Volumetric Data Analysis via Spherical Wave Decomposition
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Solution Overview
Problem
Current methods for characterizing complex shapes in volumetric medical imaging data, such as MRI and CT scans, are inefficient and prone to errors due to the need for surface segmentation and inflation, which are time-consuming and computationally intensive, especially when dealing with noisy and high-contrast data.
Innovation Solution
The use of spherical wave decomposition (SWD) that combines angular-only basis functions of SPHARM with spherical Bessel functions to form a complete 3D basis, allowing for direct analysis of volumetric data without segmentation or inflation, providing a more detailed and accurate description of internal structures and overall shape.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If surface based methods are used for characterizing complex shapes in volumetric data, then the analysis can be performed with existing tools, but the process becomes time consuming and computationally intensive due to segmentation and inflation steps
Solution Approach 1:
The patent extracts and removes the problematic segmentation and inflation steps from the traditional surface-based analysis pipeline. By directly fitting spherical harmonics to volumetric data without requiring intermediate surface extraction, the method eliminates time-consuming preprocessing while maintaining characterization accuracy.
Solution Approach 2:
The patent transitions from analyzing 2D surface representations to directly analyzing 3D volumetric data. By working in the volumetric domain with spherical harmonics expansion, the method captures internal structures and three-dimensional geometry more efficiently, avoiding the dimensional reduction to surfaces that necessitates segmentation.
2Manufacturing precision
If surface segmentation is performed to satisfy uniqueness or stability of surface fitting algorithms, then the surface fitting can be performed, but the process becomes error prone and time consuming
Solution Approach 1:
The patent removes the segmentation step entirely from the analysis pipeline. By formulating the problem to work directly with volumetric data and spherical harmonics, the method achieves surface fitting precision without requiring the intermediate extraction and manipulation of surface meshes, thereby reducing process complexity and error sources.
Solution Approach 2:
Instead of the traditional approach of segmenting surfaces first and then fitting mathematical models, the patent inverts the workflow by directly fitting spherical harmonics to volumetric data. This reversal eliminates the need for surface segmentation while achieving comparable or superior fitting precision.
3Measurement precision
If traditional volumetric analysis methods are used, then the entire data volume can be analyzed, but the computational intensity increases significantly
Solution Approach 1:
The patent changes the mathematical parameters and basis functions used for volumetric analysis. By employing spherical harmonics expansion with radial and angular components, the method provides detailed internal structure characterization while improving computational efficiency through the mathematical properties of spherical harmonics, which allow for efficient calculation and reduced data processing requirements.
Data Source
AI summary
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.