加速HKTex：无需网格特征系统的局部展开与随机热特征
Accelerating HKTex without Mesh Eigensystems: Local Unfolding and Randomized Thermal Features
- New York University Abu Dhabi（纽约大学阿布扎比分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出LocalHK和ThermalRF两种方法，分别通过局部展开和随机热特征加速HKTex，无需网格特征系统，在保持PSNR的同时大幅减少计算开销。
AI中文摘要：
热核纹理（HKTex）利用内在各向异性核表示表面外观，但评估它们需要50次全局Laplace-Beltrami特征分解以及一个形状的驻留基[50,V,256]。我们研究了两种互补的方法来消除这一瓶颈，同时保持训练器GeodesicOpt、密度控制和合成不变。LocalHK利用训练核的实测局部性，用半径有界铰链展开和解析对数映射核替代谱评估。在10个Objaverse网格和一个8网格低多边形保留集上，它将平均视图PSNR分别从31.35提高到32.00，从29.82提高到30.76 dB，同时将初始化时间减少40.5倍，并支持一个749,570顶点的代理支撑运行，而谱基线在此失败。ThermalRF则保留离散各向异性热半群：GPU稀疏Chebyshev作用和随机范围查找构造全局低秩热因子，无需网格大小的特征向量，编译评估器混合四个相邻热响应。在spot和细茎挑战上，ThermalRF将端到端预处理、初始化和5,000步优化分别减少29.3%和24.4%，每个表面、图集或视图PSNR变化在0.12 dB以内，训练分配减少约90%。这两种途径揭示了一个有用的设计选择：最大局部性和规模与对热PDE的保真度之间的权衡。更广泛的热特征评估和真实大场景仍是未来工作。
英文摘要：
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.
