Geometric Convolutional Neural Network for Point Cloud Object Classification

Point cloud object classification has many challenges related to the quality of the data used to perform the classification in real time applications like robotic navigation. The quality of the data is related to the sensor calibration, data acquisition methodology and noise or perturbances on the measurement process. It is required for real time practical applications a solution that performs well even with medium quality data. In this paper, a novel method is presented to design and implement a geometric convolutional system that works using the mathematical framework of conformal algebra to reduce the impact of having object point clouds that are incomplete, occluded, or noisy, which causes deformations on the objects to classify. We accomplish this by designing three preprocesing layers in our convolutional system, that use conformal geometric operations to perform transformations of the input cloud point: a mapping from 3D to conformal space, a search for the best object perspective and an adjustment of the distance between sampling planes that describe the object.