# CoFie: Learning Compact Neural Surface Representations with Coordinate Fields

arXiv: https://arxiv.org/abs/2406.03417 · HTML: https://mlsanity.com/paper/2406.03417/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 55 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Builds on (most cited first, 30 of 36)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [LRM: Large Reconstruction Model for Single Image to 3D](https://mlsanity.com/paper/2311.04400/) (2023)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [CLAY: A Controllable Large-scale Generative Model for Creating High-quality 3D Assets](https://mlsanity.com/paper/2406.13897/) (2024)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [SDFusion: Multimodal 3D Shape Completion, Reconstruction, and Generation](https://mlsanity.com/paper/2212.04493/) (2022)
- [Mixture of Volumetric Primitives for Efficient Neural Rendering](https://mlsanity.com/paper/2103.01954/) (2021)
- [AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation](https://mlsanity.com/paper/2203.09516/) (2022)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [SDM-NET: Deep Generative Network for Structured Deformable Mesh](https://mlsanity.com/paper/1908.04520/) (2019)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations](https://mlsanity.com/paper/2205.02825/) (2022)
- [LEAP: Liberate Sparse-view 3D Modeling from Camera Poses](https://mlsanity.com/paper/2310.01410/) (2023)
- [Few-View Object Reconstruction with Unknown Categories and Camera Poses](https://mlsanity.com/paper/2212.04492/) (2022)
- [Mosaic-SDF for 3D Generative Models](https://mlsanity.com/paper/2312.09222/) (2023)
- [GIFS: Neural Implicit Function for General Shape Representation](https://mlsanity.com/paper/2204.07126/) (2022)
- [Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian](https://mlsanity.com/paper/2309.01793/) (2023)
- [DSG-Net: Learning Disentangled Structure and Geometry for 3D Shape Generation](https://mlsanity.com/paper/2008.05440/) (2020)
- [OctField: Hierarchical Implicit Functions for 3D Modeling](https://mlsanity.com/paper/2111.01067/) (2021)
- [Make-A-Shape: a Ten-Million-scale 3D Shape Model](https://mlsanity.com/paper/2401.11067/) (2024)

## Built on by (most cited first, 5 of 5)

- [MegaSynth: Scaling Up 3D Scene Reconstruction with Synthesized Data](https://mlsanity.com/paper/2412.14166/) (2024)
- [Mesh Compression with Quantized Neural Displacement Fields](https://mlsanity.com/paper/2504.01027/) (2025)
- [GNF: Gaussian Neural Fields for Multidimensional Signal Representation and Reconstruction](https://mlsanity.com/paper/2503.06762/) (2025)
- [efunc: An Efficient Function Representation without Neural Networks](https://mlsanity.com/paper/2505.21319/) (2025)
- [Hierarchical Neural Surfaces for 3D Mesh Compression](https://mlsanity.com/paper/2512.15985/) (2025)

## Abstract (arXiv)

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.