Method and system for analysis of volumetric data
A method is provided for modeling complex shapes from volumetric data utilizing spherical wave decomposition (SWD) by combining angular-only basis functions of the SPHARM with radial basis functions obtained by asymptotic expansion as a series of sine and cosine Fourier transforms to form the complete 3D basis. The 3D basis is used to expand the volumetric data. The resulting 3D volume representation allows construction of images of both surface and internal structures of the target object.
1. A method for generating a three-dimensional model of brain morphology, comprising:
acquiring, via an imaging system, volumetric MRI data for a subject's brain, the volumetric MRI data comprising three-dimensional datapoints comprising Cartesian coordinates;
inputting the volumetric MRI data into a computer processor having instructions stored therein for causing the computer processor to execute the steps of:
transforming the volumetric MRI data into spherical coordinates comprising radial and angular variables and computing spherical wave decomposition by;
expanding the transformed spherical coordinates into 3D basis functions by:
expanding angular variables into angular-only spherical harmonic basis functions having preselected angular degree to determine angular coefficients; and
expanding the radial variables into radial basis functions having preselected radial degrees by asymptotic expansion as a series of sine and cosine Fourier transforms to determine radial coefficients, wherein the series of sine and cosine Fourier transforms have the form
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combining angular coefficients and radial coefficients to construct a signature for a 3D volume representation of the brain morphology in spherical coordinates;
transforming the signature into a 3D volume representation of the brain morphology into Cartesian coordinates; and
displaying the transformed 3D volume representation of the brain morphology on a graphical user interface.
2. The method of claim 1 , wherein the step of transforming the volumetric data comprises convolving the volumetric data with a resampling filter having the form
ƒ( r )=∫∫∫ x ( x−x ′)ƒ( x ′) d 3 x′.
3. The method of claim 2 , wherein the resampling filter is balanced between speed and quality by varying between nearest neighbor to complex multipoint interpolation.
4. The method of claim 1 , wherein the step of transforming the 3D volume representation comprises convolving the 3D volume data with a resampling filter having the form
ƒ( x )=∫∫∫ r ( r−r ′)ƒ( r ′) dV′.
5. The method of claim 4 , wherein the resampling filter is balanced between speed and quality by varying between nearest neighbor to complex multipoint interpolation.
6. A computer-program product embodied in a non-transitory computer-readable medium which, when executed by a computer processor cause the processor to generate a three-dimensional model of brain morphology by:
receiving volumetric data generated by an MRI scanning system for a subject's brain scan, the volumetric data comprising 3-dimensional data points comprising Cartesian coordinates;
transforming the volumetric data into spherical coordinates comprising radial and angular variables;
computing spherical wave decomposition (SWD) by expanding the transformed spherical coordinates into 3D basis functions by:
expanding angular variables into angular-only spherical harmonic basis functions having preselected angular degrees to determine angular coefficients; and
expanding the radial variables into radial basis functions having preselected radial degrees by asymptotic expansion as a series of sine and cosine Fourier transforms to determine radial coefficients;
combining angular coefficients and radial coefficients to construct a signature for a 3D volume representation of the brain morphology in spherical coordinates;
transforming the signature into a 3D volume representation of the brain morphology into Cartesian coordinates; and
displaying the transformed 3D volume representation of the brain morphology on a graphical user interface in communication with the computer processor.
7. A computer-program product embodied in a non-transitory computer-readable medium which, when executed by a computer processor, cause the processor to model brain morphology of a subject's brain from input volumetric MRI data by:
combining angular-only basis functions of SPHARM with radial basis functions comprising a series of sine and cosine Fourier transforms to form a complete 3D basis;
expanding the input volumetric MRI data using the complete 3D basis to generate a signature for brain morphology; and
generating an output comprising displaying a 3D volume representation of the brain morphology.
8. The computer-program product of claim 7 , wherein the step of combining includes:
transforming the volumetric data into spherical coordinates comprising radial and angular variables; and
expanding angular variables into spherical harmonic basis functions to determine angular coefficients and expanding radial variables into radial basis functions to determine radial coefficients.
9. The computer-program product of claim 7 , wherein the step of generating comprises transforming the 3D volume representation of the structure into Cartesian coordinates.
10. The computer-program product of claim 6 , wherein the computer processor transforms the volumetric data by convolving the volumetric data with a resampling filter having the form
ƒ( r )=∫∫∫ x ( x−x ′)ƒ( x ′) d 3 x′.
11. The computer-program product of claim 10 , wherein the resampling filter is balanced between speed and quality by varying between nearest neighbor to complex multipoint interpolation.
12. The computer-program product of claim 6 , wherein the computer processor transforms the 3D volume representation by convolving the 3D volume data with a resampling filter having the form
ƒ( x )=∫∫∫ r ( r−r ′)ƒ( r ′) dV′.
13. The computer-program product of claim 12 , wherein the wherein the resampling filter is balanced between speed and quality by varying between nearest neighbor to complex multipoint interpolation.
14. The computer-program product of claim 6 , wherein the series of sine and cosine Fourier transforms have the form:
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15. The computer-program product of claim 7 , wherein the series of sine and cosine Fourier transforms have the form:
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