用凸优化修复变形网格，保留细节同时纠正结构缺陷
MeshCone: Second-Order Cone Programming for Geometrically-Constrained Mesh Enhancement
- 将网格优化建模为二阶锥规划，利用参考几何引导顶点位置调整
- 在ShapeNet和ThreeDScans上56类物体测试，精度优于拉普拉斯平滑
- 适合有参考几何的场景，如模板生成、扫描对齐与资产质检
现代网格生成流程（无论是学习型还是传统方法）产生的输出常需后处理才能达到生产级几何质量。本文提出MeshCone，一种基于凸优化的引导式网格精炼框架，利用参考几何修正变形或退化的网格。我们将问题建模为二阶锥规划，优化顶点位置以对齐目标几何，同时通过凸边长正则化保证平滑性。MeshCone实现几何感知优化，在保留细粒度特征的同时修复结构缺陷。我们在ShapeNet和ThreeDScans的56个多样化物体类别上验证了其鲁棒性，相比拉普拉斯平滑和未优化基线，显著提升精炼质量，且推理时间保持在亚秒级。该方法特别适用于存在参考几何的应用场景，如基于模板的网格生成、扫描到CAD对齐以及资产生产流水线中的质量保证。
原文摘要 · Abstract (English)
Modern mesh generation pipelines whether learning-based or classical often produce outputs requiring post-processing to achieve production-quality geometry. This work introduces MeshCone, a convex optimization framework for guided mesh refinement that leverages reference geometry to correct deformed or degraded meshes. We formulate the problem as a second-order cone program where vertex positions are optimized to align with target geometry while enforcing smoothness through convex edge-length regularization. MeshCone performs geometry-aware optimization that preserves fine details while correcting structural defects. We demonstrate robust performance across 56 diverse object categories from ShapeNet and ThreeDScans, achieving superior refinement quality compared to Laplacian smoothing and unoptimized baselines while maintaining sub-second inference times. MeshCone is particularly suited for applications where reference geometry is available, such as mesh-from-template workflows, scan-to-CAD alignment, and quality assurance in asset production pipelines.
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