Manifold-Valued Data in Medical Imaging Applications

DOI10.1007/978-3-030-31351-7_22OpenAlexW3014171276MaRDI QIDQ3300558

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://doi.org/10.1007/978-3-030-31351-7_22

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)

Uses Software

Camino

Cites Work

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Mumford-Shah and Potts regularization for manifold-valued data
Incremental proximal methods for large scale convex optimization
A Riemannian approach to anisotropic filtering of tensor fields
Median and related local filters for tensor-valued images
Regularizing flows for constrained matrix-valued images
Translation, scale, and deformation weighted polar active contours
Geodesic regression and the theory of least squares on Riemannian manifolds
Riemannian geometries on spaces of plane curves
Overview of the geometries of shape spaces and diffeomorphism groups
Visualization and processing of tensor fields.
A Riemannian framework for tensor computing
A Second Order Nonsmooth Variational Model for Restoring Manifold-Valued Images
A Generalized Forward-Backward Splitting
Computing Medians and Means in Hadamard Spaces
Optimal approximations by piecewise smooth functions and associated variational problems
Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces
Finite-differences discretizations of the mumford-shah functional
Active contours without edges
Persistent angular structure: new insights from diffusion magnetic resonance imaging data
Joint Segmentation and Shape Regularization With a Generalized Forward–Backward Algorithm
Total Generalized Variation for Manifold-Valued Data
Means and Averaging in the Group of Rotations
Left-Invariant Riemannian Geodesics on Spatial Transformation Groups
Total Variation Regularization for Manifold-Valued Data
Second Order Differences of Cyclic Data and Applications in Variational Denoising
Joint image reconstruction and segmentation using the Potts model
Robust Estimation of a Location Parameter

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