Affine-invariant skeleton of 3D shapes

Abstract

Different application fields have shown increasing interest in shape description oriented to recognition and similarity issues. Beyond the application aims, the capability of handling details separating them from building elements, the invariance to a set of geometric transformations, the uniqueness and stability to noise represent fundamental properties of each proposed model. This paper defines an affine-invariant skeletal representation; starting from global features of a 3D shape, located by curvature properties, a Reeb graph is defined using the topological distance as a quotient function. If the mesh has uniformly spaced vertices, this Reeb graph can also be rendered as a geometric skeleton defined by the barycenters of pseudo-geodesic circles sequentially expanded from all the feature points.