We propose a novel unsupervised learning approach to 3D shape correspondence
that builds a multiscale matching pipeline into a deep neural network. This
approach is based on smooth shells, the current state-of-the-art axiomatic
correspondence method, which requires an a priori stochastic search over the
space of initial poses. Our goal is to replace this costly preprocessing step
by directly learning good initializations from the input surfaces. To that end,
we systematically derive a fully differentiable, hierarchical matching pipeline
from entropy regularized optimal transport. This allows us to combine it with a
local feature extractor based on smooth, truncated spectral convolution
filters. Finally, we show that the proposed unsupervised method significantly
improves over the state-of-the-art on multiple datasets, even in comparison to
the most recent supervised methods. Moreover, we demonstrate compelling
generalization results by applying our learned filters to examples that
significantly deviate from the training set.

采用多尺度匹配管道和深度神经网络的无监督学习方法实现 3D 形状对应，其使用基于优化传输的最优正则 化方法来创建完全可微的层次匹配管道，并利用光滑的截断谱卷积滤 波器提取本地特征，其在多个数据集上比最新的监督方法显著改善， 并能够很好地推广到偏离训练集的示例