Abstract
Methods for registering first and second images which are offset by an x and/or y displacement in subpixel locations are provided. A preferred implementation of the methods includes the steps of: multiplying the first image by a window function to create a first windowed image; transforming the first windowed image with a Fourier transform to create a first image Fourier transform; multiplying the second image by the window function to create a second windowed image; transforming the second windowed image with a Fourier transform to create a second image Fourier transform; computing a collection of coordinate pairs from the first and second image Fourier transforms such that at each coordinate pair the values of the first and second image Fourier transforms are likely to have very little aliasing noise; computing an estimate of a linear Fourier phase relation between thefirst and second image Fourier transforms using the Fourier phases of the first and second image Fourier transforms at the coordinate pairs in a minimumleast squares sense; and computing the displacements in the x and/or y directions from the linear Fourier phase relationship. Also provided are a computer program having computer readable program code and program storage device having a program of instructions for executing and performing the methods of the present invention, respectively.
Claims

A method for registering first and second images which are offset by an x and/or y displacement in subpixel locations, the method comprises the steps of:
multiplying the first image by a window function to create a first windowed image;
transforming the first windowed image with a Fourier transform to create a first image Fourier transform;
multiplying the second image by the window function to create a second windowed image;
transforming the second windowed image with a Fourier transform to create a second image Fourier transform;
computing a collection of coordinate pairs from the first and second image Fourier transforms such that at each coordinate pair the values of the first and second image Fourier transforms are likely to have very little aliasing noise;
computing an estimate of a linear Fourier phase relation between the first and second image Fourier transforms using the Fourier phases of the first and second image Fourier transforms at the coordinate pairs in a minimumleast squares sense; and
computing the displacements in the x and/or y directions from the linear Fourier phase relationship.
 The method of claim 1 , wherein the window is a periodic window function.
 The method of claim 2 , wherein the periodic window function is a 3term Blackman window.
 The method of claim 2 , wherein the periodic window function is a 4term BlackmanHarris window.
 The method of claim 1 , wherein the window function is a symmetric window function.
 The method of claim 5 , wherein the symmetric window function is a 3term Blackman window.
 The method of claim 5 , wherein the symmetric window function is a 4term BlackmanHarris window.
 The method of claim 1 , wherein the step of computing a collection of coordinate pairs comprises fixing the coordinate pairs to lie within a fixed distance of a central peak.
 The method of claim 1 , wherein the step of computing a collection of coordinate pairs comprises fixing the Fourier magnitude of the first image Fourier transform and of the second image Fourier transform to be among the highest predetermined percent of the magnitudes within a fixed distance of a central peak.
 The method of claim 1 , wherein the step of computing a collection of coordinate pairs comprises setting the ratio of the Fourier magnitude of the first image transform to the Fourier magnitude of the second image transform to lie between 1/(1+ρ) and 1+ρ, where ρ is a positive number.
 The method of claim 10 , wherein ρ is between 0.8 and 1.5.

The method of claim 1 , wherein the step of computing a collection of coordinate pairs comprises a conjunction of two or more of the following:
fixing the coordinate pairs to lie within a fixed distance of a central peak;
fixing the Fourier magnitude of the first image Fourier transform and of the second image Fourier transform to be among the highest predetermined percent of the magnitudes within a fixed distance of a central peak; and
setting the ratio of the Fourier magnitude of the first image transform to the Fourier magnitude of the second image transform to lie between 1/(1+ρ) and 1+ρ, where ρ is a positive number.

A method for registering first and second images which are offset by an x and/or y displacement in subpixel locations, the method comprises the steps of:
registering the first and second images to the nearest pixel location; and
registering the first and second images to the nearest subpixel location, wherein the registering of the first and second images to the nearest subpixel location comprises the steps of:
multiplying the first image by a window function to create a first windowed image;
transforming the first windowed image with a Fourier
transform to create a first image Fourier transform;
multiplying the second image by the window function to create a second windowed image;
transforming the second windowed image with a Fourier transform to create a second image Fourier transform;
computing a collection of coordinate pairs from the first and second image Fourier transforms such that at each coordinate pair the values of the first and second image Fourier transforms are likely to have very little aliasing noise;
computing an estimate of a linear Fourier phase relation between the first and second image Fourier transforms using the Fourier phases of the first and second image Fourier transforms at the coordinate pairs in a minimumleast squares sense; and
computing the displacements in the x and/or y directions from the linear Fourier phase relationship.
 The method of claim 13 , wherein the window is a periodic window function.
 The method of claim 14 , wherein the periodic window function is a 3term Blackman window.
 The method of claim 14 , wherein the periodic window function is a 4term BlackmanHarris window.
 The method of claim 13 , wherein the window function is a symmetric window function.
 The method of claim 17 , wherein the symmetric window function is a 3term Blackman window.
 The method of claim 17 , wherein the symmetric window function is a 4term BlackmanHarris window.
 The method of claim 13 , wherein the step of computing a collection of coordinate pairs comprises fixing the coordinate pairs to lie within a fixed distance of a central peak.
 The method of claim 13 , wherein the step of computing a collection of coordinate pairs comprises fixing the Fourier magnitude of the first image Fourier transform and of the second image Fourier transform to be among the highest predetermined percent of the magnitudes within a fixed distance of a central peak.
 The method of claim 13 , wherein the step of computing a collection of coordinate pairs comprises setting the ratio of the Fourier magnitude of the first image transform to the Fourier magnitude of the second image transform to lie between 1/(1+ρ) and 1+ρ, where ρ is a positive number.
 The method of claim 22 , wherein ρ is between 0.8 and 1.5.

