Rotation-Equivariant Multi-Layer Perceptron for Point Cloud Classification and Segmentation

Point cloud data processing faces challenges due to the disorder and irregularity of point cloud data. Traditional approaches, typically revolving around local or global geometric feature extraction, often struggle with rotational robustness and are resource-intensive. The recent Vector Neurons (VN) framework marks a significant advancement, enhancing generalization and robustness in handling point cloud inputs. To extract both local and global features from objects, we propose a novel rotation-equivariant multi-layer perceptron (ReMLP) in this paper. ReMLP comprises a normalized vector neuron residual block (VN-ResBlock) and rotation-equivariant transformer. The VN-ResBlock extends classic rectified linear unit (ReLU) to three-dimensional vector neurons, keeping rotation equivariance. Leveraging the property, we have developed a rotation equivariant transformer to capture the relationship between local and global features effectively. Theoretically, the rotation equivariance of both components is proven. Besides, ReMLP incorporates a channel adaptive normalization to address point cloud irregularity, balancing local and global normalization via channel count. Notably, this approach represents one of the successful attempts to use the 3D coordinates of point clouds to preserve spatial information. Experimental results show that our method performs comparably well in accuracy and robustness with other state-of-the-art methods on classification and part segmentation tasks.