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

TL;DR

MicroRicci is a novel self-tuning, local Ricci-flow solver that significantly accelerates mesh smoothing by combining greedy algorithms with neural modules, achieving high-quality results in real-time with minimal parameters.

Contribution

It introduces MicroRicci, the first self-tuning local Ricci-flow solver that uses a greedy syndrome-decoding approach and neural modules for adaptive vertex and step size selection.

Findings

Reduces iteration count from 950+ to 400+ (2.4x speedup)

Achieves high correlation (r = -0.93) between UV-distortion and MOS

Adds only 0.25 ms per iteration, enabling real-time performance

Abstract

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.