US4084255A
Expired / Lapsed
US
⏱️ 0.0 years remaining
Positional, rotational and scale invariant optical correlation method and apparatus
Assignee: United States Department of the Navy
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Filing: 1976-11-02
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Granted: 1978-04-11
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Expires: 1996-11-02
Abstract
Abstract A method and electro-optical apparatus for correlating two functions, f 1 (x,y) and f 2 (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, |F 1 (ω x , ω y )| and |F 2 (ω x ,ω y )| and then a polar coordinate conversion is performed, and the resultant functions F 1 (r,θ) and F 2 (r,θ) are logarithmically scaled in the r coordinate. The functions thus produced F 1 (e.sup.ρ,θ) and F 2 (e.sup.ρ,θ) are Fourier transformed to produce the Mellin transforms M 1 (ω.sub.ρ, ω.sub.θ) and M 2 (ω.sub.ρ,ω.sub.θ). 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.
Inventors
- 👤 David Paul Casasent
- 👤 Demetri Psaltis
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-23 12:15
CPC Classifications
G; G06; G06E; G06E3/00; G06E3/001; G06E3/005
Claims Analysis
Total Claims: 14
Claim 1
Independent Claim
176 words
A method for correlating two functions f 1 (x,y) and f 2 (x,y) which are scaled and rotated versions of each other, comprising the steps of obtaining |F 1 (ω x ,ω y )|, and |F 2 (ω x ,ω y )|, the magnitudes of the Fourier transforms of these functions; performing a polar coordinate conversion on |F 1 (ω x ,ω y )| and |F 2 (ω x ,ω y )| thereby to obtain the functions F 1 (r,θ) and F 2 (r,θ); logarithmically scaling the coordinate r in the functions F 1 (r,θ) and F 2 (r,θ) thereby to obtain the functions F 1 (e.sup.ρ,θ) and F 2 (e.sup.ρ,θ); Fourier transforming F 1 (e.sup.ρ,θ) and F 2 (e.sup.ρ,θ) thereby to obtain the Mellin transforms M 1 (ω.sub.ρ,ω.sub.θ) and M 2 (ω.sub.ρ,ω.sub.θ); obtaining the conjugate Mellin transform M 1 *(ω.sub.ρ,ω.sub.θ); producing the product M 1 *M 2 ; 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.
Claim 2
Independent Claim
176 words
A method for correlating two functions f 1 (x,y) and f 2 (x,y) which are scaled and rotated versions of each other, comprising the steps of obtaining |F 1 (ω x ,ω y )|, and |F 2 (ω x ,ω y )|, the magnitudes of the Fourier transforms of these functions; performing a polar coordinate conversion on |F 1 (ω x ,ω y )| and |F 2 (ω x ,ω y )| thereby to obtain the functions F 1 (r,θ) and F 2 (r,θ); logarithmically scaling the coordinate r in the functions F 1 (r,θ) and F 2 (r,θ) thereby to obtain the functions F 1 (e.sup.ρ,θ) and F 2 (e.sup.ρ,θ); Fourier transforming F 1 (e.sup.ρ,θ) and F 2 (e.sup.ρ,θ) thereby to obtain the Mellin transforms M 1 (ω.sub.ρ,ω.sub.θ) and M 2 (ω.sub.ρ,ω.sub.θ); obtaining the conjugate Mellin transform M 1 *(ω.sub.ρ,ω.sub.θ); producing the product M 1 *M 2 ; 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.
Claim 3
Dependent Claim
81 words
In a method as defined in claim 1 wherein said function f 1 (x,y) is in the form of an optical transmittance pattern and the magnitude of the Fourier transform of this function F 1 (ω x ,ω y ) is obtained by positioning said pattern in the front focal plane of a lens and illuminating said pattern with coherent light whereby the light distribution pattern in the back focal plane of said lens corresponds to Fourier transformation of said function.
Claim 4
Dependent Claim
41 words
In a method as defined in claim 1 wherein the conjugate Mellin transform M 1 *(ω.sub.ρ,ω.sub.θ) is recorded as a film transparency of the interference pattern between a reference plane wave and a light distribution pattern corresponding to F 1 (e.sup.ρ,θ).
Claim 5
Dependent Claim
52 words
In a method as defined in claim 1 wherein the product M 1 *M 2 is produced by positioning said film transparency having M 1 *(ω.sub.ρ,ω.sub.θ) recorded thereon in the front focal plane of a lens and illuminating said film with a light distribution pattern produced by Fourier transforming F 2 (e.sup.ρ,θ).
