We consider the problem of computing dense correspondences between non-rigid
shapes with potentially significant partiality. Existing formulations tackle
this problem through heavy manifold optimization in the spectral domain, given
hand-crafted shape descriptors. In this paper, we propose the first learning
method aimed directly at partial non-rigid shape correspondence. Our approach
uses the functional map framework, can be trained in a supervised or
unsupervised manner, and learns descriptors directly from the data, thus both
improving robustness and accuracy in challenging cases. Furthermore, unlike
existing techniques, our method is also applicable to partial-to-partial
non-rigid matching, in which the common regions on both shapes are unknown a
priori. We demonstrate that the resulting method is data-efficient, and
achieves state-of-the-art results on several benchmark datasets. Our code and
data can be found online: this https URL

本文提出一种基于功能映射框架的学习方法，用于直接解决非刚性形状对应问题，包括局部对应和参考地图未知情况下的对应，该方法可以在监督或无监督的情况下进行训练，从数据中直接学习描述符，提高了模型的稳健性和精度，在多个基准数据集上取得了最新的研究成果。

DPFM: 深度部分函数映射

DPFM: Deep Partial Functional Maps

Despite deep convolutional neural networks' great success in object
classification, it suffers from severe generalization performance drop under
occlusion due to the inconsistency between training and testing data. Because
of the large variance of occluders, our goal is a model trained on
occlusion-free data while generalizable to occlusion conditions. In this work,
we integrate prototypes, partial matching and top-down attention regulation
into deep neural networks to realize robust object classification under
occlusion. We first introduce prototype learning as its regularization
encourages compact data clusters, which enables better generalization ability
under inconsistent conditions. Then, attention map at intermediate layer based
on feature dictionary and activation scale is estimated for partial matching,
which sifts irrelevant information out when comparing features with prototypes.
Further, inspired by neuroscience research that reveals the important role of
feedback connection for object recognition under occlusion, a top-down feedback
attention regulation is introduced into convolution layers, purposefully
reducing the contamination by occlusion during feature extraction stage. Our
experiment results on partially occluded MNIST and vehicles from the PASCAL3D+
dataset demonstrate that the proposed network significantly improves the
robustness of current deep neural networks under occlusion. Our code will be
released.

本文介绍了将原型学习、部分匹配和自上而下的注意力调节集成到深度学习神经网络中，以实现在遮挡情况下的稳健目标分类。实验结果表明，所提出的网络显著提高了当前深度神经网络在遮挡下的鲁棒性。