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.

本文提出了一种改进神经 UDF 学习的方法，通过集中学习表面边缘来提高神经 UDF 对原始 3D 表面的保真度，并提出了一种基于统计学方法的表面边缘检测技术。