Revisiting Map Relations for Unsupervised Non-Rigid Shape Matching
Dongliang Cao Paul Roetzer Florian Bernard
We propose a novel unsupervised learning approach for non-rigid 3D shape
matching. Our approach improves upon recent state-of-the art deep functional
map methods and can be applied to a broad range of different challenging
scenarios. Previous deep functional map methods mainly focus on feature
extraction and aim exclusively at obtaining more expressive features for
functional map computation. However, the importance of the functional map
computation itself is often neglected and the relationship between the
functional map and point-wise map is underexplored. In this paper, we
systematically investigate the coupling relationship between the functional map
from the functional map solver and the point-wise map based on feature
similarity. To this end, we propose a self-adaptive functional map solver to
adjust the functional map regularisation for different shape matching
scenarios, together with a vertex-wise contrastive loss to obtain more
discriminative features. Using different challenging datasets (including
non-isometry, topological noise and partiality), we demonstrate that our method
substantially outperforms previous state-of-the-art methods.