Isometric deformation invariant 3D shape recognition

Intra-shape deformations complicate 3D shape recognition and therefore need proper modeling. Thereto, an isometric deformation model is used in this paper. The method proposed does not need explicit point correspondences for the comparison of 3D shapes. The geodesic distance matrix is used as an isometry-invariant shape representation. Two approaches are described to arrive at a sampling order invariant shape descriptor: the histogram of geodesic distance matrix values and the set of largest singular values of the geodesic distance matrix. Shape comparison is performed by comparison of the shape descriptors using the χ 2 - distance as dissimilarity measure. For object recognition, the results obtained demonstrate the singular value approach to outperform the histogram-based approach, as well as the state-of-the-art multidimensional scaling technique, the ICP baseline algorithm and other isometric deformation modeling methods found in literature. Using the TOSCA database, a rank-1 recognition rate of 100% is obtained for the identification scenario, while the verification experiments are characterized by a 1.58% equal error rate. External validation demonstrates that the singular value approach outperforms all other participants for the non-rigid object retrieval contests in SHREC 2010 as well as SHREC 2011. For 3D face recognition, the rank-1 recognition rate is 61.9% and the equal error rate is 11.8% on the BU-3DFE database. This decreased performance is attributed to the fact that the isometric deformation assumption only holds to a limited extent for facial expressions. This is also demonstrated in this paper.