Spherical-GMM: A Rotation and Scale Invariant Method for Point Cloud Classification

3D Point Cloud data structure has been widely used in a number of industries such as auto-driving, general surveying system and object reconstruction. The classification task with point cloud data is especially helpful in radar or scanning-based conditions which require auto recognition of objects. Convolutional Neural Network (CNN) has become the top choice for learning problems involving 2D planar images. However, CNN usually does not preserve in-variance for rotation nor scaling. In this paper, we introduce a new method which implements Gaussian Mixture Model (GMM) to project point cloud features onto the surfaces of a varied matrix of enclosing spheres and uses Spherical CNNs which contain spherical cross-correlation that is both expressive and rotation-invariant. The method achieves 82.09% accuracy in random rotations and 86.70% in static conditions while trained in static 3D MNIST dataset.