MeshCone: Second-Order Cone Programming for Geometrically-Constrained Mesh Enhancement

TL;DR

MeshCone is a convex optimization framework that refines meshes by leveraging reference geometry, improving quality and detail preservation efficiently across diverse datasets.

Contribution

Introduces MeshCone, a second-order cone programming approach for guided mesh refinement that preserves details and corrects structural issues using convex optimization.

Findings

Outperforms Laplacian smoothing and baselines in quality

Achieves refinement in under a second

Works effectively across diverse object categories

Abstract

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.