  While dealing with matching shapes to their parts, we often apply a tool
known as functional maps. The idea is to translate the shape matching problem
into ``convenient'' spaces by which matching is performed algebraically by
solving a least squares problem. Here, we argue that such formulations, though
popular in this field, introduce errors in the estimated match when partiality
is invoked. Such errors are unavoidable even for advanced feature extraction
networks, and they can be shown to escalate with increasing degrees of shape
partiality, adversely affecting the learning capability of such systems. To
circumvent these limitations, we propose a novel approach for partial shape
matching. Our study of functional maps led us to a novel method that
establishes direct correspondence between partial and full shapes through
feature matching bypassing the need for functional map intermediate spaces. The
Gromov distance between metric spaces leads to the construction of the first
part of our loss functions. For regularization we use two options: a term based
on the area preserving property of the mapping, and a relaxed version that
avoids the need to resort to functional maps. The proposed approach shows
superior performance on the SHREC'16 dataset, outperforming existing
unsupervised methods for partial shape matching. Notably, it achieves
state-of-the-art results on the SHREC'16 HOLES benchmark, superior also
compared to supervised methods. We demonstrate the benefits of the proposed
unsupervised method when applied to a new dataset PFAUST for part-to-full shape
correspondence
