Gaussian curvature-based geometric invariance

In this paper we derive a novel geometric invariance on surfaces that it is preserved under affine and weak perspective transformations, and it is local, intrinsic and computed from the differential geometry of the surface. Our 3D shape features are based on the Gaussian curvature and Mean curvature. When a surface undergoes an affine transformation, the shape features are the affine transformed shape features of the original surface, i.e., they are preserved and hence can be used for shape matching. We have tested robustness of the shape feature on the 3D facial data for various linear geometric transformations. The results show that our purposed shape feature is suitable for further application to 3D face identification due to its robustness to geometric transformation.