VariGrad: A Novel Feature Vector Architecture for Geometric Deep Learning on Unregistered Data

Abstract

We present a novel geometric deep learning layer that leverages the varifold gradient (VariGrad) to compute feature vector representations of 3D geometric data. These feature vectors can be used in a variety of downstream learning tasks such as classification, registration, and shape reconstruction. Our model's use of parameterization independent varifold representations of geometric data allows our model to be both trained and tested on data independent of the given sampling or parameterization. We demonstrate the efficiency, generalizability, and robustness to resampling demonstrated by the proposed VariGrad layer.