Bijective upsampling and learned embedding for point clouds correspondences

In this paper, we present a novel pipeline to compute and refine a data-driven solution for estimating the correspondence between 3D point clouds. Our method is compatible with the functional map framework, so it relies on a functional representation of the correspondence, but, differently from other similar approaches, this method is specifically designed to exploit this functional scenario for point cloud matching. Our new method merges a data-driven approach to compute functional basis and descriptors on the shape's surface and a new refinement method designed for the learned basis. This refinement algorithm arises from a different way of converting functional operators into point-to-point correspondence, which we prove to promote bijectivity between maps, exploiting a theoretical result. Iterating this procedure and performing basis upsampling in the same way as other similar methods, ours increases the accuracy of the correspondence, leading to more bijective correspondences. Different from other approaches, our method allows us to train a functional basis, considering the refinement stage. Combining our new pipeline with an improved feature extractor, our solution outperforms previous methods in various evaluations and settings. We test our method over different datasets, comprising near-isometric and non-isometric pairs