Interpolatory Multiscale Representation for Functions between Manifolds
نویسنده
چکیده
We investigate interpolatory multiscale transformations for functions between manifolds which are based on interpolatory subdivision rules. We characterize the HölderZygmund smoothness of a function between manifolds in terms of the coe cient decay w.r.t. this multiscale transform.
منابع مشابه
On Convergent Interpolatory Subdivision Schemes in Riemannian Geometry
We show the convergence (for all input data) of refinement rules in Riemannian manifolds which are analogous to the linear four-point scheme and similar univariate interpolatory schemes, and which are generalized to the Riemannian setting by the so-called log/exp analogy. For this purpose we use a lemma on the Hölder regularity of limits of contractive refinement schemes in metric spaces. In co...
متن کاملSmoothness of interpolatory multivariate subdivision in Lie groups
Nonlinear subdivision schemes that operate on manifolds are of use whenever manifold valued data have to be processed in a multiscale fashion. This paper considers the case where the manifold is a Lie group and the nonlinear subdivision schemes are derived from linear interpolatory ones by the so-called log-exp analogy. The main result of the paper is that a multivariate interpolatory Lie group...
متن کاملSmoothness of interpolatory multivariate subdivision schemes in Lie groups
Nonlinear subdivision schemes that operate on manifolds are of use whenever manifold valued data have to be processed in a multiscale fashion. This paper considers the case where the manifold is a Lie group and the nonlinear subdivision schemes are derived from linear interpolatory ones by the so-called log-exp analogy. The main result of the paper is that a multivariate interpolatory Lie group...
متن کاملMultiscale Analysis of Data Sets with Diffusion Wavelets
Analysis of functions of manifolds and graphs is essential in many tasks, such as learning, classification, clustering. The construction of efficient decompositions of functions has till now been quite problematic, and restricted to few choices, such as the eigenfunctions of the Laplacian on a manifold or graph, which has found interesting applications. In this paper we propose a novel paradigm...
متن کاملMultiscale Representations for Manifold-Valued Data
We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere S2, the special orthogonal group SO(3), the positive definite matrices SPD(n), and the Grassmann manifolds G(n, k). The representations are based on the deployment of Deslauriers–Dubuc and average-interpolating pyramids “in the tangent plane” of such manifolds, using th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Math. Analysis
دوره 44 شماره
صفحات -
تاریخ انتشار 2012