This paper introduces CoFie, a novel local geometry-aware neural surface representation. CoFie is motivated by the theoretical analysis of local SDFs with quadratic approximation. We find that local shapes are highly compressive in an aligned coordinate frame defined by the normal and tangent directions of local shapes. Accordingly, we introduce Coordinate Field, which is a composition of coordinate frames of all local shapes. The Coordinate Field is optimizable and is used to transform the local shapes from the world coordinate frame to the aligned shape coordinate frame. It largely reduces the complexity of local shapes and benefits the learning of MLP-based implicit representations. Moreover, we introduce quadratic layers into the MLP to enhance expressiveness concerning local shape geometry. CoFie is a generalizable surface representation. It is trained on a curated set of 3D shapes and works on novel shape instances during testing. When using the same amount of parameters with prior works, CoFie reduces the shape error by 48% and 56% on novel instances of both training and unseen shape categories. Moreover, CoFie demonstrates comparable performance to prior works when using only 70% fewer parameters.

本文介绍了一种新颖的局部几何感知神经表面表示方法CoFie，该方法通过对局部SDF的二次逼近进行理论分析得到。CoFie将局部形状在由法线和切线方向定义的对齐坐标框架中进行压缩表示，通过优化可变的坐标场将局部形状从世界坐标系转换到对齐形状坐标系，从而显著降低了局部形状的复杂性，提高了基于MLP的隐式表示的学习效果。此外，本文还引入了二次层以增强对局部形状几何特征的表达能力。CoFie是一种通用的表面表示方法，在经过精心筛选的3D形状集上进行训练，可在测试时适用于新的形状实例。与先前的方法使用相同数量的参数相比，CoFie在训练和未见过的形状类别的新实例上将形状误差降低了48%和56%。此外，仅使用70%更少的参数，CoFie表现出与先前方法相媲美的性能。

CoFie: 使用坐标场学习紧凑的神经表面表示