3D Tumor Scale Estimation via Mean Shift Covariance Analysis
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Solution Overview
Problem
Existing methods for characterizing 3D local structures of tumors across various scales in medical images are prone to signal noise sensitivity and accuracy degradation when target shapes differ significantly from isolated Gaussian shapes, which is common in medical imaging where tumors often appear as irregular shapes within noisy backgrounds.
Innovation Solution
A method using a mean shift-based gradient ascent to estimate an extended mean-shift vector, grouping convergent data points to form local structure candidates, and determining underlying scales through a constrained least-squares method for covariance matrix estimation, followed by a stability test across analysis scales to find optimal scale estimates for each local target.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional methods are used for characterizing 3D local structures of tumors, then the analysis can be performed, but the results are highly sensitive to signal noise and accuracy degrades when target shapes differ from isolated Gaussian
Solution Approach 1:
The patent transforms the tumor characterization problem from assuming fixed Gaussian parameters to estimating fully parameterized covariance matrices that adapt to the actual tumor geometry. By changing the mathematical model parameters from simplified assumptions to data-driven estimates, the method achieves robustness against noise and irregular shapes while improving measurement precision of tumor scales
Solution Approach 2:
The patent replaces traditional mechanical filtering approaches with a statistical field theory-based method. Instead of using fixed kernel convolutions, the invention employs mean-shift-based gradient ascent and constrained least-squares optimization to estimate covariance matrices, substituting rigid mechanical analogies with flexible statistical modeling that adapts to complex tumor geometries and noise conditions
2Adaptability or versatility
If traditional Gaussian-based methods are used, then the analysis is simpler, but the methods cannot accurately represent complex 3D structures of tumors with irregular shapes
Solution Approach 1:
The patent segments the tumor analysis into distinct computational stages: first identifying local extrema through mean-shift-based gradient ascent, then estimating covariance matrices for each detected structure, and finally performing stability tests across scales. This segmentation of the complex analysis process into manageable steps enables accurate representation of irregular 3D tumor structures while controlling computational complexity through systematic decomposition
Solution Approach 2:
The patent extends the analysis from 3D spatial coordinates to 4D scale-space by incorporating scale as an additional dimension. By performing stability tests across multiple analysis scales and estimating fully parameterized covariance matrices that include scale information, the method captures complex 3D tumor structures in a higher-dimensional space, enabling versatile representation while managing complexity through scale-based decomposition
Data Source
AI summary
A method for determining the location, shape and orientation of a tumor in a medical image includes finding a plurality of spatial extrema μ of a D-dimensional spatial signal f for a set of bandwidths H by performing mean shift-based gradient-ascent iterations for a set of bandwidths H and then determining a D-dimensional spread and orientation of the signal about each extrema μ by estimating a covariance Σ of the signal f for each extrema μ. The optimal estimate of μ and Σ is determined by performing a Jensen-Shannon divergence on the full set of μ and Σ.