Using Structural Similarity and Kolmogorov-Arnold Networks for Anatomical Embedding of Cortical Folding Patterns

TL;DR

The paper tackles the lack of cross-subject correspondence for the fine-scale 3-hinge gyrus folding pattern by introducing a self-supervised anatomical embedding framework. It leverages a structural similarity–enhanced hierarchical multi-hop encoding and Kolmogorov-Arnold Network (KAN) to produce robust, cross-subject embeddings of 3HGs, paired with a selective reconstruction loss to improve representation of nonzero features. Using a large HCP dataset and a rigorous experimental setup, the method demonstrates improved cross-subject correspondences and ROI connectivity patterns, particularly for 3-hop features. The approach enables mapping 3HGs across individuals without one-to-one mappings and offers a scalable path toward population-wide 3HG-based network analyses and disease-related studies. Future work includes incorporating multimodal features and adaptive weighting to further enhance cross-subject alignment.

Abstract

The 3-hinge gyrus (3HG) is a newly defined folding pattern, which is the conjunction of gyri coming from three directions in cortical folding. Many studies demonstrated that 3HGs can be reliable nodes when constructing brain networks or connectome since they simultaneously possess commonality and individuality across different individual brains and populations. However, 3HGs are identified and validated within individual spaces, making it difficult to directly serve as the brain network nodes due to the absence of cross-subject correspondence. The 3HG correspondences represent the intrinsic regulation of brain organizational architecture, traditional image-based registration methods tend to fail because individual anatomical properties need to be fully respected. To address this challenge, we propose a novel self-supervised framework for anatomical feature embedding of the 3HGs to build the correspondences among different brains. The core component of this framework is to construct a structural similarity-enhanced multi-hop feature encoding strategy based on the recently developed Kolmogorov-Arnold network (KAN) for anatomical feature embedding. Extensive experiments suggest that our approach can effectively establish robust cross-subject correspondences when no one-to-one mapping exists.

Figures (4)

• Figure 1: Overall architecture of the proposed self-supervised framework. The framework constructs a structural similarity enhanced multi-hop feature encoding strategy and uses recent proposed Kolmogorov-Arnold network for anatomical feature embedding of the 3HGs.
• Figure 2: ROI embedding connectivity. The Top-5 connections (PCC between pairs of ROIs) from the learned ROI embeddings $\Phi_{ROI}$ are derived using 1-hop, 2-hop, and 3-hop features. The division of ROIs is based on the Destrieux Atlas. Within each row, connections are ordered by their rank from left to right. Color lookup table provided by Freesurfer.
• Figure 3: Quantitative evaluation. Evaluation of different hyperparameter setting and ablation analysis of the proposed selective reconstruction loss (w/o SR) via MSE, PCC and SSIM. Note that the y-axis is on a log-scale.
• Figure 4: Illustration of cross-subject correspondence. All 3HGs are represented as bubbles, with yellow indicating exemplars, blue indicating the identified corresponding points in other subjects, and red indicating the candidate points with cosine similarity close to the corresponding point.