Method of and apparatus for improved image correlation
First Claim
Patent Images
1. A method of correlating a first image and a second image, said first image being in the form of a first real array having a size M by N and said second image being in the form of a second real array having a size M by N, M and N being positive integers, the method comprising the computer implemented steps of:
- (a) performing a first domain transform on said first real array to produce a first complex array having a size M by (N/2+1);
(b) performing a second domain transform on said second real array to produce a second complex array having a size M by (N/2+1);
(c) multiplying a conjugate of said first complex array by said second complex array to produce an intermediate complex array having a size M by (N/2 +1);
(d) performing a first inverse domain transform on each of the columns of the intermediate complex array to produce an inverse transformed intermediate complex array;
(e) producing an supplemented complex array having size M by N from said inverse transformed intermediate complex array by determining elements for additional columns by symmetry for each row;
(f) performing a second inverse domain transform on each of the M rows of said supplemented complex array to produce a real correlation matrix having a size M by N; and
(g) correlating said first image and said second image on the basis of said real correlation matrix.
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Abstract
A method of and apparatus for computing correlating images using the one dimensional Fast Fourier Transform (FFT) and the symmetry property of the Fourier Transform. In one aspect, the invention is a method of correlating images in the form of a pair of real number arrays. Apparatus for carrying the method out is also disclosed and claimed.
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Citations
16 Claims
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1. A method of correlating a first image and a second image, said first image being in the form of a first real array having a size M by N and said second image being in the form of a second real array having a size M by N, M and N being positive integers, the method comprising the computer implemented steps of:
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(a) performing a first domain transform on said first real array to produce a first complex array having a size M by (N/2+1); (b) performing a second domain transform on said second real array to produce a second complex array having a size M by (N/2+1); (c) multiplying a conjugate of said first complex array by said second complex array to produce an intermediate complex array having a size M by (N/2 +1); (d) performing a first inverse domain transform on each of the columns of the intermediate complex array to produce an inverse transformed intermediate complex array; (e) producing an supplemented complex array having size M by N from said inverse transformed intermediate complex array by determining elements for additional columns by symmetry for each row; (f) performing a second inverse domain transform on each of the M rows of said supplemented complex array to produce a real correlation matrix having a size M by N; and (g) correlating said first image and said second image on the basis of said real correlation matrix. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
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10. Apparatus for correlating a first image and a second image, said first image being in the form of a first real array having a size M by N and said second image being in the form of a second real array having a size M by N, M and N being positive integers, the apparatus comprising:
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a first domain transformer for performing a first domain transform on said first real array to produce a first complex array having a size M by (N/2+1); a second domain transformer for performing a second domain transform on said second real array to produce a second complex array having a size M by (N/2 +1); a multiplier, responsive to said first domain transformer and said second domain transformer, for multiplying a conjugate of said first complex array by said second complex array to produce an intermediate complex array having a size M by (N/2+1); first inverse domain transform means, responsive to the multiplier, for performing a first inverse domain transform on each of the columns of the intermediate complex array to produce an inverse transformed intermediate complex array; supplementing means, responsive to the first inverse domain transform means, for producing a supplemented complex array having size M by N from said inverse transformed intermediate complex array by determining elements for additional columns by symmetry for each row; second inverse domain transform means, responsive to the supplementing means, for performing a second inverse domain transform on each of the M rows of the completed complex array to produce a real correlation matrix having a size M by N; and correlating means, responsive to the second inverse transform means, for correlating said first image and said second image on the basis of said real correlation matrix. - View Dependent Claims (11, 12, 13, 14, 15, 16)
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Specification