Shape reconstruction from imaging volumes is a recurring need in medical
image analysis. Common workflows start with a segmentation step, followed by
careful post-processing and,finally, ad hoc meshing algorithms. As this
sequence can be timeconsuming, neural networks are trained to reconstruct
shapes through template deformation. These networks deliver state-ofthe-art
results without manual intervention, but, so far, they have primarily been
evaluated on anatomical shapes with little topological variety between
individuals. In contrast, other works favor learning implicit shape models,
which have multiple benefits for meshing and visualization. Our work follows
this direction by introducing deep medial voxels, a semi-implicit
representation that faithfully approximates the topological skeleton from
imaging volumes and eventually leads to shape reconstruction via convolution
surfaces. Our reconstruction technique shows potential for both visualization
and computer simulations.

通过模板变形和深度介质体方法实现形状重建，以应用于医学成像、可视化和计算机模拟。

深度中心体：用于解剖形状建模的学习中心轴近似

Deep Medial Voxels: Learned Medial Axis Approximations for Anatomical  Shape Modeling

This paper proposes a correspondence-free method for point cloud rotational
registration. We learn an embedding for each point cloud in a feature space
that preserves the SO(3)-equivariance property, enabled by recent developments
in equivariant neural networks. The proposed shape registration method achieves
three major advantages through combining equivariant feature learning with
implicit shape models. First, the necessity of data association is removed
because of the permutation-invariant property in network architectures similar
to PointNet. Second, the registration in feature space can be solved in
closed-form using Horn's method due to the SO(3)-equivariance property. Third,
the registration is robust to noise in the point cloud because of the joint
training of registration and implicit shape reconstruction. The experimental
results show superior performance compared with existing correspondence-free
deep registration methods.

本文提出了一种基于等变特征学习和隐式形状模型的无对应点云旋转配准方法，可实现无需数据关联、在特征空间中闭式求解和对噪声鲁棒。实验结果表明，该方法优于现有基于深度学习的无对应点云配准方法。