CoFie: Learning Compact Neural Surface Representations with Coordinate Fields

UT Austin
arXiv Code

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.

Coordinate Field

CoFie is a local geometry-aware shape representation. (Left) CoFie divides a shape into non-overlapping local patches, where each local patch is represented by an MLP-based Signed Distance Function. (Right) CoFie introduces Coordinate Field, which attaches a coordinate frame to each local patch. It transforms local patches from the world coordinate system to an aligned coordinate system, reducing shape complexity.

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Training and Inference

(Left) For preparing the data for training the MLP-based local implicit functions, we split the training shapes into local shapes and initialize their coordinate frames using PCA. (Right) During training, a point will be transformed to the aligned coordinate of all local shapes using the coordinate frame. The MLP takes the transformed point and the latent code of the local shape to predict its SDF value. During testing, we fix the MLP, optimizing the latent codes and coordinate fields of valid cells.

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Comparison with Generalizable Methods

(All methods use one Model/MLP to represent any shape on ShapeNet.)


Comparison with Shape-specific Methods

(NGLOD uses one Model/MLP to overfit one shape, while CoFie uses one MLP for any shapes. CoFie achieves comparable performance with NGLOD.)


CoFie as a Compact Representation

CoFie using a latent code length of 48 achieves better performance than DeepLS which uses a latent code length of 128. The result desmonstrates that CoFie is a compact neural surface representation, reducing the shape parameters by 70%.

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BibTeX

@inproceedings{jiang2024cofie,
   title={CoFie: Learning Compact Neural Surface Representations with Coordinate Fields},
   author={Jiang, Hanwen and Yang, Haitao and Pavlakos, Georgios and Huang, Qixing},
   journal={arXiv preprint arXiv:2406.03417},
   year={2022}
}