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Positional, rotational and scale invariant optical correlation method and apparatus

  • US 4,084,255 A
  • Filed: 11/02/1976
  • Issued: 04/11/1978
  • Est. Priority Date: 11/02/1976
  • Status: Expired due to Term
First Claim
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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 ofobtaining |F1

  • x

    y)|, and |F2

    x

    y)|, the magnitudes of the Fourier transforms of these functions;

    performing a polar coordinate conversion on |F1

    x

    y)| and |F2

    x

    y)| 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 (e.sup.ρ



    ) and F2 (e.sup.ρ



    );

    Fourier transforming F1 (e.sup.ρ



    ) and F2 (e.sup.ρ



    ) thereby to obtain the Mellin transforms M1

    .sub.ρ



    .sub.θ

    ) and M2

    .sub.ρ



    .sub.θ

    );

    obtaining the conjugate Mellin transform M1 *(ω

    .sub.ρ



    .sub.θ

    );

    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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