MicroRicci: A Greedy and Local Ricci Flow Solver for Self-Tuning Mesh Smoothing

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.

@article{anh2025_2506.15571,
  title={ MicroRicci: A Greedy and Local Ricci Flow Solver for Self-Tuning Mesh Smoothing },
  author={ Le Vu Anh and Nguyen Viet Anh and Mehmet Dik and Tu Nguyen Thi Ngoc },
  journal={arXiv preprint arXiv:2506.15571},
  year={ 2025 }
}