ViscoReg: Neural Signed Distance Functions via Viscosity Solutions

TMLR Paper7242 Authors

Abstract: Implicit Neural Representations (INRs) that learn Signed Distance Functions (SDFs) from point cloud data represent the state-of-the-art for geometrically accurate 3D scene reconstruction. However, training these Neural SDFs often involves enforcing the Eikonal equation, an ill-posed equation that also leads to unstable gradient flows. Numerical Eikonal solvers have relied on viscosity approaches for regularization and stability. Motivated by this well-established theory, we introduce ViscoReg, a novel regularizer for Neural SDF methods that provably stabilizes training. Empirically, ViscoReg outperforms state-of-the-art approaches such as SIREN, DiGS, StEik, and HotSpot across most metrics on ShapeNet, Surface Reconstruction Benchmark, 3D scene reconstruction and reconstruction from real scans. We also establish novel generalization error estimates for Neural SDFs in terms of the training error, using the theory of viscosity solutions. Our empirical and theoretical results provide confidence in the general applicability of our method.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Julius_Berner1

Submission Number: 7242