Measuring 3D shape similarity by matching the medial scaffolds

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 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 the form of a hypergraph. The MS representation is both hierarchical and complete. Our approach finds the optimal deformation path between two shapes by modelling shape deformations as discrete topological changes (transitions) of the MS, with costs associated with each transition. We first regularize the MS hypergraphs and use 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, and sheets. Early results on matching carpal bones and other shapes promise its potential in a range of applications.