A topological variational model for image singularities

Image singularities are prominent landmarks and their detection, recognition, and classification is a crucial step in image processing and computer vision. Such singularities carry important information for further operations, such as image registration, shape analysis, motion estimation, and object recognition. We propose a topological gradient descent flow for image singularities. The approach is expressed in the higher order variational framework as a minimizer of a variational integral involving the gradient and the Hessian matrix of the height function defined on a manifold. We demonstrate through numerical simulations the power of the proposed technique in preserving image singularities.