We present a novel method for computing correspondences across 3D shapes
using unsupervised learning. Our method computes a non-linear transformation of
given descriptor functions, while optimizing for global structural properties
of the resulting maps, such as their bijectivity or approximate isometry. To
this end, we use the functional maps framework, and build upon the recent FMNet
architecture for descriptor learning. Unlike that approach, however, we show
that learning can be done in a purely \emph{unsupervised setting}, without
having access to any ground truth correspondences. This results in a very
general shape matching method that we call SURFMNet for Spectral Unsupervised
FMNet, and which can be used to establish correspondences within 3D shape
collections without any prior information. We demonstrate on a wide range of
challenging benchmarks, that our approach leads to state-of-the-art results
compared to the existing unsupervised methods and achieves results that are
comparable even to the supervised learning techniques. Moreover, our framework
is an order of magnitude faster, and does not rely on geodesic distance
computation or expensive post-processing.

本篇论文提出一种新方法，使用无监督学习计算三维形状之间的对应关系。该方法使用描述符函数的非线性变换，并同时优化映射结果的全局结构性质，例如双射性或近似等度性，在最近邻域上进行匹配，从而有望在不需要先验信息的情况下建立三维形状集合内部的对应关系。