Generalization Analysis and Improved Shape Representation with Neural Signed Distance Functions

Meenakshi Krishnan, Ramani Duraiswami

Keywords: implicit neural representations, eikonal equation, surface reconstruction

Abstract: Implicit Neural Representations (INRs) that learn Signed Distance Functions (SDFs) from point cloud data are the state-of-the-art for 3D surface reconstruction. However, training these Neural SDFs often requires enforcing the Eikonal equation, an ill-posed PDE that also leads to unstable gradient flows when used as a constraint. Numerical Eikonal solvers have relied on viscosity approaches for regularization and stability. Motivated by this, we introduce ViscoReg, a regularizer that provably stabilizes Neural SDF training. Empirically, ViscoReg outperforms state-of-the-art approaches such as DiGS, StEik, and HotSpot on the Surface Reconstruction Benchmark, and 3D scene reconstruction. We also establish generalization error estimates for Neural SDFs in terms of the training error, using the theory of viscosity solutions.

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Submission Number: 104