Adjoint Bijective ZoomOut: Efficient Upsampling for Learned Linearly-invariant Embedding

In this paper, we present a novel method for refining correspondences between 3D point clouds. Our method is compatible with the functional map framework, so it relies on the spectral representation of the correspondence. Although, differently from other similar approaches, this algorithm is specifically for a particular functional setting, being the only refinement method compatible with a recent data-driven approach, more suitable for point cloud matching. Our 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 spectral upsampling in the same way as other similar methods, ours increases the accuracy of the correspondence, leading to more bijective correspondences. We tested our method over different datasets. It outperforms the previous methods in terms of map accuracy in all the tests considered.