3D Face Recognition using Euclidean Integral Invariants Signature

A novel 3D face representation and recognition approach is presented in this paper. We represent a 3D face by a set of level curves of geodesic function starting from the nose tip, which is invariant under isometric transformation of the surfaces. A pose change induces a special Euclidean transformation (a composition of a rotation and a translation) of the surface that represents a face and leads to the Euclidean transformation of the iso-geodesic curves. A change of facial expression induces isometric transformation of the iso-geodesic curves. Although the set of isometric transformations of a surface is larger than the set of Euclidean transformations in 3D, we assume that iso-geodesic curves undergo piecewise Euclidean transformations, i.e. the transformation of relatively small segments of the level curves is Euclidean. A Euclidean invariant integral signature for curves in 3D is presented in this paper. Euclidean invariant integral signature provides a classification of spatial curves which is independent of their position in 3D space and parameterization, and is not sensitive to noise. A recognition procedure based on comparing face feature in the invariant signature space is proposed. Substantiating examples are provided with an achieved classification accuracy of 95% for faces with various poses and facial expressions.