🤖 AI Summary
This work addresses the limitations of traditional UV parametrization methods, which are prone to poor initialization, local minima, and topological foldovers that compromise mapping validity under a fixed atlas. The authors reformulate the problem as a continuous neural reparameterization task, leveraging an untrained SIREN network to implicitly map vertex features into UV space, with its weights optimized via geometric energy minimization. Key innovations include using Laplace–Beltrami spectral coordinates as input, Tutte residual warm-starting, a C² determinant expansion, an injectivity barrier, and a validity-check fallback mechanism, collectively forming a verification-first robust solver. Experiments demonstrate that the method achieves 42 and 47 flip-free valid parametrizations on Thingi10K and xatlas-cut benchmarks, respectively—all compact atlases being flip-free—and attains 1,000/1,000 strictly locally valid, flip-free UV atlases on the Amara Spatial dataset.
📝 Abstract
Traditional UV unwrapping relies on direct optimization of geometric distortion energies and can fail through invalid initialization, local minima, or topological foldovers. We recast fixed-chart UV unwrapping as continuous neural reparameterization: an untrained SIREN maps per-vertex mesh features to UV coordinates, and its weights are optimized for a geometric objective. The practical contribution is a robust chart-solver recipe, combining Laplace--Beltrami spectral inputs, Tutte residual warm-up, a $C^2$ determinant extension, an injectivity barrier, and validity-checked retry/fallback routing, rather than a claim that any single component guarantees validity or that recutting methods should be replaced. NTK--LBO diagnostics show that spectral conditioning changes update geometry, especially at initialization and mid-rank subspaces, but does not by itself predict chart success. On compact pre-cut charts and a 47-chart stratified Thingi10K/xatlas-cut benchmark, the neural solver produces zero flips on all compact charts and 42/47 valid zero-flip stratified solves. BFF and OptCuts comparisons sharpen the scope: recutting can be faster and lower-distortion when allowed, while the neural solver targets supplied-chart validity and validation-first atlas construction. On Amara Spatial generated meshes, the full atlas construction path gives packed-atlas coverage on a 25-asset set and 1000/1000 strict locally valid atlases with zero UV flips in a large-scale Rust atlas run after fallback routing.