Claim 6
Dependent Claim
43 words
In a method as defined in claim 1 wherein the conjugate Mellin transform M 2 *(ω.sub.ρ,ω.sub.θ) is obtained by having a reference wave interfere with a Fourier transformation of F 2 (e.sup.ρ,ω), the resultant interference pattern containing a term corresponding to said conjugate.
Claim 7
Dependent Claim
41 words
In a method as defined in claim 1 wherein the product M 1 M 2 * is obtained by illuminating a film transparency having M 2 * recorded therein with the light distribution pattern resulting from Fourier transforming F 1 (e.sup.ρ,θ).
Claim 8
Independent Claim
180 words
A method for correlating two functions f 1 (x,y) and f 2 (x,y) which are scaled and rotated versions of each other, comprising the steps of producing an optical representation of |F 2 (ω x ,ω y )|, the magnitude of the Fourier transform of f 2 (x,y); performing a polar coordinate conversion on this representation of |F 2 (ω x ,ω y )| thereby to obtain an optical representation of the function F 2 (r,θ); logarithmically scaling the coordinate r in the function F 2 (r,θ) thereby to obtain an optical representation of the function F 2 (e.sup.ρ,θ); Fourier transforming F 2 (e.sup.ρ,θ) thereby to obtain a light distribution pattern corresponding to the Mellin transform M 2 (ω.sub.ρ,ω.sub.θ); pouring a film transparency having an interference pattern recorded therein which contain a term that is proportional to the conjugate Mellin transform M 1 *(ω.sub.ρ,ω.sub.θ); illuminating said film transparency with said light distribution pattern thereby to produce a light distribution pattern corresponding to the produce M 1 *M 2 ; Fourier transforming said last-mentioned light pattern; and recording the results thereof.
Claim 9
Independent Claim
180 words
A method for correlating two functions f 1 (x,y) and f 2 (x,y) which are scaled and rotated versions of each other, comprising the steps of producing an optical representation of |F 2 (ω x ,ω y )|, the magnitude of the Fourier transform of f 2 (x,y); performing a polar coordinate conversion on this representation of |F 2 (ω x ,ω y )| thereby to obtain an optical representation of the function F 2 (r,θ); logarithmically scaling the coordinate r in the function F 2 (r,θ) thereby to obtain an optical representation of the function F 2 (e.sup.ρ,θ); Fourier transforming F 2 (e.sup.ρ,θ) thereby to obtain a light distribution pattern corresponding to the Mellin transform M 2 (ω.sub.ρ,ω.sub.θ); pouring a film transparency having an interference pattern recorded therein which contain a term that is proportional to the conjugate Mellin transform M 1 *(ω.sub.ρ,ω.sub.θ); illuminating said film transparency with said light distribution pattern thereby to produce a light distribution pattern corresponding to the produce M 1 *M 2 ; Fourier transforming said last-mentioned light pattern; and recording the results thereof.
Claim 10
Dependent Claim
185 words
Apparatus for correlating two functions f 1 (x,y) and f 2 (x,y) which are shifted, scaled and rotated versions of each other, comprising in combination an optical correlator having an input plane P 0 , a frequency plane P 1 and an output plane P 2 ; a film transparency having an interference pattern recorded therein which contain a term proportional to the conjugate Mellin transform M 2 *(ω.sub.ρ,ω.sub.θ), said film transparency being positioned at plane P 1 ; means for creating a light pattern leaving plane P 0 that corresponds to F 1 (e.sup.ρ,θ), said light pattern being Fourier transformed by lens means within said correlator located between planes P 0 and P 1 and the illumination of said film transparency by the resultant light pattern producing a light pattern leaving plane P 1 that corresponds to the product M 2 *(ω.sub.ρ,ω.sub.θ) M 1 (ω.sub.ρ,ω.sub.θ), said last-mentioned light pattern being Fourier transformed by other lens means within said correlator located between planes P 1 and P 2 ; and means positioned at plane P 2 for recording the results of said last-mentioned Fourier transformation.
