论文标题
隐式表面表示和推理的神经矢量场
Neural Vector Fields for Implicit Surface Representation and Inference
论文作者
论文摘要
隐式字段最近显示出在准确表示和学习3D形状方面的成功越来越大。签名的距离字段和占用字段已有数十年的历史，但仍然是首选的表示，尽管它们限于封闭的表面，但均具有良好的属性。借助神经网络，已经提出了其他几种变体和培训原则，以代表所有形状。在本文中，我们开发了一种考虑3D空间中单元向量的小说却又是一个基本表示，并将其称为矢量场（VF）：在$ \ mathbb {r}^3 $中的每个点上，VF在表面上的最接近点。从理论上讲，我们可以通过计算磁通密度来轻松地转化为表面密度。与其他标准表示不同，VF直接编码表面的重要物理特性，即正常。我们进一步展示了VF表示的优势，在学习开放，封闭或多层以及分段平面表面方面。我们比较了几个数据集上的方法，其中提出的新神经隐式场在表示任何类型的形状方面表现出卓越的准确性，超过了其他标准方法。代码可在https://github.com/edomel/implicitvf上找到。
Implicit fields have recently shown increasing success in representing and learning 3D shapes accurately. Signed distance fields and occupancy fields are decades old and still the preferred representations, both with well-studied properties, despite their restriction to closed surfaces. With neural networks, several other variations and training principles have been proposed with the goal to represent all classes of shapes. In this paper, we develop a novel and yet a fundamental representation considering unit vectors in 3D space and call it Vector Field (VF): at each point in $\mathbb{R}^3$, VF is directed at the closest point on the surface. We theoretically demonstrate that VF can be easily transformed to surface density by computing the flux density. Unlike other standard representations, VF directly encodes an important physical property of the surface, its normal. We further show the advantages of VF representation, in learning open, closed, or multi-layered as well as piecewise planar surfaces. We compare our method on several datasets including ShapeNet where the proposed new neural implicit field shows superior accuracy in representing any type of shape, outperforming other standard methods. Code is available at https://github.com/edomel/ImplicitVF.
