Fig. 1.

(Left) Two deformable shapes are represented as weighted graphs with edge weights proportional to the pairwise geodesic distances between the corresponding vertices. Optimal isomorphism in the sense of $\text{dis}=\Vert \mathbf{A}-{\mathbf{\Pi }}^{\text{T}}\mathbf{B}\mathbf{\Pi }\Vert$ quantifies how isometric these two discrete metric spaces are and is related to the Gromov−Hausdorff distance (12). (Right) Limitation of the former distortion criterion. The bottom graphs are both 1-isomorphic to the top one, without distinguishing between exact partial isomorphism (Bottom Left; isomorphic subgraphs are marked in red) and inexact full isomorphism (Bottom Right).