Inelastic Deformation Invariant Modal Representation for Non-rigid 3D Object Recognition

Intra-shape deformations complicate 3D object recognition and retrieval and need therefore proper modeling. A method for inelastic deformation invariant object recognition is proposed, representing 3D objects by diffusion distance tensors (DDT), i.e. third order tensors containing the average diffusion distance for different diffusion times between each pair of points on the surface. In addition to the DDT, also geodesic distance matrices (GDM) are used to represent the objects independent of the reference frame. Transforming these distance tensors into modal representations provides a sampling order invariant shape descriptor. Different dissimilarity measures can be used for comparing these shape descriptors. The final object pair dissimilarity is the sum or product of the dissimilarities obtained by modal representations of the GDM and DDT. The method is validated on the TOSCA non-rigid world database and the SHREC 2010 dataset of non-rigid 3D models indicating that our method combining these two representations provides a more noise robust but still inter-subject shape variation sensitive method for the identification and the verification scenario in object retrieval.