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

We propose to measure 3D shape similarity by matching a medial axis (MA)(MA) based representation—the medial scaffold  (MS)(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 MSMS. This approach is an extension of an approach to match 2D shapes by matching their shock graphs  , whereas here in 3D the MSMS is in an extended form of a hypergraph. The MSMS 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 MSMS hypergraphs, where each graphical transition is associated with a cost measurement defined by the transition. Our algorithm first regularizes the MSMS 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 MSMS 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.

Research highlights
► Measure 3D shape similarity by matching a medial axis (MA) based representation.
► Represent shape similarity as the minimum extent of deformation guided by the MS.
► Model shape deformation path as transitions of the MS associated with a cost.
► Define compatibility functions to measure the similarity between MS components.
► Results on matching shapes from standard dataset promise potential in applications.