Reeb Graph Lesion Shape Analysis in Breast MR Imaging
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Solution Overview
Problem
Existing shape features in breast MR imaging are scalar-based and have limited descriptive power, failing to effectively differentiate complex lesion boundaries, which hampers accurate detection of malignant lesions.
Innovation Solution
The use of a Reeb graph structure to represent lesion shapes, calculated using an isolation measure function, provides a detailed graph structure for shape analysis, allowing for the discrimination of malignant lesions by analyzing the number of branches and isolation measures in the graph.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If scalar shape features (S1/2/V1/3, fractal dimension) are used to represent lesion complexity, then the analysis is simple and fast, but the descriptive power is limited and cannot effectively differentiate complex lesion boundaries
Solution Approach 1:
The patent segments the lesion shape into a graph structure where nodes represent boundary points and edges represent connectivity between points. This segmentation allows complex boundary geometries to be represented as discrete graph elements, enabling detailed analysis of lesion morphology while maintaining computational tractability through graph processing algorithms.
Solution Approach 2:
The patent transitions from scalar shape features (zero-dimensional summary statistics) to graph-based representations (multi-dimensional structural information). By representing lesions as graphs with nodes, edges, and topological relationships, the system captures complex boundary geometries in multiple dimensions simultaneously, providing rich descriptive power for malignancy differentiation.
2Loss of information
If fractal dimension is used to represent carcinoma shape complexity, then a single scalar value is obtained, but the descriptive power is limited because it is only a one-dimensional projection of complicated features
Solution Approach 1:
The patent segments the continuous boundary into discrete graph nodes and edges, preserving geometric information while enabling computational analysis. This segmentation prevents information loss by maintaining detailed boundary representations rather than reducing them to single scalar values.
Solution Approach 2:
The patent elevates the representation from one-dimensional scalars to multi-dimensional graph structures. The graph captures spatial relationships, connectivity, and topological features simultaneously, preserving comprehensive shape information without the dimensional reduction inherent in fractal dimension approaches.
3Measurement precision
If Reeb graph structure is used to represent lesion shapes, then detailed graph structure provides enhanced discriminatory power, but the calculation and analysis process becomes more complex
Solution Approach 1:
The patent segments the lesion boundary into graph nodes and edges, creating a discrete representation that can be systematically analyzed. This segmentation enables complex shape features to be computed through standard graph algorithms, balancing detailed representation with computational feasibility.
Solution Approach 2:
The patent creates a simplified graph model (Reeb graph) that copies essential topological features of the complex lesion boundary. By representing only the critical structural information (nodes at critical points and edges connecting them), the system maintains discriminatory power while reducing computational complexity compared to analyzing the full boundary geometry.
Data Source
AI summary
A method for analyzing a shape of a region of interest in a medical image of a body part, including: finding a region of interest in the medical image; calculating a Reeb graph of the region of interest, and determining whether the region of interest is a malignant lesion candidate based on a shape characteristic of the Reeb graph.