ReSDF: Redistancing Implicit Surfaces using Neural Networks

TL;DR

This paper introduces ReSDF, a neural network method for accurately reconstructing signed distance functions of hypersurfaces, improving interface capture and gradient regularization through a novel training loss.

Contribution

The paper presents a new neural network architecture with an auxiliary output for SDF and a three-term loss function, enhancing accuracy and gradient regularity over existing methods.

Findings

Accurately captures complex hypersurface interfaces.

Outperforms physics-informed neural networks and fast marching methods.

Effective in 2D and 3D complex geometries.

Abstract

This paper proposes a deep-learning-based method for recovering a signed distance function (SDF) of a given hypersurface represented by an implicit level set function. Using the flexibility of constructing a neural network, we use an augmented network by defining an auxiliary output to represent the gradient of the SDF. There are three advantages of the augmented network; (i) the target interface is accurately captured, (ii) the gradient has a unit norm, and (iii) two outputs are approximated by a single network. Moreover, unlike a conventional loss term which uses a residual of the eikonal equation, a novel training objective consisting of three loss terms is designed. The first loss function enforces a pointwise matching between two outputs of the augmented network. The second loss function leveraged by a geometric characteristic of the SDF imposes the shortest path obtained by the gradient. The third loss function regularizes a singularity of the SDF caused by discontinuities of the gradient. Numerical results across a wide range of complex and irregular interfaces in two and three-dimensional domains confirm the effectiveness and accuracy of the proposed method. We also compare the results of the proposed method with physics-informed neural networks approaches and the fast marching method.