On the Curvature of Pattern Transformation Manifolds: Numerical Estimation and Applications

This paper addresses the numerical estimation of the principal curvature of pattern transformation manifolds. When a visual pattern undergoes a geometric transformation, it forms a (sub)manifold in the ambient space, which is usually called the transformation manifold. The manifold curvature is an important property characterizing the manifold geometry, with several applications in manifold learning. We propose an efficient numerical algorithm for estimating the principal curvature at a certain point on the transformation manifold.