Structured Bitmap-to-Mesh triangulation for geometry-aware discretization of image-derived domains

Abstract

We introduce a template-driven triangulation framework for embedding discrete boundaries into a regular triangular grid, enabling raster- or segmentation-derived domains to support structure-preserving, numerically stable PDE discretization. Unlike constrained Delaunay triangulation (CDT), which requires global connectivity updates, our method retriangulates only boundary-intersecting triangles, preserving the base mesh and enabling synchronization-free parallel execution. To ensure determinism and scalability, all local intersection patterns are classified under discrete equivalence and triangle symmetry, forming a finite symbolic lookup table mapping each case to a conflict-free retriangulation template. The resulting mesh is provably closed, angle-bounded, and compatible with cotangent-based discretizations and finite element methods. Numerical experiments – including elliptic and parabolic PDEs, signal interpolation, and structural evaluation – demonstrate fewer slivers, more equilateral elements, and greater geometric fidelity near complex boundaries. These properties make the framework well suited for real-time geometric analysis and physically grounded simulation over image-derived domains.