We present a novel learning-based approach for computing correspondences
between non-rigid 3D shapes. Unlike previous methods that either require
extensive training data or operate on handcrafted input descriptors and thus
generalize poorly across diverse datasets, our approach is both accurate and
robust to changes in shape structure. Key to our method is a feature-extraction
network that learns directly from raw shape geometry, combined with a novel
regularized map extraction layer and loss, based on the functional map
representation. We demonstrate through extensive experiments in challenging
shape matching scenarios that our method can learn from less training data than
existing supervised approaches and generalizes significantly better than
current descriptor-based learning methods. Our source code is available at:
this https URL

提出了一种基于学习的方法，用于计算非刚性三维形状之间的对应关系。该方法利用从原始形状几何中直接学习的特征提取网络，结合一种基于功能映射表示的正则化地图提取层和损失函数，能够从比现有的监督方法少的训练数据中学习，并且比当前基于描述符学习的方法更加普适。

深度几何函数映射：形状对应的鲁棒特征学习

Deep Geometric Functional Maps: Robust Feature Learning for Shape  Correspondence

We introduce a new method for non-rigid registration of 3D human shapes. Our
proposed pipeline builds upon a given parametric model of the human, and makes
use of the functional map representation for encoding and inferring shape maps
throughout the registration process. This combination endows our method with
robustness to a large variety of nuisances observed in practical settings,
including non-isometric transformations, downsampling, topological noise, and
occlusions; further, the pipeline can be applied invariably across different
shape representations (e.g. meshes and point clouds), and in the presence of
(even dramatic) missing parts such as those arising in real-world depth sensing
applications. We showcase our method on a selection of challenging tasks,
demonstrating results in line with, or even surpassing, state-of-the-art
methods in the respective areas.

本文介绍了一种针对三维人体形状的非刚性配准方法，该方法基于人体的参数化模型，并利用功能映射表示来在整个配准过程中编码和推断形状映射。该方法具有鲁棒性，可以应对实际环境中出现的各种干扰问题，包括非等距变换、降采样、拓扑噪声和遮挡等，在不同的形状表示下都可以适用，并且即使在出现缺失部分的情况下，也可以应用于实际的深度感测应用中。我们展示了该方法在一系列具有挑战性的任务上的效果，并且证明了该方法在相应领域达到了甚至超越了同类方法的效果。