“…Previous unsupervised methods for learning shape descriptors have generally used either probabilistic models [Xie et al, 2018, Shi et al, 2020, generative adversarial networks (GANs) [Wu et al, 2015, Achlioptas et al, 2018, Han et al, 2019, or autoencoders [Girdhar et al, 2016, Sharma et al, 2016, Wu et al, 2015, Yang et al, 2018. One approach that has been relatively unexplored for deep learning methods but common in hand-crafted methods is to design shape descriptors that are invariant to transforms that preserve distances, either the extrinsic (Euclidean) distance [Belongie et al, 2001, Johnson and Hebert, 1999, Manay et al, 2004, Gelfand et al, 2005, Pauly et al, 2003 or intrinsic (geodesic) distance [Elad and Kimmel, 2003, Rustamov, 2007, Sun et al, 2009, Aubry et al, 2011.…”