Neural shape representation generally refers to representing 3D geometry using neural networks, e.g., computing a signed distance or occupancy value at a specific spatial position. In this paper we present a neural-network architecture suitable for accurate encoding of 3D shapes in a single forward pass. Our architecture is based on a multi-scale hybrid system incorporating graph-based and voxel-based components, as well as a continuously differentiable decoder. The hybrid system includes a novel way of voxelizing point-based features in neural networks, which we show can be used in combination with oriented point-clouds to obtain smoother and more detailed reconstructions. Furthermore, our network is trained to solve the eikonal equation and only requires knowledge of the zero-level set for training and inference. This means that in contrast to most previous shape encoder architectures, our network is able to output valid signed distance fields without explicit prior knowledge of non-zero distance values or shape occupancy. It also requires only a single forward-pass, instead of the latent-code optimization used in auto-decoder methods. We further propose a modification to the loss function in case that surface normals are not well defined, e.g., in the context of non-watertight surfaces and non-manifold geometry, resulting in an unsigned distance field. Overall, our system can help to reduce the computational overhead of training and evaluating neural distance fields, as well as enabling the application to difficult geometry.

翻译：神经形状表示通常指使用神经网络表示三维几何，例如计算特定空间位置处的有符号距离或占据值。本文提出一种适用于单次前向传播中精确编码三维形状的神经网络架构。该架构基于多尺度混合系统，融合了基于图与基于体素的组件，并配备连续可微解码器。混合系统包含一种新颖的基于点的特征体素化方法，我们证明该方法可与定向点云结合以获得更平滑、更精细的重建结果。此外，我们的网络通过求解程函方程进行训练，且训练与推断仅需零水平集信息。这意味着与大多数先前的形状编码器架构不同，本网络无需非零距离值或形状占据的显式先验知识即可输出有效的有符号距离场。同时仅需单次前向传播，无需自解码器方法中使用的隐码优化。针对表面法线未明确定义的情况（如非水密表面与非流形几何），我们进一步提出损失函数改进方案，从而生成无符号距离场。总体而言，本系统有助于降低神经距离场训练与评估的计算开销，并能应用于复杂几何场景。