Neural implicit surfaces can be used to recover accurate 3D geometry from imperfect point clouds. In this work, we show that state-of-the-art techniques work by minimizing an approximation of a one-sided Chamfer distance. This shape metric is not symmetric, as it only ensures that the point cloud is near the surface but not vice versa. As a consequence, existing methods can produce inaccurate reconstructions with spurious surfaces. Although one approach against spurious surfaces has been widely used in the literature, we theoretically and experimentally show that it is equivalent to regularizing the surface area, resulting in over-smoothing. As a more appealing alternative, we propose DiffCD, a novel loss function corresponding to the symmetric Chamfer distance. In contrast to previous work, DiffCD also assures that the surface is near the point cloud, which eliminates spurious surfaces without the need for additional regularization. We experimentally show that DiffCD reliably recovers a high degree of shape detail, substantially outperforming existing work across varying surface complexity and noise levels. Project code is available at https://github.com/linusnie/diffcd.

翻译：神经隐式曲面可用于从非完美点云中恢复精确的三维几何形状。本工作中，我们指出现有最先进技术通过最小化单侧倒角距离的近似值来实现。该形状度量不具备对称性，因其仅确保点云靠近曲面，反之则不然。因此，现有方法可能产生带有伪表面的不精确重建结果。尽管文献中已广泛使用一种抑制伪表面的方法，但我们通过理论与实验证明该方法等效于对曲面面积进行正则化，会导致过度平滑现象。作为更具吸引力的替代方案，我们提出DiffCD——一种对应于对称倒角距离的新型损失函数。与先前工作不同，DiffCD同时确保曲面靠近点云，从而无需额外正则化即可消除伪表面。实验表明，DiffCD能可靠恢复高精度形状细节，在不同曲面复杂度与噪声水平下均显著优于现有方法。项目代码发布于https://github.com/linusnie/diffcd。