A Geodesic Landmark Shooting Algorithm for Template Matching and Its Applications

We present an efficient landmark shooting algorithm for template matching and its applications. The novelties of the algorithm include the use of a constant matrix to update the search direction of the geodesic shooting, instead of the traditional methods of forwardbackward integration for updating the gradient or Newton’s optimization, and the use of a non-smooth conic kernel for the particle system that accelerates the convergence of matching. In addition to the warping algorithm, we explore the potential of using the Hamiltonian metric for clustering analysis. We introduce a deformation decomposition method that decomposes the momentum field and the Hamiltonian metric into components, where the components carry essential features of the deformation at different scales. Our numerical experiments show that the decomposition method is advantageous for template matching, as well as classification analysis when used as feature vectors for downstream classifiers such as classical neural networks. keywords: landmark, geodesic shooting, template matching, particle system, deformation decomposition, Hamiltonian metric, neural networks.