3D shape matching is a long-standing problem in computer vision and computer
graphics. While deep neural networks were shown to lead to state-of-the-art
results in shape matching, existing learning-based approaches are limited in
the context of multi-shape matching: (i) either they focus on matching pairs of
shapes only and thus suffer from cycle-inconsistent multi-matchings, or (ii)
they require an explicit template shape to address the matching of a collection
of shapes. In this paper, we present a novel approach for deep multi-shape
matching that ensures cycle-consistent multi-matchings while not depending on
an explicit template shape. To this end, we utilise a shape-to-universe
multi-matching representation that we combine with powerful functional map
regularisation, so that our multi-shape matching neural network can be trained
in a fully unsupervised manner. While the functional map regularisation is only
considered during training time, functional maps are not computed for
predicting correspondences, thereby allowing for fast inference. We demonstrate
that our method achieves state-of-the-art results on several challenging
benchmark datasets, and, most remarkably, that our unsupervised method even
outperforms recent supervised methods.

本研究提出了一种深度学习多形状匹配算法，利用 shape-to-universe 多匹配表示，并结合强大的 functional map 正则化，从而在不依赖于显式模板形状的情况下确保循环一致的多匹配，并在几个具有挑战性的基准数据集上取得了最新的最好结果。