Structured Bitmap-to-Mesh Triangulation for Geometry-Aware Discretization of Image-Derived Domains
This addresses the need for efficient and stable geometry-aware discretization for real-time geometric analysis and physically based simulation over image-derived domains, though it appears incremental compared to constrained Delaunay triangulation.
The paper tackles the problem of generating stable triangular meshes from image-derived boundaries for PDE discretization by proposing a template-driven triangulation framework that retriangulates only boundary-intersected triangles while preserving the base mesh. The result is a deterministic, parallelizable method that produces closed meshes with bounded angles, leading to fewer sliver elements, more regular triangles, and improved geometric fidelity in experiments on elliptic/parabolic PDEs and signal interpolation.
We propose a template-driven triangulation framework that embeds raster- or segmentation-derived boundaries into a regular triangular grid for stable PDE discretization on image-derived domains. Unlike constrained Delaunay triangulation (CDT), which may trigger global connectivity updates, our method retriangulates only triangles intersected by the boundary, preserves the base mesh, and supports synchronization-free parallel execution. To ensure determinism and scalability, we classify all local boundary-intersection configurations up to discrete equivalence and triangle symmetries, yielding a finite symbolic lookup table that maps each case to a conflict-free retriangulation template. We prove that the resulting mesh is closed, has bounded angles, and is compatible with cotangent-based discretizations and standard finite element methods. Experiments on elliptic and parabolic PDEs, signal interpolation, and structural metrics show fewer sliver elements, more regular triangles, and improved geometric fidelity near complex boundaries. The framework is well suited for real-time geometric analysis and physically based simulation over image-derived domains.