MicroRicci实现高效自调参网格平滑，速度提升2.4倍。
MicroRicci: A Greedy and Local Ricci Flow Solver for Self-Tuning Mesh Smoothing
- 基于编码理论的贪心纠错机制，局部快速修正最大曲率误差。
- 迭代次数从950次降至400次，曲率分布更均匀，视觉失真与感知质量相关性达-0.93。
- 仅增加0.25毫秒/迭代，适合实时图形与资源受限场景。
大规模实时网格平滑仍具挑战：传统Ricci流求解器需代价高昂的全局更新，而贪心启发式方法收敛慢或调参脆弱。我们提出MicroRicci，首个真正自调参、局部Ricci流求解器，借鉴编码理论思想，仅用1K+200参数实现。其核心为贪心校验解码步骤，可在O(E)时间内定位并修正最大曲率误差，并辅以两个微型神经模块，动态选择顶点与步长。在110个SJTU-TMQA网格上，迭代次数由950±140降至400±80（提速2.4倍），曲率分布范围从0.19缩至0.185，UV失真与感知质量评分相关性达r = -0.93。每迭代仅增0.25毫秒（总耗时0.80至1.05毫秒），相比现有最优方法实现1.8倍端到端加速。线性时间更新、自动超参调节与高质量几何及感知结果，使其适用于图形、仿真等实时、低资源场景。
原文摘要 · Abstract (English)
Real-time mesh smoothing at scale remains a formidable challenge: classical Ricci-flow solvers demand costly global updates, while greedy heuristics suffer from slow convergence or brittle tuning. We present MicroRicci, the first truly self-tuning, local Ricci-flow solver that borrows ideas from coding theory and packs them into just 1K + 200 parameters. Its primary core is a greedy syndrome-decoding step that pinpoints and corrects the largest curvature error in O(E) time, augmented by two tiny neural modules that adaptively choose vertices and step sizes on the fly. On a diverse set of 110 SJTU-TMQA meshes, MicroRicci slashes iteration counts from 950+=140 to 400+=80 (2.4x speedup), tightens curvature spread from 0.19 to 0.185, and achieves a remarkable UV-distortion-to-MOS correlation of r = -0.93. It adds only 0.25 ms per iteration (0.80 to 1.05 ms), yielding an end-to-end 1.8x runtime acceleration over state-of-the-art methods. MicroRicci's combination of linear-time updates, automatic hyperparameter adaptation, and high-quality geometric and perceptual results makes it well suited for real-time, resource-limited applications in graphics, simulation, and related fields.
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