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

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.

Neural radiance representations in Gaussian Splatting (GS) deliver high-fidelity color detail but impose substantial rendering overhead from network evaluations. We present a learned sparse scene representation based on 2D surfels, which enables baking the neural component into a hardware-accelerated 2D texture atlas and eliminates runtime network inference. Our 2D surfels carry low-frequency geometry and view-dependent appearance, while view-independent, per-primitive high-frequency texture is encoded with a spatial hash grid and converted into the texture atlas. A novel sparsity objective that penalizes per-primitive kernel falloffs achieves a substantially sparser representation than prior methods. With a compute-optimized ray-surfel intersection shader our approach renders roughly $7$ to $9\times$ faster than 3DGS on common benchmarks, and over an order of magnitude faster on individual scenes, while surpassing the perceptual quality and speed of the fastest sparsification methods (FastGS and Speedy-Splat) at PSNR parity. A quality-optimized variant matches the perceptual quality of the strongest baseline while still rendering several times faster. Because inference is one texture fetch per fragment, frame rates can be pushed to $2{,}700$--$4{,}400$ FPS with no loss in quality when using the GPU hardware rasterizer.

Thermal imaging remains effective under adverse illumination, yet passive long-wave infrared (LWIR) measurements often lack fine texture. Existing thermal texture imaging approaches commonly rely on spectral sensing or registered auxiliary modalities, incurring substantial data throughput or vulnerability to cross-modal degradation. We introduce T$^2$exture, a sparsely perturbed thermal texture imaging framework that aims to reconstruct temporally dense thermal texture sequences from densely sampled passive frames and a few actively perturbed keyframes. We define thermal texture as the residual between a source-on observation and its corresponding source-off passive state. Under sparse LWIR illumination and rapid quasi-steady paired acquisition, this residual attenuates the passive-emission background and approximates a source-induced reflected response, exposing localized material- and geometry-dependent texture. T$^2$exture reconstructs a dense sequence of this source-conditioned response through two stages. Stage 1 estimates the unobserved source-off passive state at each active instant from neighboring passive frames to obtain reliable differential texture anchors. Stage 2 combines sparse anchors with passive structural context near each target time to reconstruct the dense sequence. On the simulated benchmark, T$^2$exture adds only 0.20M parameters to AMT-L while improving PSNR by 6.66 dB. Extensive evaluations on simulated and real acquisitions further show clearer texture recovery and stronger structural preservation than representative VFI baselines. These results establish T$^2$exture as a practical framework for thermal texture imaging under sparse active acquisition.