Claim 11
Dependent Claim
185 words
Apparatus for correlating two functions f 1 (x,y) and f 2 (x,y) which are shifted, scaled and rotated versions of each other, comprising in combination an optical correlator having an input plane P 0 , a frequency plane P 1 and an output plane P 2 ; a film transparency having an interference pattern recorded therein which contain a term proportional to the conjugate Mellin transform M 2 *(ω.sub.ρ,ω.sub.θ), said film transparency being positioned at plane P 1 ; means for creating a light pattern leaving plane P 0 that corresponds to F 1 (e.sup.ρ,θ), said light pattern being Fourier transformed by lens means within said correlator located between planes P 0 and P 1 and the illumination of said film transparency by the resultant light pattern producing a light pattern leaving plane P 1 that corresponds to the product M 2 *(ω.sub.ρ,ω.sub.θ) M 1 (ω.sub.ρ,ω.sub.θ), said last-mentioned light pattern being Fourier transformed by other lens means within said correlator located between planes P 1 and P 2 ; and means positioned at plane P 2 for recording the results of said last-mentioned Fourier transformation.
Claim 12
Dependent Claim
198 words
Apparatus for correlating two functions f 1 (x,y) and f 2 (x,y) which are shifted, scaled and rotated versions of each other, comprising optical means for Fourier transforming f 1 (x,y) so as to obtain |F 1 (ω x ,ω y )|, the magnitude of the Fourier transform of this function; means for performing a polar coordinate conversion on |F 1 (ω x ,ω y )| so as to obtain the function F 1 (r,θ); means for logarithmically scaling the r coordinate in the function F 1 (r,θ) so as to obtain F 1 (e.sup.ρ,θ), |F 1 (ω x ,ω y )|, F 1 (r,θ) and F 1 (e.sup.ρ,θ) occurring as optical images; optical means for Fourier transforming F 1 (e.sup.ρ,θ) so as to obtain a light pattern corresponding to the Mellin transform M 1 (ω.sub.ρ,ω.sub.θ); a film transparency having an interference pattern recorded therein which contains an optical representation of the conjugate Mellin transform M 2 *(ω.sub.ρ,ω.sub.θ); means for illuminating said film transparency with said light pattern so as to obtain a light pattern corresponding to M 1 M 2 *; optical means for Fourier transforming said last-mentioned light pattern; and means for recording the results thereof.
Claim 13
Dependent Claim
198 words
Apparatus for correlating two functions f 1 (x,y) and f 2 (x,y) which are shifted, scaled and rotated versions of each other, comprising optical means for Fourier transforming f 1 (x,y) so as to obtain |F 1 (ω x ,ω y )|, the magnitude of the Fourier transform of this function; means for performing a polar coordinate conversion on |F 1 (ω x ,ω y )| so as to obtain the function F 1 (r,θ); means for logarithmically scaling the r coordinate in the function F 1 (r,θ) so as to obtain F 1 (e.sup.ρ,θ), |F 1 (ω x ,ω y )|, F 1 (r,θ) and F 1 (e.sup.ρ,θ) occurring as optical images; optical means for Fourier transforming F 1 (e.sup.ρ,θ) so as to obtain a light pattern corresponding to the Mellin transform M 1 (ω.sub.ρ,ω.sub.θ); a film transparency having an interference pattern recorded therein which contains an optical representation of the conjugate Mellin transform M 2 *(ω.sub.ρ,ω.sub.θ); means for illuminating said film transparency with said light pattern so as to obtain a light pattern corresponding to M 1 M 2 *; optical means for Fourier transforming said last-mentioned light pattern; and means for recording the results thereof.
Claim 14
Dependent Claim
112 words
The apparatus as defined in claim 9 wherein said means for creating a light pattern leaving plane P 0 that corresponds to F 1 (e.sup.ρ,θ) includes means for Fourier transforming an optical representation of the function f 1 (x,y) so as to obtain |F 1 (ω x ,ω y )|, the magnitude of the Fourier transform of this function; means for performing a polar coordinate conversion on the light pattern resulting from said transformation so as to obtain a light pattern cooresponding to the function F 1 (r,θ); and means for logarithmically scaling the r coordinate in said last-mentioned light pattern thereby to obtain a light pattern corresponding to F 1 (e.sup.ρ,θ).
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USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1981-04-10 | 1981-10-10 | 1982-04-11 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1985-04-10 | 1985-10-10 | 1986-04-11 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1989-04-10 | 1989-10-10 | 1990-04-11 | $7700.00 | Window Closed / Lapsed |