Learning 3D Equivariant Implicit Function with Patch-Level Pose-Invariant Representation

In this work, we are motivated by the fact that the local 3D patches repeatedly appear on 3D shapes/surfaces if the factor of poses is removed. Based on this observation, we propose the 3D patch-level equivariant implicit function (PEIF) based on the 3D patch-level pose-invariant representation, allowing us to reconstruct 3D surfaces by estimating equivariant displacement vector fields for query points. Specifically, our model is based on the pose-normalized query/patch pairs and enhanced by the proposed intrinsic patch geometry representation, modeling the intrinsic 3D patch geometry feature by learnable multi-head memory banks. Extensive experiments show that our model achieves state-of-the-art performance on multiple surface reconstruction datasets, and also exhibits better generalization to crossdataset shapes and robustness to arbitrary rotations.