Neural shape representation generally refers to representing 3D geometry using neural networks, e.g., to compute a signed distance or occupancy value at a specific spatial position. In this paper, we present a novel encoder-decoder neural network for embedding 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. Furthermore, the 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 work, our network is able to output valid signed distance fields without explicit prior knowledge of non-zero distance values or shape occupancy. We further propose a modification of 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. Overall, this can help reduce the computational overhead of training and evaluating neural distance fields, as well as enabling the application to difficult shapes. We finally demonstrate the efficacy, generalizability and scalability of our method on datasets consisting of deforming shapes, both based on simulated data and raw 3D scans. We further show single-class and multi-class encoding, on both fixed and variable vertex-count inputs, showcasing a wide range of possible applications.

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的符号距离或占据值。本文提出一种新颖的编码器-解码器神经网络，可在单次前向传播中嵌入三维形状。我们的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以及连续可微解码器。此外，该网络通过训练求解Eikonal方程，仅需零水平集知识即可完成训练与推理。这意味着与大多数先前工作不同，我们的网络无需非零距离值或形状占据的显式先验知识，即可输出有效的符号距离场。针对表面法线定义不明确的情况（例如非水密表面与非流形几何），我们进一步提出损失函数的修正方案。总体而言，这有助于降低神经距离场训练与评估的计算开销，并使其能够应用于复杂形状。最后，我们在包含变形形状的数据集上（基于模拟数据和原始三维扫描）验证了方法的有效性、泛化性与可扩展性。我们进一步展示了在固定与可变顶点数输入下的单类与多类编码，突显了广泛的应用前景。