提出可微分的梯度距离函数，让非封闭曲面在深度学习中更稳定地表示。
Gradient Distance Function
- 用三维向量的模和方向定义新距离函数，表面处仍可微分。
- 在多个数据集上实现单形状与类别级重建，效果优于传统无符号距离函数。
- 适合需要平滑梯度的3D生成或重建任务，如形状建模与逆向设计。
无符号距离函数（UDFs）可用于深度学习框架中表示非封闭曲面。然而，由于表面恰好位于UDF不可微的位置，其学习过程往往脆弱且困难。本文提出梯度距离函数（GDF），在保持能表示开放曲面的同时，使表面处依然可微。具体而言，每个3D点关联一个三维向量，其模长为到表面的无符号距离，方向指向最近的表面点。我们在ShapeNet Car、Multi-Garment和3D-Scene数据集上验证了GDF的有效性，采用单形状重建网络或类别级自编码器均取得良好表现。
原文摘要 · Abstract (English)
Unsigned Distance Functions (UDFs) can be used to represent non-watertight surfaces in a deep learning framework. However, UDFs tend to be brittle and difficult to learn, in part because the surface is located exactly where the UDF is non-differentiable. In this work, we show that Gradient Distance Functions (GDFs) can remedy this by being differentiable at the surface while still being able to represent open surfaces. This is done by associating to each 3D point a 3D vector whose norm is taken to be the unsigned distance to the surface and whose orientation is taken to be the direction towards the closest surface point. We demonstrate the effectiveness of GDFs on ShapeNet Car, Multi-Garment, and 3D-Scene datasets with both single-shape reconstruction networks or categorical auto-decoders.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。