  Many innovative applications require establishing correspondences among 3D
geometric objects. However, the countless possible deformations of smooth
surfaces make shape matching a challenging task. Finding an embedding to
represent the different shapes in high-dimensional space where the matching is
easier to solve is a well-trodden path that has given many outstanding
solutions. Recently, a new trend has shown advantages in learning such
representations. This novel idea motivated us to investigate which properties
differentiate these data-driven embeddings and which ones promote
state-of-the-art results. In this study, we analyze, for the first time,
properties that arise in data-driven learned embedding and their relation to
the shape-matching task. Our discoveries highlight the close link between
matching and smoothness, which naturally emerge from training. Also, we
demonstrate the relation between the orthogonality of the embedding and the
bijectivity of the correspondence. Our experiments show exciting results,
overcoming well-established alternatives and shedding a different light on
relevant contexts and properties for learned embeddings.
