Mumford and Shah Model and Its Applications to Image Segmentation and Image Restoration

DOI10.1007/978-1-4939-0790-8_25zbMath1331.94011OpenAlexW2135605743MaRDI QIDQ2789829

Ginmo Chung, Miyoun Jung, Tony F. Chan, Nahum Kiryati, Leah Bar, Nir Sochen, Luminita A. Vese

Publication date: 2 March 2016

Published in: Handbook of Mathematical Methods in Imaging (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4939-0790-8_25

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)

Related Items (4)

A consistent approximation of the total perimeter functional for topology optimization algorithms ⋮ A three-stage approach for segmenting degraded color images: smoothing, lifting and thresholding (SLaT) ⋮ Shape-based image reconstruction using linearized deformations ⋮ An Algorithm for Second Order Mumford--Shah Models Based on a Taylor Jet Formulation

Uses Software

• Mathematica

Cites Work

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• Nonlinear total variation based noise removal algorithms
• Image segmentation using a multilayer level-set approach
• Image deblurring in the presence of impulsive noise
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• A variational method in image segmentation: Existence and approximation results
• Free-discontinuity problems via functionals involving the \(L^1\)-norm of the gradient and their approximations
• An introduction to \(\Gamma\)-convergence
• Non-local approximation of the Mumford-Shah functional
• A new proof of regularity for two-shaded image segmentations
• A variational approach to remove outliers and impulse noise
• Implementation of an adaptive finite-element approximation of the Mumford-Shah functional
• Singular sets of minimizers for the Mumford-Shah functional
• The gradient theory of phase transitions and the minimal interface criterion
• A multiphase level set framework for image segmentation using the Mumford and Shah model
• A variational level set approach to multiphase motion
• An approximation of the Mumford--Shah energy by a family of discrete edge-preserving functionals
• Optimal segmentation of unbounded functions
• Optimal approximations by piecewise smooth functions and associated variational problems
• Nonlocal Operators with Applications to Image Processing
• Approximation of functional depending on jumps by elliptic functional via t-convergence
• Nonlocal Linear Image Regularization and Supervised Segmentation
• Convergence of an Iterative Method for Variational Deconvolution and Impulsive Noise Removal
• Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
• A Multiscale Algorithm for Image Segmentation by Variational Method
• Active contours without edges
• Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification
• Fast, robust total variation-based reconstruction of noisy, blurred images
• Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers
• Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations
• An Iterative Regularization Method for Total Variation-Based Image Restoration
• A Review of Image Denoising Algorithms, with a New One
• Image Processing and Analysis
• Robust Statistics

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