相关论文: H\"older Regularity of Geometric Subdivision Schem…
In this paper we define a family of nonlinear, stationary, interpolatory subdivision schemes with the capability of reproducing conic shapes including polynomials upto second order. Linear, non-stationary, subdivision schemes do also…
We link regularity and smoothness analysis of multivariate vector subdivision schemes with network flow theory and with special linear optimization problems. This connection allows us to prove the existence of what we call optimal…
We study in this paper nonlinear subdivision schemes in a multivariate setting allowing arbitrary dilation matrix. We investigate the convergence of such iterative process to some limit function. Our analysis is based on some conditions on…
In this paper, we introduce a novel non-linear uniform subdivision scheme for the generation of curves in $\mathbb{R}^n$, $n\geq2$. This scheme is distinguished by its capacity to reproduce second-degree polynomial data on non-uniform grids…
Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
In this paper, we present a new matrix approach for the analysis of subdivision schemes whose non-stationarity is due to linear dependency on parameters whose values vary in a compact set. Indeed, we show how to check the convergence in…
Subdivision schemes have become an important tool for approximation of manifold-valued functions. In this paper, we describe a construction of manifold-valued subdivision schemes for geodesically complete manifolds. Our construction is…
We develop a unified framework for nonlinear subdivision schemes on complete metric spaces (CMS). We begin with CMS preliminaries and formalize refinement in CMS, retaining key structural properties, such as locality. We prove a convergence…
We consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision…
In this paper, we study scalar multivariate non-stationary subdivision schemes with integer dilation matrix M=mI, m >=2, and present a general approach for checking their convergence and for determining their H\"older regularity. The…
In this paper we describe a general, computationally feasible strategy to deduce a family of interpolatory non-stationary subdivision schemes from a symmetric non-stationary, non-interpolatory one satisfying quite mild assumptions. To…
This paper is devoted to the presentation and the analysis of a new nonlinear subdivision scheme eliminating the Gibbs oscillations close to discontinuities. Its convergence, stability and order of approximation are analyzed. It is proved…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Convergence and normal continuity analysis of a bivariate non-stationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically…
The paper proposes, an algorithm to produce novel m-point (for any integer m>=2) binary non-stationary subdivision scheme. It has been developed using uniform trigonometric B-spline basis functions and smoothness is being analyzed using the…
This article continues the investigation started in [9] on subdivision schemes refining 2D point-normal pairs, obtained by modifying linear subdivision schemes using the circle average. While in [9] the convergence of the Modified…
Pseudo-splines form a family of subdivision schemes that provide a natural blend between interpolating schemes and approximating schemes, including the Dubuc-Deslauriers schemes and B-spline schemes. Using a generating function approach, we…
This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multi-resolution transforms. These schemes are defined as a perturbation of a linear subdivision scheme. Assuming a…
In this paper, motivated by applications in computer graphics and animation, we study the numerical methods for checking $C^k-$regularity of vector multivariate subdivision schemes with dilation 2I. These numerical methods arise from the…