Connectivity-Preserving Cortical Surface Tetrahedralization

TL;DR

The paper addresses the challenge of generating volumetric tetrahedral meshes from cortical surfaces while preserving the original surface connectivity, even in the presence of self-intersections and defects. It introduces a connectivity-preserving tetrahedralization that uses a twin-point scheme, a Delaunay triangulation, removal of tetrahedra crossing the surface, and flood-fill to isolate the main interior component, followed by restoring twin points. A dedicated connectivity metric based on landmark geodesic distances quantifies how well the input connectivity is retained, and the method is evaluated against state-of-the-art approaches on a large cortical surface, showing superior connectivity preservation and deformation behavior close to ground truth. The approach offers a robust alternative for neuroimaging and biomechanical simulations, with potential applicability to other domains requiring topology-preserving mesh generation from imperfect surface data.

Abstract

A prerequisite for many biomechanical simulation techniques is discretizing a bounded volume into a tetrahedral mesh. In certain contexts, such as cortical surface simulations, preserving input surface connectivity is critical. However, automated surface extraction often yields meshes containing self-intersections, small holes, and faulty geometry, which prevents existing constrained and unconstrained meshers from preserving this connectivity. We address this issue by developing a novel tetrahedralization method that maintains input surface connectivity in the presence of such defects. We also present a metric to quantify the preservation of surface connectivity and demonstrate that our method correctly maintains connectivity compared to existing solutions.

Figures (3)

• Figure 1: Illustration of the 2D version of our algorithm on a mesh with self-intersecting regions. (A) Input surface with overlapping regions indicated by arrows. (B) Construction of the point set $\mathbf{P}$ with twin points determined by node normal directions. (C) Addition of approximately uniform internal points to $\mathbf{P}$. (D) Triangulation of the point set $\mathbf{P}$. (E) Removal of any tetrahedra (or triangles in 2D) intersecting the original faces. (F) Elimination of disconnected components, keeping only the main connected component. (G) Restoration of twin nodes to their original positions, yielding the final mesh. Input nodes and edges are colored blue, triangulation edges are orange, and twin nodes are highlighted in yellow.
• Figure 2: Comparison of tetrahedralized mesh surface connectivity. Each surface vertex $v$ is colored by linear interpolation between green (low discrepancy) and red (high discrepancy), with the interpolation factor determined by the connectivity metric $C(v)$ described in \ref{['section-tet-method']}. Green indicates good agreement between the reference surface connectivity and the tetrahedral mesh surface connectivity, while red indicates significant differences.
• Figure 3: Comparison of smoothing simulation applied to tetrahedral meshes, highlighting connectivity issues. Top left: Input surface. Top right: Input surface after iterative smoothing. Bottom row: Results of smoothing applied to meshes generated by Isosurface Stuffing (left), TetWild (center), and our method (right).