method works well.

© 1989 Optical Society of America

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References

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  1. P.-E. Danielsson, “Rotation-Invariant Pattern Recognition Using Circular Harmonic Expansion: a Comment,” Appl. Opt. 28, 000–000 (1989).
    [CrossRef]
  2. M. Levesque, H. H. Arsenault, “Rotation Invariant Pattern Recognition Using the Phase of Circular Harmonic Filter Correlations,” Opt. Commun. 58, 161–166 (1986).
    [CrossRef]
  3. J. Shamir, H. J. Caulfield, J. Rosen, “Pattern Recognition Using Reduced Information Content Filters,” Appl. Opt. 26, 2311–2314 (1987).
    [CrossRef] [PubMed]
  4. A. Jouan, H. H. Arsenault, “Invariant Principal Components for Pattern Recognition”, J. Opt. Soc. Am. A 4(13), P 4 (1987).

1989 (1)

P.-E. Danielsson, “Rotation-Invariant Pattern Recognition Using Circular Harmonic Expansion: a Comment,” Appl. Opt. 28, 000–000 (1989).
[CrossRef]

1987 (2)

A. Jouan, H. H. Arsenault, “Invariant Principal Components for Pattern Recognition”, J. Opt. Soc. Am. A 4(13), P 4 (1987).

J. Shamir, H. J. Caulfield, J. Rosen, “Pattern Recognition Using Reduced Information Content Filters,” Appl. Opt. 26, 2311–2314 (1987).
[CrossRef] [PubMed]

1986 (1)

M. Levesque, H. H. Arsenault, “Rotation Invariant Pattern Recognition Using the Phase of Circular Harmonic Filter Correlations,” Opt. Commun. 58, 161–166 (1986).
[CrossRef]

Arsenault, H. H.

A. Jouan, H. H. Arsenault, “Invariant Principal Components for Pattern Recognition”, J. Opt. Soc. Am. A 4(13), P 4 (1987).

M. Levesque, H. H. Arsenault, “Rotation Invariant Pattern Recognition Using the Phase of Circular Harmonic Filter Correlations,” Opt. Commun. 58, 161–166 (1986).
[CrossRef]

Caulfield, H. J.

Danielsson, P.-E.

P.-E. Danielsson, “Rotation-Invariant Pattern Recognition Using Circular Harmonic Expansion: a Comment,” Appl. Opt. 28, 000–000 (1989).
[CrossRef]

Jouan, A.

A. Jouan, H. H. Arsenault, “Invariant Principal Components for Pattern Recognition”, J. Opt. Soc. Am. A 4(13), P 4 (1987).

Levesque, M.

M. Levesque, H. H. Arsenault, “Rotation Invariant Pattern Recognition Using the Phase of Circular Harmonic Filter Correlations,” Opt. Commun. 58, 161–166 (1986).
[CrossRef]

Rosen, J.

Shamir, J.

Appl. Opt. (2)

P.-E. Danielsson, “Rotation-Invariant Pattern Recognition Using Circular Harmonic Expansion: a Comment,” Appl. Opt. 28, 000–000 (1989).
[CrossRef]

J. Shamir, H. J. Caulfield, J. Rosen, “Pattern Recognition Using Reduced Information Content Filters,” Appl. Opt. 26, 2311–2314 (1987).
[CrossRef] [PubMed]

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

A. Jouan, H. H. Arsenault, “Invariant Principal Components for Pattern Recognition”, J. Opt. Soc. Am. A 4(13), P 4 (1987).

Opt. Commun. (1)

M. Levesque, H. H. Arsenault, “Rotation Invariant Pattern Recognition Using the Phase of Circular Harmonic Filter Correlations,” Opt. Commun. 58, 161–166 (1986).
[CrossRef]

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Equations (3)

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

f ( r , ϕ ) = f m ( r ) exp ( i m ϕ ) ,
g ( r , ϕ ) = g m ( r ) exp ( i m ϕ ) ,
g m ( r ) = f m ( r ) exp ( i α m ) .

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