VariGrad: A Novel Feature Vector Architecture for Geometric Deep Learning on Unregistered Data
This addresses a challenge in geometric deep learning for applications like classification and shape reconstruction, though it appears incremental as it builds on existing varifold representations.
The paper tackles the problem of learning from 3D geometric data that lacks consistent registration or parameterization by introducing a novel layer called VariGrad, which uses varifold gradients to compute feature vectors, resulting in demonstrated efficiency, generalizability, and robustness to resampling.
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.