Heat Kernel Textures -- the Geodesic Gaussians That Do Not Splat

3D Gaussian Splatting has recently revolutionised novel viewsynthesis as well as many other 3D vision methods and applications.Drawing inspiration from this representation, we now rethink texturesto overcome the main issues of UV mapping while considerably lower-ing their memory footprint. Heat Kernel Textures (HKTex) eliminateUV unwrapping as well as their persistent issues of wasted UV space,seams, distortions, vertex-duplication, and varying resolution. Groundedin discrete Riemannian geometry and intrinsically defined on any man-ifold surface discretised as a triangular mesh, HKTex uses anisotropicheat kernels as geodesic equivalents to Gaussians. Like our kernels, alsothe optimisation of their position and the adaptive densification strate-gies were redefined to operate on the surface of the object to be tex-tureised. Our novel representation is also fully integrated with a physi-cally based renderer and can be optimised either from existing texturesor multi-view images. Our project page and code are available at circle-group.github.io/research/HeatKernelTextures.