  This paper introduces the 3DCapsule, which is a 3D extension of the recently
introduced Capsule concept that makes it applicable to unordered point sets.
The original Capsule relies on the existence of a spatial relationship between
the elements in the feature map it is presented with, whereas in point
permutation invariant formulations of 3D point set classification methods, such
relationships are typically lost. Here, a new layer called ComposeCaps is
introduced that, in lieu of a spatially relevant feature mapping, learns a new
mapping that can be exploited by the 3DCapsule. Previous works in the 3D point
set classification domain have focused on other parts of the architecture,
whereas instead, the 3DCapsule is a drop-in replacement of the commonly used
fully connected classifier. It is demonstrated via an ablation study, that when
the 3DCapsule is applied to recent 3D point set classification architectures,
it consistently shows an improvement, in particular when subjected to noisy
data. Similarly, the ComposeCaps layer is evaluated and demonstrates an
improvement over the baseline. In an apples-to-apples comparison against
state-of-the-art methods, again, better performance is demonstrated by the
3DCapsule.
