Affine invariant non-rigid shape analysis

Shape recognition deals with the study geometric structures. Modern surface processing methods can cope with non-rigidity by measuring the lack of isometry, deal with similarity by multiplying the Euclidean arc-length by the Gaussian curvature, and manage equi-affine transformations by resorting to the special affine arc-length definition in classical affine geometry. Here, we propose a computational framework that is invariant to the affine group of transformations (similarity and equi-affine) and thus, by construction, can handle non-rigid shapes. Technically, we add the similarity invariant property to an equi-affine invariant one. Diffusion geometry encapsulates the resulting measure to robustly provide signatures and computational tools for affine invariant surface matching and comparison.