A general formalism to impose topology preserving regularity on a given irregular deformation field is presented. The topology preservation conditions are derived with regard to the discrete approximations to the deformation field Jacobian in a two-dimensional image registration problem. The problem of enforcing topology preservation onto a given deformation field is formulated in terms of the ...

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

nanotechnology involves the ability to see and control individual atoms and molecules which are about 100 nanometer or smaller. one of the major tools used in this field is atomic force microscopy which uses a wealth of techniques to measure the topography and investigates the surface forces in nanoscale. friction force is the representation of the surface interaction between two surfaces an...