We propose a novel learning-based approach for robust 3D shape matching. Our
method builds upon deep functional maps and can be trained in a fully
unsupervised manner. Previous deep functional map methods mainly focus on
predicting optimised functional maps alone, and then rely on off-the-shelf
post-processing to obtain accurate point-wise maps during inference. However,
this two-stage procedure for obtaining point-wise maps often yields sub-optimal
performance. In contrast, building upon recent insights about the relation
between functional maps and point-wise maps, we propose a novel unsupervised
loss to couple the functional maps and point-wise maps, and thereby directly
obtain point-wise maps without any post-processing. Our approach obtains
accurate correspondences not only for near-isometric shapes, but also for more
challenging non-isometric shapes and partial shapes, as well as shapes with
different discretisation or topological noise. Using a total of nine diverse
datasets, we extensively evaluate the performance and demonstrate that our
method substantially outperforms previous state-of-the-art methods, even
compared to recent supervised methods. Our code is available at
this https URL

我们提出了一种新的基于学习的方法来进行 3D 形状匹配，可以在完全非监督的情况下进行训练，并可准确处理非等距形状、局部形状、不同离散化或拓扑噪声的形状。

强度谱形匹配的无监督学习

Unsupervised Learning of Robust Spectral Shape Matching

We present the first utterly self-supervised network for dense correspondence
mapping between non-isometric shapes. The task of alignment in non-Euclidean
domains is one of the most fundamental and crucial problems in computer vision.
As 3D scanners can generate highly complex and dense models, the mission of
finding dense mappings between those models is vital. The novelty of our
solution is based on a cyclic mapping between metric spaces, where the distance
between a pair of points should remain invariant after the full cycle. As the
same learnable rules that generate the point-wise descriptors apply in both
directions, the network learns invariant structures without any labels while
coping with non-isometric deformations. We show here state-of-the-art-results
by a large margin for a variety of tasks compared to known self-supervised and
supervised methods.

该研究提出了一个基于自我监督的网络，用于在非等度形状之间进行密集的对应映射，解决了在非欧几里得域中对齐的问题，相较于已知的自我监督和监督方法取得了最先进的结果。