3D Equivariant Graph Implicit Functions

AbstractIn 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 such representations, failing to capture local geometric fine details, and learn from generalize unseen transformations. To end, introduce a novel family graph functions equivariant layers that facilitates details guaranteed robustness various groups transformations, through k-NN embeddings sparse point set observations at multiple resolutions. Our method improves over the existing rotation-equivariant function 0.69 0.89 (IoU) on ShapeNet reconstruction task. We also show our can be extended other types similarity transformations generalizes translations scaling.KeywordsImplicit representationsEquivarianceGraph networks3D reconstructionTransformation