New methods speed up surface texture rendering without heavy calculations
Accelerating HKTex without Mesh Eigensystems: Local Unfolding and Randomized Thermal Features
Computer Vision and Pattern RecognitionGraphics
Summary
Rendering detailed surface textures often relies on complex calculations that slow down the process. The authors introduce two new ways to speed this up without sacrificing quality: one method uses local information and simpler math, while the other uses randomized techniques to approximate global effects more efficiently. Both approaches significantly reduce computation time and memory needs while keeping image quality high. These improvements make it possible to handle much larger 3D models than before.
What this means in practice
- •For 3d graphics developers: Render detailed surface textures faster on complex 3D models by reducing the need for expensive global shape decompositions while maintaining visual quality.
- •For gpu optimization engineers: Cut preprocessing and optimization times in GPU-based texture pipelines by using local or randomized thermal feature approximations instead of full eigensystems.
Authors
Zhewen He, Junyi Hu, Yi Fang
Abstract
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.