Geometric Subdivision and Multiscale Transforms

DOI10.1007/978-3-030-31351-7_4OpenAlexW2960329672MaRDI QIDQ3300535

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Publication date: 29 July 2020

Published in: Handbook of Variational Methods for Nonlinear Geometric Data (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.07550

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Related Items (2)

Non-uniform interpolatory subdivision schemes with improved smoothness ⋮ Shape-preserving interpolation on surfaces via variable-degree splines

Cites Work

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• Subdivision schemes for positive definite matrices
• On convergent interpolatory subdivision schemes in Riemannian geometry
• A necessary and sufficient proximity condition for smoothness equivalence of nonlinear subdivision schemes
• Stability of manifold-valued subdivision schemes and multiscale transformations
• Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces
• Subdivision schemes with general dilation in the geometric and nonlinear setting
• A unified approach to subdivision algorithms near extraordinary vertices
• Smoothing nonlinear subdivision schemes by averaging
• Manifold-valued subdivision schemes based on geodesic inductive averaging
• Interpolatory wavelets for manifold-valued data
• Smoothness equivalence properties of univariate subdivision schemes and their projection analogues
• Smoothness analysis of subdivision schemes by proximity
• Optimal a priori discretization error bounds for geodesic finite elements
• Median and related local filters for tensor-valued images
• Nonlinear subdivision schemes on irregular meshes
• Approximation order from stability for nonlinear subdivision schemes
• A 4-point interpolatory subdivision scheme for curve design
• Symmetric iterative interpolation processes
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• Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature
• Definability and stability of multiscale decompositions for manifold-valued data
• Convergence of subdivision schemes on Riemannian manifolds with nonpositive sectional curvature
• Subdivision surfaces
• Convergence and \(C^1\) analysis of subdivision schemes on manifolds by proximity
• $C^1$ Analysis of Hermite Subdivision Schemes on Manifolds
• A global approach to the refinement of manifold data
• Interpolatory Multiscale Representation for Functions between Manifolds
• Approximation order equivalence properties of manifold-valued data subdivision schemes
• On a New Proximity Condition for Manifold-Valued Subdivision Schemes
• A General Proximity Analysis of Nonlinear Subdivision Schemes
• Smoothness Equivalence Properties of General Manifold-Valued Data Subdivision Schemes
• Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity
• Subdivision schemes in geometric modelling
• Smoothness Properties of Lie Group Subdivision Schemes
• Smoothness Equivalence Properties of Manifold‐Valued Data Subdivision Schemes Based on the Projection Approach
• Smoothness equivalence properties of interpolatory Lie group subdivision schemes
• Stationary subdivision
• Riemannian center of mass and mollifier smoothing
• Convergence of refinement schemes on metric spaces
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• Smoothness of interpolatory multivariate subdivision in Lie groups
• Multiscale Representations for Manifold-Valued Data
• Stochastic Aspects of Nonlinear Refinement Schemes

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