Abstract:

We present a novel framework for sampling data using random rays and the nearest neighbor mapping. Random rays are cast into the Euclidean space in which data are embedded. These rays are projected onto the data set based on the nearest neighbor mapping. The recorded information are called the "ray signatures."  We show some features and statistical invariant properties of the signatures.  Finally, we present a deep neural network model that takes as input a ray signature and classifies discrete unstructured 3D point clouds or surfaces. We present comparisons to some existing prominent neural network models.