# Heat Kernel Textures: the Geodesic Gaussians That Do Not Splat

arXiv: https://arxiv.org/abs/2609.07557 · HTML: https://mlsanity.com/paper/2609.07557/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 52 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [Relightable 3D Gaussians: Realistic Point Cloud Relighting with BRDF Decomposition and Ray Tracing](https://mlsanity.com/paper/2311.16043/) (2023)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [NeuTex: Neural Texture Mapping for Volumetric Neural Rendering](https://mlsanity.com/paper/2103.00762/) (2021)
- [Texture-GS: Disentangling the Geometry and Texture for 3D Gaussian Splatting Editing](https://mlsanity.com/paper/2403.10050/) (2024)
- [Don't Splat your Gaussians: Volumetric Ray-Traced Primitives for Modeling and Rendering Scattering and Emissive Media](https://mlsanity.com/paper/2405.15425/) (2024)
- [Image-GS: Content-Adaptive Image Representation via 2D Gaussians](https://mlsanity.com/paper/2407.01866/) (2024)
- [The Vector Heat Method](https://mlsanity.com/paper/1805.09170/) (2018)
- [Large Images are Gaussians: High-Quality Large Image Representation with Levels of 2D Gaussian Splatting](https://mlsanity.com/paper/2502.09039/) (2025)
- [GeoSplatting: Towards Geometry Guided Gaussian Splatting for Physically-based Inverse Rendering](https://mlsanity.com/paper/2410.24204/) (2024)
- [Intrinsic Neural Fields: Learning Functions on Manifolds](https://mlsanity.com/paper/2203.07967/) (2022)
- [MeshGS: Adaptive Mesh-Aligned Gaussian Splatting for High-Quality Rendering](https://mlsanity.com/paper/2410.08941/) (2024)
- [Neural Shell Texture Splatting: More Details and Fewer Primitives](https://mlsanity.com/paper/2507.20200/) (2025)
- [UVGS: Reimagining Unstructured 3D Gaussian Splatting using UV Mapping](https://mlsanity.com/paper/2502.01846/) (2025)
- [Uncertainty for SVBRDF Acquisition using Frequency Analysis](https://mlsanity.com/paper/2406.17774/) (2024)
- [Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images](https://mlsanity.com/paper/1409.6498/) (2014)
- [MeshFeat: Multi-Resolution Features for Neural Fields on Meshes](https://mlsanity.com/paper/2407.13592/) (2024)
- [Parallelised Differentiable Straightest Geodesics for 3D Meshes](https://mlsanity.com/paper/2603.15780/) (2026)

## Built on by (most cited first, 1 of 1)

- [Accelerating HKTex without Mesh Eigensystems: Local Unfolding and Randomized Thermal Features](https://mlsanity.com/paper/2609.14105/) (2026)

## Abstract (arXiv)

3D Gaussian Splatting has recently revolutionised novel view synthesis as well as many other 3D vision methods and applications. Drawing inspiration from this representation, we now rethink textures to overcome the main issues of UV mapping while considerably lowering their memory footprint. Heat Kernel Textures (HKTex) eliminate UV unwrapping as well as their persistent issues of wasted UV space, seams, distortions, vertex-duplication, and varying resolution. Grounded in discrete Riemannian geometry and intrinsically defined on any manifold surface discretised as a triangular mesh, HKTex uses anisotropic heat kernels as geodesic equivalents to Gaussians. Like our kernels, also the optimisation of their position and the adaptive densification strategies were redefined to operate on the surface of the object to be textureised. Our novel representation is also fully integrated with a physically based renderer and can be optimised either from existing textures or multi-view images. Our project page and code are available at circle-group.github.io/research/HeatKernelTextures.