Variational Beltrami flows over manifolds

In this paper, we study, in this paper, the problem of denoising images/data which are defined are nonflat surfaces. This problem arises often in many medical imaging tasks. The Beltrami flow which was defined in an explicit-intrinsic manner is generalized here to nonflat surfaces and is defined in an implicit way. We formulate the flow in a variational way which is generalized to a scalar field defined over an n-dimensional manifold. The implementation scheme of this flow is presented and various experimental results obtained on a set of real images illustrate the performances of the approach as well as the differences between various flows of interests.