Measuring 3D shape similarity by graph-based matching of the medial scaffolds

Abstract

We propose to measure 3D shape similarity by matching a medial axis ( MA ) based representation—the medial scaffold ( MS ) . Shape similarity is measured as the minimum extent of deformation necessary for one shape to match another, guided by representing the shapes using the MS . This approach is an extension of an approach to match 2D shapes by matching their shock graphs, whereas here in 3D the MS is in an extended form of a hypergraph. The MS representation is both hierarchical and complete. Our approach approximates the theoretical optimal deformation path between two shapes by modeling shape deformations as discrete topological changes (the transitions) of the MS hypergraphs, where each graphical transition is associated with a cost measurement defined by the transition. Our algorithm first regularizes the MS hypergraphs and uses the graduated assignment graph-matching scheme to match the hypergraphs. A set of compatibility functions is defined to measure the pairwise similarity between the MS nodes, curves (graph links), and sheets (hyperlinks). Results on matching carpal bones and shapes from the SHREC’10 non-rigid dataset promise its potential in a range of applications.