Variational Beltrami flows over manifolds
نویسندگان
چکیده
We study, in this paper, the problem of denoising images/data which are defined over non-flat 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 non-flat 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.
منابع مشابه
Regularization of Mappings Between Implicit Manifolds of Arbitrary Dimension and Codimension
We study in this paper the problem of regularization of mappings between manifolds of arbitrary dimension and codimension using variational methods. This is of interest in various applications such as diffusion tensor imaging and EEG processing on the cortex. We consider the cases where the source and target manifold are represented implicitly, using multiple level set functions, or explicitly,...
متن کاملCovariantising the Beltrami equation in W-gravity
Recently, certain higher dimensional complex manifolds were obtained in [1] by associating a higher dimensional uniformisation to the generalised Teichmüller spaces of Hitchin. The extra dimensions are provided by the “times” of the generalised KdV hierarchy. In this paper, we complete the proof that these manifolds provide the analog of superspace for W-gravity and that Wsymmetry linearises on...
متن کاملContact Topology and Hydrodynamics
We draw connections between the field of contact topology and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb fields (vector fields which preserve a transverse nowhere-integrable plane field) up to scaling and rotational Beltrami fields on three-manifolds. Thus, we characterise Beltrami fields in a metric-indep...
متن کاملCONTACT TOPOLOGY AND HYDRODYNAMICS I: Beltrami fields and the Seifert Conjecture
We draw connections between the field of contact topology (the study of totally nonintegrable plane distributions) and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb fields (vector fields which preserve a transverse nowhere-integrable plane field) up to scaling and rotational Beltrami fields (nonzero fields pa...
متن کاملMultiscale Analysis for Images on Riemannian Manifolds
Abstract. In this paper we study multiscale analyses for images defined on Riemannian manifolds and extend the axiomatic approach proposed by Álvarez, Guichard, Lions, and Morel to this general case. This covers the case of twoand three-dimensional images and video sequences. After obtaining the general classification, we consider the case of morphological scale spaces, which are given in terms...
متن کامل