  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: https://github.com/pvnieo/DPFM
