Deep implicit functions (DIFs) have emerged as a potent and articulate means
of representing 3D shapes. However, methods modeling object categories or
non-rigid entities have mainly focused on single-object scenarios. In this
work, we propose MODIF, a multi-object deep implicit function that jointly
learns the deformation fields and instance-specific latent codes for multiple
objects at once. Our emphasis is on non-rigid, non-interpenetrating entities
such as organs. To effectively capture the interrelation between these entities
and ensure precise, collision-free representations, our approach facilitates
signaling between category-specific fields to adequately rectify shapes. We
also introduce novel inter-object supervision: an attraction-repulsion loss is
formulated to refine contact regions between objects. Our approach is
demonstrated on various medical benchmarks, involving modeling different groups
of intricate anatomical entities. Experimental results illustrate that our
model can proficiently learn the shape representation of each organ and their
relations to others, to the point that shapes missing from unseen instances can
be consistently recovered by our method. Finally, MODIF can also propagate
semantic information throughout the population via accurate point
correspondences

通过多物体深度隐式函数模型（MODIF），我们提出了一种学习多个非刚性实例的变形场和实例特定潜在代码的方法，以实现精确、无碰撞的形状表示，并在医学基准测试中展示了其优越性能。