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 Title: |
US4084255:
Positional, rotational and scale invariant optical correlation method and apparatus
[ Derwent Title ]
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| Country: |
US United States of America
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| Inventor: |
Casasent, David Paul; Pittsburgh, PA
Psaltis, Demetri; Thessaloniki, Greece
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| Assignee: |
The United States of America as represented by the Secretary of the Navy, Washington, DC
other patents from UNITED STATES OF AMERICA, NAVY (597270) (approx. 13,239)
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| Published / Filed: |
1978-04-11
/ 1976-11-02
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| Application Number: |
US1976000738781
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| IPC Code: |
Advanced:
G06E 3/00;
Core:
more...
IPC-7:
G06G 7/19;
G06G 9/00;
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| ECLA Code: |
G06E3/00A2;
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| U.S. Class: |
Current:
382/278;
359/029;
359/107;
359/561;
382/280;
708/816;
708/820;
Original:
364/822;
340/146.3Q;
350/003.82;
350/162.SF;
364/515;
364/826;
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| Field of Search: |
235/181,197-198
340/146.3 Q
350/162 SF
364/826,827,822
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| Priority Number: |
| 1976-11-02 |
US1976000738781 |
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| Abstract: |
A method and electro-optical apparatus for correlating two functions, f1 (x,y) and f2 (x,y) which are shifted, scaled and rotated versions of each other without loss of signal-to-noise and signal-to-clutter ratios as compared to the autocorrelation case. The coordinates of two correlation peaks provide an indication of the scale and orientation differences between the two functions. In performing the method, the magnitudes of the Fourier transforms of the functions are obtained, |F1 (ωx, ωy)| and |F2 (ωx,ωy)| and then a polar coordinate conversion is performed, and the resultant functions F1 (r,θ) and F2 (r,θ) are logarithmically scaled in the r coordinate. The functions thus produced F1 (eρ,θ) and F2 (eρ,θ) are Fourier transformed to produce the Mellin transforms M1 (ωρ, ωθ) and M2 (ωρ,ωθ). The conjugate of one of these Mellin transforms is obtained, and the product of this conjugate with the other Mellin transform is produced and, subsequently, Fourier transformed to complete the correlation process.
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| Attorney, Agent or Firm: |
Sciascia, R. S. ;
Shrago, L. I. ;
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| Primary / Asst. Examiners: |
Gruber, Felix D.;
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| Family: |
None
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First Claim:
Show all 10 claims |
What is claimed is:
1. A method for correlating two functions f1 (x,y) and f2 (x,y) which are scaled and rotated versions of each other, comprising the steps of
- obtaining |F1 (ωx,ωy)|, and |F2 (ωx,ωy)|, the magnitudes of the Fourier transforms of these functions;
- performing a polar coordinate conversion on |F1 (ωx,ωy)| and |F2 (ωx,ωy)| thereby to obtain the functions F1 (r,θ) and F2 (r,θ);
- logarithmically scaling the coordinate r in the functions F1 (r,θ) and F2 (r,θ) thereby to obtain the functions F1 (eρ,θ) and F2 (eρ,θ);
- Fourier transforming F1 (eρ,θ) and F2 (eρ,θ) thereby to obtain the Mellin transforms M1 (ωρ,ωθ) and M2 (ωρ,ωθ);
- obtaining the conjugate Mellin transform M1 *(ωρ,ωθ);
- producing the product M1 *M2 ;
- Fourier transforming said product, all of the aforementioned steps being performed by optical or electro-optical means; and
- recording on film the results of said last-mentioned Fourier transformation.
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| Background / Summary: |
Show background / summary
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| Drawing Descriptions: |
Show drawing descriptions
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| Description: |
Show description
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| Forward References: |
Show 31 U.S. patent(s) that reference this one
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| Foreign References: |
None
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| Other References: |
Beard, Imaging by correlation of intensity Fluctuations, Applied Physics ters, vol. 15, No. 7, Oct. 1969, pp. 227-229.
Gerardi: Application of Mellin and Hankel Transforms to Networks with Time-Varying Parameters, IRE Transactions on Circuit Theory, vol. CT-6, June 1959, pp. 197/208.
Baudelaire: Linear Stretch-Invariant Systems, Proceedings IEEE vol. 61, Apr. 1973, pp. 467, 468.
(2 pages)
Cited by 2 patents
Robbins: Inverse Filtering for Linear Shift-Variant Imaging Systems, Proceedings of the IEEE, vol. 60, No. 7, July 1972, pp. 862-872.
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