Deep Hierarchical Rotation Invariance Learning with Exact Geometry Feature Representation for Point Cloud Classification

Rotation invariance is a crucial property for 3D object classification, which is still a challenging task. State-of-the-art deep learning-based works require a massive amount of data augmentation to tackle this problem. This is however inefficient and classification accuracy suffers a sharp drop in experiments with arbitrary rotations. We introduce a new descriptor that can globally and locally capture the surface geometry properties and is based on a combination of spherical harmonics energy and point feature representation. The proposed descriptor is proven to fulfill the rotation-invariant property. A limited bandwidth spherical harmonics energy descriptor globally describes a 3D shape and its rotation-invariant property is proven by utilizing the properties of a Wigner D-matrix, while the point feature representation captures the local features with a KNN to build the connection to its neighborhood. We propose a new network structure by extending PointNet++ with several adaptations that can hierarchically and efficiently exploit local rotation-invariant features. Extensive experimental results show that our proposed method dramatically outperforms most state-of-the-art approaches on standard rotation-augmented 3D object classification benchmarks as well as in robustness experiments on point perturbation, point density, and partial point clouds.