Shrinking: Reconstruction of Parameterized Surfaces from Signed Distance Fields

Abstract--We propose a novel method for reconstructing explicit parameterized surfaces from Signed Distance Fields (SDFs), a widely used implicit neural representation (INR) for 3D surfaces. While traditional reconstruction methods like Marching Cubes extract discrete meshes that lose the continuous and differentiable properties of INRs, our approach iteratively contracts a parameterized initial sphere to conform to the target SDF shape, preserving differentiability and surface parameterization throughout. Each step Implicit Neural Representations (INRs) [1] have become involves remeshing to maintain uniform distribution, ensuring popular 3D models in computer graphics, with applications surface continuity and smooth parameterization. in scientific simulation, photogrammetry, generative modeling, Our experiments demonstrate that this approach not only and inverse physics [2]. INRs encode continuous signals generates differentiable parameterizations but also achieves via neural networks that map spatial coordinates to signal competitive reconstruction quality compared to mainstream values [3], offering advantages like efficient storage, smooth methods. Our contributions include: (1) Introducing a interpolations, and differentiable features, surpassing traditional shrinking-based method for extracting high-quality meshes grid-based methods [4].