3D Equivariant Graph Implicit Functions
- URL: http://arxiv.org/abs/2203.17178v1
- Date: Thu, 31 Mar 2022 16:51:25 GMT
- Title: 3D Equivariant Graph Implicit Functions
- Authors: Yunlu Chen, Basura Fernando, Hakan Bilen, Matthias Nie{\ss}ner,
Efstratios Gavves
- Abstract summary: We introduce a novel family of graph implicit functions with equivariant layers that facilitates modeling fine local details.
Our method improves over the existing rotation-equivariant implicit function from 0.69 to 0.89 on the ShapeNet reconstruction task.
- Score: 51.5559264447605
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In 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 of such representations, in failing to capture
local 3D geometric fine details, and to learn from and generalize to shapes
with unseen 3D transformations. To this end, we introduce a novel family of
graph implicit functions with equivariant layers that facilitates modeling fine
local details and guaranteed robustness to various groups of geometric
transformations, through local $k$-NN graph embeddings with sparse point set
observations at multiple resolutions. Our method improves over the existing
rotation-equivariant implicit function from 0.69 to 0.89 (IoU) on the ShapeNet
reconstruction task. We also show that our equivariant implicit function can be
extended to other types of similarity transformations and generalizes to unseen
translations and scaling.
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