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.

翻译：3D 形状为隐含功能,其深心神经表示显示产生高忠诚度模型,超过透视和点云明确表示所面临的分辨率-模拟交换模型,但是,大多数这类方法侧重于代表封闭形状。最近提出了未指派的距离函数(UDF)法,作为代表开放和封闭形状的有希望的替代方法。然而,由于UDF的梯度在表面消失,因此很难估计当地(不同)的几何特性,如在视觉和图形中的许多下游应用所需的普通和正切平面。在以低微足迹高效计算这些属性方面还存在额外的挑战。本文展示了一种新颖的方法,即利用被称为最接近表面和封闭形状的新的隐含表示法(UDF)模型来模拟这些表面。我们表明,由于UD的梯度(开放或封闭)在表面消失,因此很难准确和有效地计算当地几何特性。我们进一步表明,它能够高效地执行下游算法,例如以低微缩图足迹方式计算这些属性。本文提出了一种新型方法,即模型模型模型模型模型模型模型模型,用以对3D 进行初步的实地评估。