  According to Aristotle, a philosopher in Ancient Greece, "the whole is
greater than the sum of its parts". This observation was adopted to explain
human perception by the Gestalt psychology school of thought in the twentieth
century. Here, we claim that observing part of an object which was previously
acquired as a whole, one could deal with both partial matching and shape
completion in a holistic manner. More specifically, given the geometry of a
full, articulated object in a given pose, as well as a partial scan of the same
object in a different pose, we address the problem of matching the part to the
whole while simultaneously reconstructing the new pose from its partial
observation. Our approach is data-driven, and takes the form of a Siamese
autoencoder without the requirement of a consistent vertex labeling at
inference time; as such, it can be used on unorganized point clouds as well as
on triangle meshes. We demonstrate the practical effectiveness of our model in
the applications of single-view deformable shape completion and dense shape
correspondence, both on synthetic and real-world geometric data, where we
outperform prior work on these tasks by a large margin.
