Diffeomorphic Cortical Alignment via Direct Warping of Streamline Endpoints
Authors: Yang Xiang, Martin Cole, Zhengwu Zhang
Organizations: Department of Statistics and Operations Research, The University of North Carolina at Chapel Hill · Department of Psychiatry, University of Rochester
Abstract
Cortical surface registration is often driven by local geometric descriptors (e.g., sulcal depth and curvature). While this approach achieves geometric correspondence, it neglects the long-range wiring constraints imposed by white-matter anatomy. Diffusion MRI tractography offers these crucial constraints; however, prior connectivity-informed pipelines typically align precomputed connectivity matrices, making the optimization highly sensitive to connectivity estimation and its resolution. In this paper, we introduce a novel connectivity-based surface registration method that aligns cortical surfaces by operating directly on white-matter fiber-tract endpoints. We model tract endpoints as a point cloud on the product manifold Ω×Ω, where Ω represents the spherical domain of the inflated cortical hemispheres. Our alignment method iteratively (i) computes a small diffeomorphic warp for Ω by minimizing connectivity mismatch, and (ii) updates the endpoints based on this warp. The method relies on a geometric framework that ensures output warps are diffeomorphisms and has a final goal that optimizes the matching of well-known fiber bundles. Experiments on Human Connectome Project (HCP) data demonstrate improved tract-level correspondence, achieving higher connectivity-level overlap coefficients on major fiber bundles and stronger robustness across grid resolutions for Ω compared to state-of-the-art methods such as ENCORE and MSMAll.
Diffusion MRI (dMRI) tractography is the only noninvasive approach for mapping white-matter pathways in the living human brain. It represents each brain as a tractogram: a large, unordered set of three-dimensional streamlines that includes information about both local streamline geometry and whole-brain anatomical organization. This structure makes tractograms a natural but challenging target for representation learning. Existing methods treat streamline classification and subject-level prediction as separate problems: streamline classifiers focus on geometric patterns, whereas subject-level prediction often depends on hand-crafted features. As a result, current methods do not learn reusable representations that connect streamline anatomy with whole-brain inter-subject variation. Here we introduce TractFM, a tractogram foundation model that learns reusable representations directly from whole-brain streamline sets. TractFM combines a local streamline encoder with a permutation-equivariant tractogram encoder, allowing all streamlines from a subject to be contextualized jointly in a single forward pass. Pretraining on dense anatomical tract parcellation, i.e., assigning anatomical labels to individual streamlines, yields two complementary representations: contextualized streamline-level embeddings for tract parcellation and compact subject-level descriptors for downstream prediction of subject phenotypes. Across three tractography algorithms and five dMRI datasets, TractFM transfers to both streamline-level and subject-level tasks. Its frozen representations achieve accurate tract parcellation and predict age and sex across independent datasets. These results show that whole-brain geometric context, learned once, can generalize across tractography pipelines, datasets, and prediction tasks.
Soft-tissue deformation remains a major limitation in image-guided neurosurgery, where intra-operative anatomy can deviate substantially from pre-operative imaging due to brain shift, compromising navigation accuracy and surgical safety. Existing compensation methods often rely on intra-operative MRI, CT, or ultrasound, which are disruptive and difficult to integrate repeatedly into the surgical workflow. In contrast, partial 3D cortical surfaces can be reconstructed as point clouds from stereoscopic microscopes or laser range scanners (LRS), capturing only a limited portion of the exposed cortex. This makes point cloud registration a practical alternative without interrupting surgery; however, such partial and noisy observations make deformation estimation highly challenging. In this study, we propose a deep learning-based framework for non-rigid volume-to-surface registration, enabling dense displacement field estimation from sparse intra-operative surface observations without explicit point correspondences or volumetric intra-operative imaging. The network leverages multi-scale point-based feature extraction and a hierarchical deformation decoder to capture both global and local deformations. The key contribution lies in integrating partial intra-operative surface information into the full pre-operative point cloud domain, enabling implicit correspondence learning and dense deformation recovery under limited visibility. Quantitative results demonstrate accurate recovery of fine-scale deformations, achieving an Endpoint Error (EPE) of 1.13 +/- 0.75 mm and RMSE of 1.33 +/- 0.81 mm under challenging partial-surface conditions. The proposed approach supports automatic, workflow-compatible brain-shift compensation from sparse surface observations.
Eashrat Jahan Muniya, Gernot Kronreif, Ander Biguri +2
Decoding brain activity is useful for characterizing brain processes and understanding the functional architecture underlying cognition. However, the inter-individual variability in brain response patterns limits the development of decoders that generalize across individuals. A solution to this challenge is functional alignment: aligning functional data across individuals before training population-level decoders. The core issue is to strike the balance between aligning functional features and preserving the anatomical structure, while maintaining computational efficiency. We introduce a new functional alignment method for fMRI, SpectralOT, that embeds cortical geometry into Laplace-Beltrami eigenmodes along functional data to regularize the alignment.