Undirected Graph Matching via Lattice Generation
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Solution Overview
Problem
Existing methods for matching undirected graphs face challenges in accuracy and efficiency, particularly when dealing with images featuring repeated patterns or severe noise, leading to unstable matching results and high computational complexity.
Innovation Solution
The method involves generating lattices for undirected graphs using non-metric multidimensional scaling (NMDS) and optimizing them based on edge and node features, followed by matching these lattices using a point set registration by preserving global and local structures (PR-GLS) algorithm, which reduces the need for solving the quadratic assignment problem and enhances matching accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing methods for matching undirected graphs are used, then the matching process can be performed, but the accuracy is low and results are unstable when dealing with images featuring repeated patterns or severe noise
Solution Approach 1:
The patent segments the graph matching problem into two distinct phases: (1) lattice generation that captures global structural features, and (2) lattice matching that operates on these simplified representations. This segmentation allows the method to focus on invariant structural properties rather than being affected by local variations such as repeated patterns or noise in the original graphs.
Solution Approach 2:
The patent introduces lattices as an intermediary representation between the original undirected graphs and the matching process. These lattices serve as simplified, noise-resistant mediators that preserve essential structural information while eliminating distracting features like repeated patterns. The matching algorithm then operates on these intermediary lattice structures rather than directly on the complex original graphs.
2Productivity
If existing graph matching methods are used, then matching can be performed, but the computational complexity is high
Solution Approach 1:
The patent divides the computationally intensive graph matching task into two separate, more manageable steps: lattice generation and lattice matching. Each step operates on simplified data structures (lattices) rather than the full complexity of the original graphs, significantly reducing the computational burden while maintaining matching quality.
Solution Approach 2:
The patent creates simplified copies of the original graphs in the form of lattices. These lattice copies retain the essential structural information needed for matching but use a more compact and computationally efficient representation. The matching algorithm then operates on these copied lattice structures, which require fewer computational resources than the original graphs.
Data Source
AI summary
A processor-implemented method includes acquiring, by a processor, a first undirected graph and a second undirected graph, generating, by the processor, a first lattice for the first undirected graph and a second lattice for the second undirected graph; matching, by the processor, the first lattice and the second lattice based on a first global structure of the first lattice and a second global structure of the second lattice, the first global structure corresponding to nodes of the first undirected graph and the second global structure corresponding to nodes of the second undirected graph, and processing the first undirected graph and the second undirected graph based on a result of the matching of the first lattice and the second lattice.