Deep neural representations of 3D shapes as implicit functions have been shown to produce high fidelity models surpassing the resolution-memory trade-off faced by the explicit representations using meshes and point clouds. However, most such approaches focus on representing closed shapes. Unsigned distance function (UDF) based approaches have been proposed recently as a promising alternative to represent both open and closed shapes. However, since the gradients of UDFs vanish on the surface, it is challenging to estimate local (differential) geometric properties like the normals and tangent planes which are needed for many downstream applications in vision and graphics. There are additional challenges in computing these properties efficiently with a low-memory footprint. This paper presents a novel approach that models such surfaces using a new class of implicit representations called the closest surface-point (CSP) representation. We show that CSP allows us to represent complex surfaces of any topology (open or closed) with high fidelity. It also allows for accurate and efficient computation of local geometric properties. We further demonstrate that it leads to efficient implementation of downstream algorithms like sphere-tracing for rendering the 3D surface as well as to create explicit mesh-based representations. Extensive experimental evaluation on the ShapeNet dataset validate the above contributions with results surpassing the state-of-the-art.

本文提出了一种新的隐式表示方法，称为最接近的表面点（CSP）表示，用于表示具有任何拓扑结构的开放或封闭形状并计算本地几何属性，可以实现高保真度和有效实现外围算法，如球追踪来呈现三维表面和创建显式基于网格的表示，并在ShapeNet数据集上验证了超越最先进结果的贡献。

深度隐式曲面点预测网络