Geometric edge convolution for rigid transformation invariant features in 3D point clouds

Extracting rigid transformation invariant features is still a challenge on 3D point clouds because rigid transformation changes the point coordinates, and relying on the point coordinates, most existing deep learning models fail. This paper addresses this challenge by proposing geometric edge convolution (GEConv). To facilitate rigid transformation invariant feature extraction, GEConv uses geometric features that are invariant to rigid transformations to construct a local graph and use shared multi-layer perceptron (MLP) on the graph edges to extract deep features. By leveraging these invariant geometric features to build the graph, GEConv effectively ensures the extraction of deep features that are also invariant to rigid transformations. By stacking GEConv, we construct a deep model called GEConvNet that hierarchically extracts different level rigid transformation invariant features for various point cloud tasks. To prove the effectiveness of GEConv, we provide experiments on four point cloud processing tasks; classification, parts segmentation, semantic segmentation, and point set registration. In the classification and segmentation tasks, GEConvNet performs better on robustness to rotation compared to existing models. Furthermore, our feature-matching-based approach for point set registration demonstrates strong performance, providing further evidence of GEConv's ability to handle rotation and translation effectively. Our code is available at http://www.github.com/saifabel/GEConv.