Neural implicit fields have recently shown increasing success in representing, learning and analysis of 3D shapes. Signed distance fields and occupancy fields are still the preferred choice of implicit representations with well-studied properties, despite their restriction to closed surfaces. With neural networks, unsigned distance fields as well as 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 to 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 surfaces. We show that, thanks to the continuity property of the neural optimization with VF, a separate distance field becomes unnecessary for extracting surfaces from the implicit field via Marching Cubes. 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. Codes are available at https://github.com/edomel/ImplicitVF.

神经内隐场最近在表示、学习和分析 3D 形状方面取得了越来越大的成功。有符号距离字段和占用字段仍然是具有经过充分研究的属性的隐式表示的首选，尽管它们仅限于闭合表面。对于神经网络，已经提出了无符号距离场以及其他几种变体和训练原则，目的是表示所有类别的形状。在本文中，我们开发了一种新颖但基本的表示形式，考虑了 3D 空间中的单位向量，并将其称为向量场 （VF）。在 \（\mathbb {R}^3\） 中的每个点，VF 都指向表面上最近的点。我们从理论上证明，通过计算磁通量密度，可以很容易地将 VF 转换为表面密度。与其他标准表示不同，VF 直接编码表面的重要物理属性，即其法线。我们进一步展示了 VF 表示在学习开放、封闭或多层表面方面的优势。我们表明，由于 VF 神经优化的连续性，通过 Marching Cube 从隐式场中提取表面时不需要单独的距离场。我们在包括 ShapeNet 在内的几个数据集上比较了我们的方法，其中提出的新神经隐含场在表示任何类型的形状方面都显示出卓越的准确性，优于其他标准方法。代码可在 https://github.com/edomel/ImplicitVF 处获得。