# Accelerating HKTex without Mesh Eigensystems: Local Unfolding and Randomized Thermal Features

arXiv: https://arxiv.org/abs/2609.14105 · HTML: https://mlsanity.com/paper/2609.14105/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 12 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Differentiable Surface Splatting for Point-based Geometry Processing](https://mlsanity.com/paper/1906.04173/) (2019)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [NeuTex: Neural Texture Mapping for Volumetric Neural Rendering](https://mlsanity.com/paper/2103.00762/) (2021)
- [The Vector Heat Method](https://mlsanity.com/paper/1805.09170/) (2018)
- [Intrinsic Neural Fields: Learning Functions on Manifolds](https://mlsanity.com/paper/2203.07967/) (2022)
- [Heat Kernel Textures: the Geodesic Gaussians That Do Not Splat](https://mlsanity.com/paper/2609.07557/) (2026)

## Abstract (arXiv)

Heat Kernel Textures (HKTex) represent surface appearance with intrinsic anisotropic kernels, but evaluate them using 50 global Laplace-Beltrami eigendecompositions and a resident basis of shape [50,V,256]. We study two complementary ways to remove this bottleneck while leaving the trainer, GeodesicOpt, density control, and compositing unchanged. LocalHK exploits the measured locality of trained kernels and replaces spectral evaluation by radius-bounded hinge unfolding and an analytic log-map kernel. On 10 Objaverse meshes and an 8-mesh low-poly holdout, it changes mean view PSNR from 31.35 to 32.00 and from 29.82 to 30.76 dB, respectively, while reducing initialization by 40.5 times and enabling a 749,570-vertex proxy-backed run where the spectral baseline fails. ThermalRF instead preserves the discrete anisotropic heat semigroup: GPU sparse Chebyshev actions and randomized range finding construct global low-rank heat factors without mesh-sized eigenvectors, and a compiled evaluator mixes four neighboring thermal responses. On spot and a thin-stem challenge, ThermalRF reduces end-to-end preprocessing, initialization, and 5,000-step optimization by 29.3% and 24.4%, with every surface, atlas, or view PSNR change within 0.12 dB and training allocation reduced by about 90%. The two routes expose a useful design choice: maximal locality and scale versus fidelity to the thermal PDE. Broader thermal-feature evaluation and real large scenes remain future work.