Learning 3D geometry directly from raw data, such as point clouds, triangle
soups, or unoriented meshes is still a challenging task that feeds many
downstream computer vision and graphics applications.
In this paper, we introduce SALD: a method for learning implicit neural
representations of shapes directly from raw data. We generalize sign agnostic
learning (SAL) to include derivatives: given an unsigned distance function to
the input raw data, we advocate a novel sign agnostic regression loss,
incorporating both pointwise values and gradients of the unsigned distance
function. Optimizing this loss leads to a signed implicit function solution,
the zero level set of which is a high quality and valid manifold approximation
to the input 3D data. The motivation behind SALD is that incorporating
derivatives in a regression loss leads to a lower sample complexity, and
consequently better fitting. In addition, we prove that SAL enjoys a minimal
length property in 2D, favoring minimal length solutions. More importantly, we
are able to show that this property still holds for SALD, i.e., with
derivatives included.
We demonstrate the efficacy of SALD for shape space learning on two
challenging datasets: ShapeNet that contains inconsistent orientation and
non-manifold meshes, and D-Faust that contains raw 3D scans (triangle soups).
On both these datasets, we present state-of-the-art results.

本文介绍了用于从点云、三角面片或未定向网格直接学习形状的方法 ——SALD（基于符号不敏感学习的带导数隐式函数表示），该方法将导数与点云数据的无符号距离函数相结合，通过优化回归损失，得到一个带符号的高质量隐式函数解。作者在 ShapeNet 和 D-Faust 数据集上进行了实验证明了此方法的高效性和在有向网格和原始三维扫描方面的表现优异。