Neural signed distance functions (SDFs) have shown remarkable capability in representing geometry with details. However, without signed distance supervision, it is still a challenge to infer SDFs from point clouds or multi-view images using neural networks. In this paper, we claim that gradient consistency in the field, indicated by the parallelism of level sets, is the key factor affecting the inference accuracy. Hence, we propose a level set alignment loss to evaluate the parallelism of level sets, which can be minimized to achieve better gradient consistency. Our novelty lies in that we can align all level sets to the zero level set by constraining gradients at queries and their projections on the zero level set in an adaptive way. Our insight is to propagate the zero level set to everywhere in the field through consistent gradients to eliminate uncertainty in the field that is caused by the discreteness of 3D point clouds or the lack of observations from multi-view images. Our proposed loss is a general term which can be used upon different methods to infer SDFs from 3D point clouds and multi-view images. Our numerical and visual comparisons demonstrate that our loss can significantly improve the accuracy of SDFs inferred from point clouds or multi-view images under various benchmarks. Code and data are available at https://github.com/mabaorui/TowardsBetterGradient .

翻译：神经符号距离函数在几何细节表示方面展现出卓越能力。然而，在没有符号距离监督的情况下，利用神经网络从点云或多视图像中推断符号距离函数仍是一项挑战。本文提出，场中由水平集平行性表征的梯度一致性是影响推断精度的关键因素。为此，我们设计了一种水平集对齐损失函数来评估水平集的平行性，通过最小化该损失可实现更优的梯度一致性。本方法的创新性在于：通过自适应方式约束查询点及其在零水平集上的投影点的梯度，能够将所有水平集对齐到零水平集。其核心思想是通过一致梯度将零水平集传播到场中所有位置，从而消除由三维点云离散性或多视图像观测缺失导致的场不确定性。所提出的损失函数具有通用性，可应用于从三维点云和多视图像推断符号距离函数的不同方法中。数值与视觉对比实验表明，该损失函数能显著提升多种基准测试下从点云或多视图像推断所得符号距离函数的精度。相关代码与数据可通过 https://github.com/mabaorui/TowardsBetterGradient 获取。