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.

翻译：隐式场近年来在精确表示和学习三维形状方面取得了越来越多的成功。有符号距离场和占据场历经数十年发展，尽管受限于封闭表面，但凭借其经过充分研究的特性，至今仍是首选表示方法。借助神经网络，研究者已提出多种变体及训练原则，旨在表示所有类别形状。在本文中，我们提出一种新颖且基础性的表示方法——向量场（VF）：对于三维空间中的每个点，VF指向表面上最近的点。我们从理论上证明了，通过计算通量密度，VF可轻松转换为表面密度。与其他标准表示不同，VF直接编码了表面的重要物理属性——法线。我们进一步展示了VF表示在开放表面、封闭表面、多层表面以及分片平面表面学习中的优势。我们在包括ShapeNet在内的多个数据集上进行了方法对比，实验表明，所提出的新型神经隐式场在表示任意类型形状时具有更高的精度，优于其他标准方法。代码已在https://github.com/edomel/ImplicitVF开源。