Non-Euclidean Graph Segmentation for Volumetric Medical Images
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Solution Overview
Problem
Graph search methods for volumetric medical images, particularly in Euclidean space, face limitations in achieving precision beyond a single unit distance between nodes and ignore partial volume effects, leading to suboptimal segmentation in layered tissues.
Innovation Solution
The approach involves generating a graph representation in non-Euclidean space, allowing non-equidistant node spacing, and calculating a deformation field to adaptively change node density, enabling subvoxel accurate segmentation while retaining global optimality and computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If graph search is performed in Euclidean space with orthogonal graph representation, then computational efficiency and global optimality are achieved, but segmentation precision is limited to single unit distance between nodes and partial volume effects are ignored
Solution Approach 1:
The patent transitions from Euclidean space to non-Euclidean space by introducing a deformation field that warps the graph representation. This dimensional transformation allows nodes to be positioned at non-uniform intervals, enabling sub-voxel precision while preserving the graph search framework's computational advantages. The deformation field adds a new dimension of flexibility to the traditional orthogonal graph structure.
Solution Approach 2:
The patent changes the fundamental parameter of node spacing from uniform (Euclidean) to non-uniform (non-Euclidean) through the application of a deformation field. This parameter change allows the graph to adapt its resolution locally, placing nodes more densely in regions requiring higher precision while maintaining coarser spacing elsewhere, thus improving segmentation precision without uniformly increasing complexity.
2Measurement precision
If uniform node spacing is used in Euclidean graph, then graph structure simplicity is maintained, but precision beyond single unit distance cannot be achieved
Solution Approach 1:
The deformation field is computed beforehand and applied to pre-process the graph structure before the actual segmentation task. This preliminary action of warping the space allows the subsequent graph search to operate on a transformed coordinate system where sub-voxel precision is naturally encoded in the node positions, without complicating the core segmentation algorithm.
Solution Approach 2:
The deformation field acts as an intermediary between the raw volumetric data and the graph representation. It mediates the transformation by warping the spatial coordinates, allowing the graph to capture partial volume effects and achieve sub-voxel precision while keeping the graph search mechanism itself relatively simple and unchanged.
3Reliability
If orthogonal graph in Euclidean space is used, then polynomial time complexity is achieved, but partial volume effects are ignored
Solution Approach 1:
The deformation field enables local quality variation by allowing different regions of the graph to have different node densities and spacing characteristics. In regions where partial volume effects are significant, the deformation warps the space to place nodes more densely, capturing local variations in tissue boundaries with higher fidelity while maintaining coarser representation in homogeneous regions.
Solution Approach 2:
By transforming from Euclidean to non-Euclidean space through the deformation field, the patent introduces an additional degree of freedom in representing spatial relationships. This dimensional change allows the graph to encode partial volume information that would be lost in a strict Euclidean orthogonal representation, improving reliability without sacrificing the polynomial time complexity advantage.
Data Source
AI summary
Disclosed are methods and systems for analyzing data. An example method can comprise receiving volume data representative of an object. A first graph can be generated based on the volume data. The first graph can comprise nodes arranged in a Euclidean space. A deformation field can be determined based on the volume data. The deformation field can be applied to the first graph to form a second graph. The second graph can comprise nodes arranged in a non-Euclidean space. The second graph can be segmented.