$\mathrm {H^{2}}$GM: A Hierarchical Hypergraph Matching Framework for Brain Landmark Alignment

Abstract

Gyral hinges (GHs) are novel brain gyrus landmarks, and their precise alignment is crucial for understanding the relationship between brain structure and function. However, accurate and robust GH alignment is challenging due to the massive cortical morphological variations of GHs between subjects. Previous studies typically construct a single-scale graph to model the GHs relations and deploy the graph matching algorithms for GH alignment but suffer from two overlooked deficiencies. First, they consider only pairwise relations between GHs, ignoring that their relations are highly complex. Second, they only consider the point scale for graph-based GH alignment, which introduces several alignment errors on small-scaled regions. To overcome these deficiencies, we propose a Hierarchical HyperGraph Matching ($\mathrm {H^{2}}$GM) framework for GH alignment, consisting of a Multi-scale Hypergraph Establishment (MsHE) module, a Multi-scale Hypergraph Matching (MsHM) module, and an Inter-Scale Consistency (ISC) constraint. Specifically, the MsHE module constructs multi-scale hypergraphs by utilizing abundant biological evidence and models high-order relations between GHs at different scales. The MsHM module matches hypergraph pairs at each scale to entangle a robust GH alignment with multi-scale high-order cues. And the ISC constraint incorporates inter-scale semantic consistency to encourage the agreement of multi-scale knowledge. Experimental results demonstrate that the $\mathrm {H^{2}}$GM improves GH alignment remarkably and outperforms state-of-the-art methods. The code is available at here.

Z. He—This work was done when Zhibin He was a visiting student at the Department of Electronic Engineering, The Chinese University of Hong Kong.