Deep Deformable Models: Learning 3D Shape Abstractions with Part
  Consistency
Di Liu Long Zhao Qilong Zhangli Yunhe Gao Ting Liu Dimitris N. Metaxas
The task of shape abstraction with semantic part consistency is challenging
due to the complex geometries of natural objects. Recent methods learn to
represent an object shape using a set of simple primitives to fit the target.
\textcolor{black}{However, in these methods, the primitives used do not always
correspond to real parts or lack geometric flexibility for semantic
interpretation.} In this paper, we investigate salient and efficient primitive
descriptors for accurate shape abstractions, and propose \textit{Deep
Deformable Models (DDMs)}. DDM employs global deformations and diffeomorphic
local deformations. These properties enable DDM to abstract complex object
shapes with significantly fewer primitives that offer broader geometry coverage
and finer details. DDM is also capable of learning part-level semantic
correspondences due to the differentiable and invertible properties of our
primitive deformation. Moreover, DDM learning formulation is based on dynamic
and kinematic modeling, which enables joint regularization of each
sub-transformation during primitive fitting. Extensive experiments on
\textit{ShapeNet} demonstrate that DDM outperforms the state-of-the-art in
terms of reconstruction and part consistency by a notable margin.