Method and system for analysis of volumetric data
Inventors
Frank, Lawrence R. • GALINSKY, Vitaly
Assignees
Office of General Counsel of VA • University of California San Diego UCSD
Publication Number
US-10297022-B2
Publication Date
2019-05-21
Expiration Date
2034-09-15
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Abstract
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.
Core Innovation
The invention provides a method and system for modeling complex shapes from volumetric data using spherical wave decomposition (SWD). This approach combines angular-only basis functions of the spherical harmonics (SPHARM) with radial basis functions obtained by asymptotic expansion as a series of sine and cosine Fourier transforms to form a complete three-dimensional (3D) basis. This 3D basis is used to expand the volumetric data, resulting in a 3D volume representation allowing construction of images capturing both surface and internal structures of the target object.
The problem addressed by the invention lies in the inefficiency, time consumption, and error proneness of traditional surface-based methods for characterizing complex shapes within volumetric data. Traditional methods require segmentation of surfaces and often subsequent inflation processes to satisfy uniqueness or stability in surface fitting algorithms, which are computationally intensive and introduce topological defects. Moreover, existing surface-based morphometry techniques, such as SPHARM, are limited to surface data and cannot directly analyze volumetric data, thereby missing internal structural information and requiring segmentation as a preprocessing step.
The inventive method directly analyzes entire volumetric data by employing a combined set of angular spherical harmonics and radial spherical Bessel functions, enabling simultaneous characterization of overall shape and internal structure. This approach obviates the need for surface segmentation and inflation steps, significantly reducing computational time and eliminating topological errors. It provides a more complete description of noisy volumetric data, is computationally more efficient, and supports robust quantitative characterization and comparison of complex 3D morphological features from high resolution voxel-based imaging modalities.
Claims Coverage
The patent contains several independent claims focusing on methods and computer-program products for generating and modeling three-dimensional representations of brain morphology using volumetric MRI data and spherical wave decomposition.
Method for generating 3D brain morphology model using spherical wave decomposition
The method involves acquiring volumetric MRI data comprising Cartesian coordinates, transforming this data into spherical coordinates with radial and angular variables, expanding the angular variables into spherical harmonic basis functions to obtain angular coefficients, expanding radial variables using radial basis functions expanded by asymptotic series of sine and cosine Fourier transforms to obtain radial coefficients, combining these coefficients to construct a 3D volume representation, transforming back to Cartesian coordinates, and displaying the 3D model.
Transformation of volumetric data by convolution with resampling filters
The volumetric data is transformed by convolving with resampling filters, which balance between speed and quality by varying from nearest neighbor to complex multipoint interpolation, both during transformation to spherical coordinates and back to Cartesian coordinates.
Computer-program product for generating 3D brain morphology model
A computer-readable medium storing instructions that, when executed, receive volumetric MRI data with Cartesian coordinates, transform it into spherical coordinates, compute the spherical wave decomposition by expanding angular variables with spherical harmonics and radial variables with radial basis functions via sine and cosine Fourier transforms, combine coefficients to form a 3D volume signature, transform it back into Cartesian coordinates, and display the model.
Computer-program product for modeling brain morphology using combined basis functions
This product models brain morphology by combining angular-only basis functions of SPHARM with radial basis functions comprising sine and cosine Fourier transforms to produce a complete 3D basis, expanding input volumetric MRI data using this basis to generate a morphology signature, and displaying a 3D volume representation.
The independent claims collectively cover methods and computer-program products that implement spherical wave decomposition on volumetric MRI data by transforming to spherical coordinates, expanding angular and radial components into respective basis functions—including spherical harmonics and sine/cosine Fourier series—and constructing and displaying three-dimensional models of brain morphology in Cartesian coordinates with efficient resampling strategies.
Stated Advantages
Significant reduction in computational time compared to traditional surface-based methods, due to elimination of surface segmentation and inflation steps.
Elimination of topological errors associated with surface inflation and segmentation processes.
More complete description of noisy volumetric data by simultaneous characterization of both overall shape and internal structure using a combined angular and radial basis.
Higher accuracy and robustness over surface-only approaches, providing superior representation of volumetric data including internal features.
Applicability to high-resolution 3D voxel-based digital imaging modalities, enabling quantitative morphological analysis and comparison across specimens.
Documented Applications
Morphological characterization of the human brain from volumetric MRI data.
Characterization of neuronal fibers and brain connectivity using diffusion tensor magnetic resonance imaging.
Anatomical mapping and quantification of changes in human anatomy, including brain changes during diseased states useful in clinical studies.
Comparative morphometry for neuroscience research and comparative biology involving high resolution volumetric data.
3D visualization of weather data such as Doppler radar for detection and prediction.
Geotechnical assessment of oil, gas, or mineral deposits and geodynamic simulations employing particle-grid based methods.
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