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Invariance and equivariance to the rotation group have been widely discussed in the 3D deep learning community for pointclouds. Yet most proposed methods either use complex mathematical tools that may limit their accessibility, or are tied to specific input data types and network architectures. In this paper, we introduce a general framework built on top of what we call Vector Neuron representations for creating SO(3)-equivariant neural networks for pointcloud processing. Extending neurons from 1D scalars to 3D vectors, our vector neurons enable a simple mapping of SO(3) actions to latent spaces thereby providing a framework for building equivariance in common neural operations -- including linear layers, non-linearities, pooling, and normalizations. Due to their simplicity, vector neurons are versatile and, as we demonstrate, can be incorporated into diverse network architecture backbones, allowing them to process geometry inputs in arbitrary poses. Despite its simplicity, our method performs comparably well in accuracy and generalization with other more complex and specialized state-of-the-art methods on classification and segmentation tasks. We also show for the first time a rotation equivariant reconstruction network.
This paper proposes a correspondence-free method for point cloud rotational registration. We learn an embedding for each point cloud in a feature space that preserves the SO(3)-equivariance property, enabled by recent developments in equivariant neur
Detecting and localizing objects in the real 3D space, which plays a crucial role in scene understanding, is particularly challenging given only a monocular image due to the geometric information loss during imagery projection. We propose MonoGRNet f
Recent improvements in generative adversarial visual synthesis incorporate real and fake image transformation in a self-supervised setting, leading to increased stability and perceptual fidelity. However, these approaches typically involve image augm
3D object detection is a key perception component in autonomous driving. Most recent approaches are based on Lidar sensors only or fused with cameras. Maps (e.g., High Definition Maps), a basic infrastructure for intelligent vehicles, however, have n
We introduce the SE(3)-Transformer, a variant of the self-attention module for 3D point clouds and graphs, which is equivariant under continuous 3D roto-translations. Equivariance is important to ensure stable and predictable performance in the prese