The method of claim 13 , wherein the step of computing a collection of coordinate pairs comprises a conjunction of two or more of the following:
fixing the coordinate pairs to lie within a fixed distance of a central peak;
fixing the Fourier magnitude of the first image Fourier transform and of the second image Fourier transform to be among the highest predetermined percent of the magnitudes within a fixed distance of a central peak; and
setting the ratio of the Fourier magnitude of the first image transform to the Fourier magnitude of the second image transform to lie between 1/(1+ρ) and 1+ρ, where ρ is a positive number.

A computer program product embodied in a computerreadable medium for registering first and second images which are offset by an x and/or y displacement in subpixel locations, the computer program product comprising:
computer readable program code means for multiplying the first image by a window function to create a first windowed image;
computer readable program code means for transforming the first windowed image with a Fourier transform to create a first image Fourier transform;
computer readable program code means for multiplying the second image by the window function to create a second windowed image;
computer readable program code means for transforming the second windowed image with a Fourier transform to create a second image Fourier transform;
computer readable program code means for computing a collection of coordinate pairs from the first and second image Fourier transforms such that at each coordinate pair the values of the first and second image Fourier transforms are likely to have very little aliasing noise;
computer readable program code means for computing an estimate of a linear Fourier phase relation between the first and second image Fourier transforms using the Fourier phases of the first and second image Fourier transforms at the coordinate pairs in a minimumleast squares sense; and
computer readable program code means for computing the displacements in the x and/or y directions from the linear Fourier phase relationship.

A program storage device readable by machine, tangibly embodying a program of instructions executable by the machine to perform method steps for registering first and second images which are offset by an x and/or y displacement in subpixel locations, the method comprises the steps of:
multiplying the first image by a window function to create a first windowed image;
transforming the first windowed image with a Fourier transform to create a first image Fourier transform;
multiplying the second image by the window function to create a second windowed image;
transforming the second windowed image with a Fourier transform to create a second image Fourier transform;
computing a collection of coordinate pairs from the first and second image Fourier transforms such that at each coordinate pair the values of the first and second image Fourier transforms are likely to have very little aliasing noise;
computing an estimate of a linear Fourier phase relation between the first and second image Fourier transforms using the Fourier phases of the first and second image Fourier transforms at the coordinate pairs in a minimumleast squares sense; and
computing the displacements in the x and/or y directions from the linear Fourier phase relationship.

A method for registering first and second images which are offset by an x and/or y displacement in subpixel locations, the method comprises the steps of:
(a) Fourier transforming the first image to produce a first image Fourier transform;
(b) Fourier transforming the second image to produce a second image Fourier transform;
(c) summing the energy of the first image Fourier transform and the energy of the second image Fourier transform and dividing the sum by 2 to produce an average image energy;
(d) selecting one or more first displacements for an iterative search;
(e) using each first displacement, the firstimage Fourier transform, and the secondimage Fourier transform to compute a first basebandplusaliasing Fourier transform;
(f) comparing the energy of the first basebandplusaliasing Fourier transform to the average image energy;
(g) stopping the search if the energy comparisons are within a fixed precision;
(h) continuing the search if the energy comparisons are not within the fixed precision by selecting a new displacement for the search;
(i) computing a second basebandplusaliasing Fourier transform using the new displacement, firstimage Fourier transform, and the secondimage Fourier transform;
(j) repeating steps (h) and (i) until the fixed precision is reached or a criterion for stopping the search unsuccessfully is satisfied.
Owners (US)

Nec Corporation
(Jan 06 2004)
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Nec Laboratories America Inc
(Nov 01 2002)
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Nec Research Institute Inc
(Mar 10 2000)
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Applicants

Nec Lab America Inc
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Inventors

Stone Harold S
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Orchard Michael T
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Chang Eechien
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Martucci Stephen
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CPC Classifications

G06T3/4084
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G06K9/6203
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G06T7/37
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IPC Classifications
Document Preview
 Publication: Sep 30, 2003

Application:
Mar 15, 2000
US 52641700 A

Priority:
Mar 15, 2000
US 52641700 A

Priority:
Oct 20, 1999
US 16059099 P