In recent years, implicit surface representations through neural networks that encode the signed distance have gained popularity and have achieved state-of-the-art results in various tasks (e.g. shape representation, shape reconstruction, and learning shape priors). However, in contrast to conventional shape representations such as polygon meshes, the implicit representations cannot be easily edited and existing works that attempt to address this problem are extremely limited. In this work, we propose the first method for efficient interactive editing of signed distance functions expressed through neural networks, allowing free-form editing. Inspired by 3D sculpting software for meshes, we use a brush-based framework that is intuitive and can in the future be used by sculptors and digital artists. In order to localize the desired surface deformations, we regulate the network by using a copy of it to sample the previously expressed surface. We introduce a novel framework for simulating sculpting-style surface edits, in conjunction with interactive surface sampling and efficient adaptation of network weights. We qualitatively and quantitatively evaluate our method in various different 3D objects and under many different edits. The reported results clearly show that our method yields high accuracy, in terms of achieving the desired edits, while at the same time preserving the geometry outside the interaction areas.

翻译：近年来，通过编码符号距离的神经网络实现的隐式表面表示方法日益流行，并在形状表示、形状重建及形状先验学习等多项任务中取得了最先进成果。然而，与多边形网格等传统形状表示不同，隐式表示难以直接编辑，且现有尝试解决此问题的研究工作极为有限。本文首次提出一种高效交互式编辑神经网络表达的符号距离函数的方法，支持自由形态编辑。受网格三维雕刻软件的启发，我们采用基于笔刷的直观框架，未来可供雕刻师与数字艺术家使用。为定位所需的表面形变，我们通过使用网络的副本对先前表达的曲面进行采样来调控网络。我们提出一种新颖框架，可模拟雕刻式表面编辑，同时结合交互式表面采样与网络权重的自适应调整。我们在多种不同的三维对象及多种编辑场景下对方法进行了定性与定量评估。报告结果清晰表明，我们的方法在实现目标编辑方面具有高精度，同时能保持交互区域之外的几何结构不变。