Shape implicit neural representations (INRs) have recently shown to be effective in shape analysis and reconstruction tasks. Existing INRs require point coordinates to learn the implicit level sets of the shape. When a normal vector is available for each point, a higher fidelity representation can be learned, however normal vectors are often not provided as raw data. Furthermore, the method's initialization has been shown to play a crucial role for surface reconstruction. In this paper, we propose a divergence guided shape representation learning approach that does not require normal vectors as input. We show that incorporating a soft constraint on the divergence of the distance function favours smooth solutions that reliably orients gradients to match the unknown normal at each point, in some cases even better than approaches that use ground truth normal vectors directly. Additionally, we introduce a novel geometric initialization method for sinusoidal INRs that further improves convergence to the desired solution. We evaluate the effectiveness of our approach on the task of surface reconstruction and shape space learning and show SOTA performance compared to other unoriented methods. Code and model parameters available at our project page https://chumbyte.github.io/DiGS-Site/.

翻译：形状隐式神经表示（INRs）近期在形状分析与重建任务中展现出有效性。现有INRs依赖点坐标学习形状的隐式水平集。若每个点具有法向量，则可学习更高保真度的表示，然而原始数据中通常不提供法向量。此外，研究表明初始化方法对曲面重建至关重要。本文提出一种无需法向量输入的散度引导形状表示学习方法。我们证明，对距离函数的散度施加软约束有利于获得平滑解，且该解能可靠地定向梯度以匹配各点未知的法向——在某些情况下甚至优于直接使用真实法向量的方法。同时，我们针对正弦型INRs提出一种新颖的几何初始化方法，进一步改善了目标解的收敛性。在曲面重建和形状空间学习任务中，我们评估了该方法的有效性，并展示了相较于其他无向方法的最优性能（SOTA）。代码与模型参数详见项目主页 https://chumbyte.github.io/DiGS-Site/。