In recent years, neural implicit representations have made remarkable
progress in modeling of 3D shapes with arbitrary topology. In this work, we
address two key limitations of such representations, in failing to capture
local 3D geometric fine details, and to learn from and generalize to shapes
with unseen 3D transformations. To this end, we introduce a novel family of
graph implicit functions with equivariant layers that facilitates modeling fine
local details and guaranteed robustness to various groups of geometric
transformations, through local $k$-NN graph embeddings with sparse point set
observations at multiple resolutions. Our method improves over the existing
rotation-equivariant implicit function from 0.69 to 0.89 (IoU) on the ShapeNet
reconstruction task. We also show that our equivariant implicit function can be
extended to other types of similarity transformations and generalizes to unseen
translations and scaling.

本文提出了一种新型的图形隐式函数族，其具有等变层，可用于捕捉 3D 几何细节并保证对各种几何变换的鲁棒性，该方法在 ShapeNet 重建任务上比现有的旋转等变隐式函数从 0.69 提高到 0.89 (IoU)，并且可以推广到其他类型的相似变换，并且具有良好的泛化能力。