DeepUME: Learning the Universal Manifold Embedding for Robust Point Cloud Registration

Registration of point clouds related by rigid transformations is one of the fundamental problems in computer vision. However, a solution to the practical scenario of aligning sparsely and differently sampled observations in the presence of noise is still lacking. We approach registration in this scenario with a fusion of the closed-form Universal Manifold Embedding (UME) method and a deep neural network. The two are combined into a single unified framework, named DeepUME, trained end-to-end and in an unsupervised manner. To successfully provide a global solution in the presence of large transformations, we employ an SO(3)-invariant coordinate system to learn both a joint-resampling strategy of the point clouds and SO(3)-invariant features. These features are then utilized by the geometric UME method for transformation estimation. The parameters of DeepUME are optimized using a metric designed to overcome an ambiguity problem emerging in the registration of symmetric shapes, when noisy scenarios are considered. We show that our hybrid method outperforms state-of-the-art registration methods in various scenarios, and generalizes well to unseen data sets. Our code is publicly available.