Dynamic Graph Analysis: A Hybrid Structural–Spatial Approach for Brain Shape Correspondence

• Published in: Machine learning and knowledge extraction Vol. 7; no. 3; p. 99
• Main Authors: Arias-García, Jonnatan, García, Hernán Felipe, Escobar-Mejía, Andrés, Cárdenas-Peña, David, Orozco, Álvaro A.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.09.2025
• Subjects: Algorithms; Assignment problem; Biological markers; Biomarkers; Brain; brain morphometry; Clustering; Computing costs; Datasets; Deformations (Mechanics); graph-based registration; Graphs; Kuhn–Munkres algorithm; Medical imaging; Methods; Morphology; Neuroimaging; non-rigid registration; Optimization; Rescaling; shape correspondence; Spectral methods; Symmetry; Topology; Colombia
• ISSN: 2504-4990; 2504-4990
• DOI: 10.3390/make7030099

Accurate correspondence of complex neuroanatomical surfaces under non-rigid deformations remains a formidable challenge in computational neuroimaging, owing to inter-subject topological variability, partial occlusions, and non-isometric distortions. Here, we introduce the Dynamic Graph Analyzer (DGA), a unified hybrid framework that integrates simplified structural descriptors with spatial constraints and formulates matching as a global linear assignment. Structurally, the DGA computes node-level metrics, degree weighted by betweenness centrality and local clustering coefficients, to capture essential topological patterns at a low computational cost. Spatially, it employs a two-stage scheme that combines global maximum distances and local rescaling of adjacent node separations to preserve geometric fidelity. By embedding these complementary measures into a single cost matrix solved via the Kuhn–Munkres algorithm followed by a refinement of weak correspondences, the DGA ensures a globally optimal correspondence. In benchmark evaluations on the FAUST dataset, the DGA achieved a significant reduction in the mean geodetic reconstruction error compared to spectral graph convolutional netwworks (GCNs)—which learn optimized spectral descriptors akin to classical approaches like heat/wave kernel signatures (HKS/WKS)—and traditional spectral methods. Additional experiments demonstrate robust performance on partial matches in TOSCA and cross-species alignments in SHREC-20, validating resilience to morphological variation and symmetry ambiguities. These results establish the DGA as a scalable and accurate approach for brain shape correspondence, with promising applications in biomarker mapping, developmental studies, and clinical morphometry.