Shrinking: Reconstruction of Parameterized Surfaces from Signed Distance Fields

TL;DR

This paper introduces a new method for reconstructing smooth, parameterized 3D surfaces from Signed Distance Fields, preserving differentiability for advanced graphics and analysis applications.

Contribution

It presents a novel iterative contraction approach that maintains surface parameterization from SDFs, unlike traditional mesh extraction methods.

Findings

Achieves competitive reconstruction quality on standard datasets.

Preserves differentiability for downstream applications.

Enables smooth surface reconstructions suitable for graphics and deep learning.

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. This enables downstream applications such as texture mapping, geometry processing, animation, and finite element analysis. Evaluated on the typical geometric shapes and parts of the ABC dataset, our method achieves competitive reconstruction quality, maintaining smoothness and differentiability crucial for advanced computer graphics and geometric deep learning applications.