Equivariant Point Cloud Analysis via Learning Orientations for Message Passing

@article{Luo2022EquivariantPC,
  title={Equivariant Point Cloud Analysis via Learning Orientations for Message Passing},
  author={Shitong Luo and Jiahan Li and Jiaqi Guan and Yufeng Su and Chaoran Cheng and Jian Peng and Jianzhu Ma},
  journal={ArXiv},
  year={2022},
  volume={abs/2203.14486}
}
Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, sim-plicity, and expressiveness — some are designed ad hoc for specific data types, some are too complex to be accessible, and some sacrifice flexible transformations. In this work, we propose a novel and simple framework to achieve equivariance for point cloud analysis based on the message passing (graph neural network) scheme. We find… 
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SHOWING 1-10 OF 46 REFERENCES
Quaternion Equivariant Capsule Networks for 3D Point Clouds
TLDR
A 3D capsule module for processing point clouds that is equivariant to 3D rotations and translations, as well as invariant to permutations of the input points, and builds a capsule network that disentangles geometry from pose, paving the way for more informative descriptors and a structured latent space.
A Rotation-Invariant Framework for Deep Point Cloud Analysis
TLDR
A new low-level purely rotation-invariant representation to replace common 3D Cartesian coordinates as the network inputs is introduced, and a network architecture is presented to embed these representations into features, encoding local relations between points and their neighbors, and the global shape structure.
Vector Neurons: A General Framework for SO(3)-Equivariant Networks
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…
A Closer Look at Rotation-invariant Deep Point Cloud Analysis
TLDR
This investigation reveals that the ambiguity problem associated with the PCA-based canonical poses is handled insufficiently in some recent works, and develops a simple pose selector module for disambiguation that presents noticeable enhancement over state-of-the-art approaches on the challenging real-world dataset.
Rotation Invariant Point Cloud Classification: Where Local Geometry Meets Global Topology
TLDR
This work has designed a two-branch network where one stream encodes local geometric RI features and the other encodes global topology-preserving RI features that achieves the state-of-the-art performance on various rotation-augmented versions of ModelNet40, ShapeNet, and ScanObjectNN.
PointCNN: Convolution On X-Transformed Points
TLDR
This work proposes to learn an Χ-transformation from the input points to simultaneously promote two causes: the first is the weighting of the input features associated with the points, and the second is the permutation of the points into a latent and potentially canonical order.
Dynamic Graph CNN for Learning on Point Clouds
TLDR
This work proposes a new neural network module suitable for CNN-based high-level tasks on point clouds, including classification and segmentation called EdgeConv, which acts on graphs dynamically computed in each layer of the network.
PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation
TLDR
This paper designs a novel type of neural network that directly consumes point clouds, which well respects the permutation invariance of points in the input and provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing.
PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space
TLDR
A hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set and proposes novel set learning layers to adaptively combine features from multiple scales to learn deep point set features efficiently and robustly.
PPFNet: Global Context Aware Local Features for Robust 3D Point Matching
TLDR
Qualitative and quantitative evaluations of the PPFNet network suggest increased recall, improved robustness and invariance as well as a vital step in the 3D descriptor extraction performance.
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