  We introduce RIM-Net, a neural network which learns recursive implicit fields
for unsupervised inference of hierarchical shape structures. Our network
recursively decomposes an input 3D shape into two parts, resulting in a binary
tree hierarchy. Each level of the tree corresponds to an assembly of shape
parts, represented as implicit functions, to reconstruct the input shape. At
each node of the tree, simultaneous feature decoding and shape decomposition
are carried out by their respective feature and part decoders, with weight
sharing across the same hierarchy level. As an implicit field decoder, the part
decoder is designed to decompose a sub-shape, via a two-way branched
reconstruction, where each branch predicts a set of parameters defining a
Gaussian to serve as a local point distribution for shape reconstruction. With
reconstruction losses accounted for at each hierarchy level and a decomposition
loss at each node, our network training does not require any ground-truth
segmentations, let alone hierarchies. Through extensive experiments and
comparisons to state-of-the-art alternatives, we demonstrate the quality,
consistency, and interpretability of hierarchical structural inference by
RIM-Net.
