Heat Kernel Textures: the Geodesic Gaussians That Do Not Splat

2026-09-07

AI Summary

为解决UV映射的问题并减少内存占用，本文提出使用基于离散黎曼几何的热核纹理（HKTex），利用各向异性热核作为高斯函数的测地线等效物。

Abstract

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.

Problem

• 3D Texture Mapping
• UV Unwrapping
• Memory Footprint
• Geodesic Gaussians
• Heat Kernels

Innovation

• Heat Kernel Textures
• anisotropic heat kernels
• discrete Riemannian geometry
• physically based renderer