Continuous Neural Reparameterization as a Deep Geometric Prior for Robust Fixed-Chart UV Repair

• URL: http://arxiv.org/abs/2606.10050v1
• Date: Mon, 08 Jun 2026 18:26:03 GMT
• Title: Continuous Neural Reparameterization as a Deep Geometric Prior for Robust Fixed-Chart UV Repair
• Abstract summary: We recast fixed-chart UV unwrapping as continuous neural reparameterization.<n>We combine Laplace--Beltrami spectral inputs, Tutte residual warm-up, a $C2$ determinant extension, and validity-checked retry/fallback routing.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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