CoFie: Learning Compact Neural Surface Representations with Coordinate Fields

TL;DR

CoFie is a new neural surface representation that uses coordinate fields and quadratic layers to efficiently model local shapes, significantly reducing shape error and parameter count while maintaining high accuracy.

Contribution

It introduces Coordinate Field and quadratic layers, enabling more compact and expressive neural surface representations with improved generalization.

Findings

Reduces shape error by up to 56% on novel instances.

Achieves comparable performance with 30% fewer parameters.

Demonstrates strong generalization across shape categories.

Abstract

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.