In the field of computer vision, the numerical encoding of 3D surfaces is crucial. It is classical to represent surfaces with their Signed Distance Functions (SDFs) or Unsigned Distance Functions (UDFs). For tasks like representation learning, surface classification, or surface reconstruction, this function can be learned by a neural network, called Neural Distance Function. This network, and in particular its weights, may serve as a parametric and implicit representation for the surface. The network must represent the surface as accurately as possible. In this paper, we propose a method for learning UDFs that improves the fidelity of the obtained Neural UDF to the original 3D surface. The key idea of our method is to concentrate the learning effort of the Neural UDF on surface edges. More precisely, we show that sampling more training points around surface edges allows better local accuracy of the trained Neural UDF, and thus improves the global expressiveness of the Neural UDF in terms of Hausdorff distance. To detect surface edges, we propose a new statistical method based on the calculation of a $p$-value at each point on the surface. Our method is shown to detect surface edges more accurately than a commonly used local geometric descriptor.

翻译：在计算机视觉领域，三维曲面的数值编码至关重要。传统上使用有符号距离函数或符号距离函数来表示曲面。对于表征学习、曲面分类或曲面重建等任务，该函数可通过名为神经距离函数的神经网络进行学习。该网络（尤其是其权重）可作为曲面的参数化隐式表征。网络必须尽可能精确地表示曲面。本文提出一种学习无符号距离函数的方法，该方法能提升神经UDF对原始三维曲面的保真度。其核心思想是将神经UDF的学习重点集中于曲面边缘。具体而言，我们证明在曲面边缘周围采样更多训练点，能够提升训练后神经UDF的局部精度，从而在豪斯多夫距离指标上改善神经UDF的全局表达能力。为检测曲面边缘，我们提出一种基于表面各点p值计算的新型统计方法。实验表明，该方法比常用的局部几何描述符能更精确地检测曲面边缘。