Deep implicit functions (DIFs), as a kind of 3D shape representation, are
becoming more and more popular in the 3D vision community due to their
compactness and strong representation power. However, unlike polygon mesh-based
templates, it remains a challenge to reason dense correspondences or other
semantic relationships across shapes represented by DIFs, which limits its
applications in texture transfer, shape analysis and so on. To overcome this
limitation and also make DIFs more interpretable, we propose Deep Implicit
Templates, a new 3D shape representation that supports explicit correspondence
reasoning in deep implicit representations. Our key idea is to formulate DIFs
as conditional deformations of a template implicit function. To this end, we
propose Spatial Warping LSTM, which decomposes the conditional spatial
transformation into multiple affine transformations and guarantees
generalization capability. Moreover, the training loss is carefully designed in
order to achieve high reconstruction accuracy while learning a plausible
template with accurate correspondences in an unsupervised manner. Experiments
show that our method can not only learn a common implicit template for a
collection of shapes, but also establish dense correspondences across all the
shapes simultaneously without any supervision.

本文提出了一种基于 Deep Implicit Templates 的新型三维形状表示方法，支持在深度隐式表示中进行显式的对应关系推理，并使用 Spatial Warping LSTM 解决推理过程中的空间变换问题，同时采用特殊的训练损失函数实现了无监督学习。实验证明，该方法不仅能够学习一个共同的隐式模板，还能够在不需要监督信号的情况下，对所有形状进行精确的无缝对应。