Image analysis – Image transformation or preprocessing – Changing the image coordinates
Reexamination Certificate
1998-12-15
2001-01-23
Tran, Phuoc (Department: 2721)
Image analysis
Image transformation or preprocessing
Changing the image coordinates
C382S275000, C382S278000, C382S280000, C382S295000, C382S296000
Reexamination Certificate
active
06178271
ABSTRACT:
BACKGROUND OF THE INVENTION
The invention relates to registering multiple frames of two-dimensional image data.
Magnetic resonance imaging (MRI) is a widely used diagnostic technique where radio frequency (RF) signals are analyzed to produce diagnostic information. Echo-planar imaging (EPI) is a subset of MRI that provides high temporal resolution achieved with faster imaging techniques, and typically resulting in large image data sets. One application of EPI is functional magnetic resonance imaging (fMRI), where a time series of images is acquired for a selected plane (or planes) of a subject. In challenge-based fMRI of the human brain, a time series of images of one or more planes within a subject's brain is collected while the subject is exposed to a sequence of stimulus conditions, to identify functional changes in brain characteristics.
The high spatial resolution of EPI makes challenge-based experiments sensitive to subject movements on the scale of millimeters or less. Stimulus-correlated movements of the subject may lead to false results. The false information introduced by the subject's movement is commonly referred to as motion artifact. In order to analyze the time series of images, motion artifacts must be removed by registering the series of images. Proper inter-frame registration of the time series of images to remove motion artifact is particularly important in studies in which the subject's motion is an integral part of the experiment, such as experiments that require spoken responses or the performance of motor tasks.
Techniques used to register image sets include the use of physical immobilization devices to maintain the subject in a known position or the placement of external fiduciary markers as landmarks for post-processing alignment.
Approaches used after the image data is acquired include landmark matching, surface matching, brute force least-squares estimation, iterative least-squares estimation, and variations thereof. Landmark matching is a manual process that requires trained personnel to accurately identify landmarks in each image.
Surface matching techniques may be computationally intensive when applied to large fMRI time series data. Also, various post-processing techniques construct the “registered” image by linear interpolation of the “misregistered” image, a technique that may introduce aliasing noise and high-spatial-frequency attenuation into the final corrected image.
SUMMARY OF THE INVENTION
The invention features methods and systems that align a first image with a second image.
To estimate a rotational correction angle that rotationally aligns the first and second images, the methods can include calculating the power spectra of the images (i.e., the modulus square of the Fourier transform of the images), or alternatively, the magnitudes of the Fourier transforms of the images (i.e., by eliminating the phase component of the Fourier transformed images) to decouple translation from rotation and produce rotationally centered images. The centered images are rotated from one another by the same angle as whatever rotation is present between the first and second image, however, the centered images do not include whatever translation is present between the first and second images. As a result, the correction angle for the first and second images equals the correction angle that rotationally aligns the centered images.
To estimate the correction angle that rotationally aligns the centered images, the methods can include converting the centered images into polar coordinates and calculating the polar cross-power spectrum of the polar centered images. The polar cross-power spectrum equals the product of the one-dimensional Fourier transform of the first polar centered image with respect to the polar angle for one or more radial distances and the complex conjugate of the one-dimensional Fourier transform of the second polar centered image with respect to the polar angle for the one or more radial distances. For example, the polar cross-power spectrum can be calculated at a single radial distance (producing a vector with values for each polar angle frequency), multiple radial distances (producing a matrix with values for each polar angle frequency and radial distance), or all of the radial distances included in the polar centered images (producing a matrix with values for each polar angle frequency and radial distance). The polar cross-power spectrum can also be calculated by averaging or weighting contributions from different radial distance coordinates. The correction angle is determined by fitting, e.g., by least squares regression, the phase profile of the polar cross-power spectrum to the product k
&thgr;
&Dgr;, where &Dgr; is the rotational correction angle and k
&thgr;
is the angular frequency coordinate of the phase profile of the cross-power spectrum.
Once the correction angle is determined, the first image is rotated by the correction angle to rotationally align the first and second images. Thereafter, the rotationally aligned images can be translationally aligned.
In general, in one aspect, the invention feature a method for estimating a correction angle that rotationally aligns a first polar centered image with a second polar centered image, wherein the first and second polar centered images include values on a polar grid having evenly spaced polar angle coordinates for each of at least one radial distance coordinate. The method includes: calculating a polar cross-power spectrum for the first and second polar centered images, the polar cross-power spectrum including a phase profile having at least polar angular frequency coordinates; and fitting a linear function of the angular frequency coordinate to the phase profile of the polar cross-power spectrum to determine the correction angle.
The method can include any of the following features. The polar cross-power spectrum and phase profile can be matrices having polar angular frequency coordinates and radial distance coordinates. Alternatively, the polar cross-power spectrum and phase profile can be vectors having only polar angular frequency coordinates. The linear function can be k
&thgr;
&Dgr; where k
&thgr;
is the polar angular frequency coordinate and &Dgr; is the correction angle. The fitting step can include using a least squares regression.
In some embodiments, the fitting step includes unwrapping values for the phase profile based on an estimate for the correction angle. The fitting step can further include determining the estimate by fitting a subset of values for the phase profile to the linear function, wherein the subset of values corresponds to angular frequencies k
&thgr;
that are less than 2&pgr; divided by an upper limit for the correction angle.
In other embodiments, the fitting step includes determining a first estimate &Dgr;
(1)
for the correction angle based by fitting a subset of values for the phase profile to the linear function, wherein the subset of values corresponds to angular frequencies k
&thgr;
that are less than 2&pgr; divided by an upper limit for the correction angle. The fitting step can further include determining a correction to the first estimate &Dgr;
(1)
by calculating a residual phase equal to the phase profile subtracted by k
&thgr;
&Dgr;
(1)
and fitting the residual phase to another linear function.
In another aspect, the invention features estimating a correction angle that rotationally aligns a first image with a second image, wherein the first and second images each include values on an evenly spaced Cartesian grid. The method includes: Fourier transforming the first and second images to produce first and second k-space images, wherein values of the first and second k-space images include complex values on an evenly spaced k-space Cartesian grid; generating first and second centered images from the first and second k-space images with a mapping function that maps the absolute value of each complex value in the first and second k-space images to generate a corresponding value in the first and second centered images; converting
Fish & Richardson P.C.
Mariam Daniel G.
The McLean Hospital Corporation
Tran Phuoc
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