Euler's Elastica and Curvature-Based Inpainting
From MaRDI portal
Publication:4785616
DOI10.1137/S0036139901390088zbMath1028.68185WikidataQ57397353 ScholiaQ57397353MaRDI QIDQ4785616
Sung Ha Kang, Jianhong Shen, Tony F. Chan
Publication date: 5 January 2003
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
transportdiffusioncurvaturebounded variationvariational methodelasticaimage restorationBayesianinpaintingnumerical PDEprior modelsvariational inpainting
Numerical optimization and variational techniques (65K10) Computing methodologies for image processing (68U10) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)
Related Items
A Cahn-Hilliard system with a fidelity term for color image inpainting ⋮ Mapping-based image diffusion ⋮ Nonlocal PDEs on graphs: from tug-of-war games to unified interpolation on images and point clouds ⋮ Coefficient identification in PDEs applied to image inpainting ⋮ Analysis of artifacts in shell-based image inpainting: why they occur and how to eliminate them ⋮ Generation of tubular and membranous shape textures with curvature functionals ⋮ Wavelet inpainting with the \(\ell_{0}\) sparse regularization ⋮ A second-order TV-type approach for inpainting and denoising higher dimensional combined cyclic and vector space data ⋮ The jump set under geometric regularisation. II: Higher-order approaches ⋮ Local block operators and TV regularization based image inpainting ⋮ A curvature-driven image inpainting approach for high-density impulse noise removal ⋮ Geodesic path based digital inpainting ⋮ Error analysis for image inpainting ⋮ A variational model for capturing illusory contours using curvature ⋮ Spatially adapted first and second order regularization for image reconstruction: from an image surface perspective ⋮ Total variation wavelet inpainting ⋮ A variational aggregation framework for patch-based optical flow estimation ⋮ A finite element method for surface restoration with smooth boundary conditions ⋮ Energetic variational approaches in modeling vesicle and fluid interactions ⋮ The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem ⋮ Simultaneously inpainting in image and transformed domains ⋮ A variational method for Abel inversion tomography with mixed Poisson-Laplace-Gaussian noise ⋮ Image structure-preserving denoising based on difference curvature driven fractional nonlinear diffusion ⋮ A numerical study of a mean curvature denoising model using a novel augmented Lagrangian method ⋮ On a variational theory of image amodal completion ⋮ The \(L^1\) gradient flow of a generalized scale invariant Willmore energy for radially non-increasing functions ⋮ ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing ⋮ Image segmentation using Euler's elastica as the regularization ⋮ A linear framework for region-based image segmentation and inpainting involving curvature penalization ⋮ Retinex by higher order total variation \(L^1\) decomposition ⋮ Regularization of discrete contour by Willmore energy ⋮ Illusory shapes via first-order phase transition and approximation ⋮ Partial differential equations for zooming, deinterlacing and dejittering ⋮ Orientation-matching minimization for image denoising and inpainting ⋮ A variational framework for exemplar-based image inpainting ⋮ A well-posedness framework for inpainting based on coherence transport ⋮ Euler's elastica-based algorithm for parallel MRI reconstruction using sensitivity encoding ⋮ Wavelet frame based blind image inpainting ⋮ Global minimum for a Finsler elastica minimal path approach ⋮ Total roto-translational variation ⋮ Augmented Lagrangian method for generalized TV-Stokes model ⋮ Speckle noise removal by energy models with new regularization setting ⋮ Existence of generalized minimizers and dual solutions for a class of variational problems with linear growth related to image recovery ⋮ Image segmentation with depth information via simplified variational level set formulation ⋮ A two-stage method for spectral-spatial classification of hyperspectral images ⋮ Two-level method for the total fractional-order variation model in image deblurring problem ⋮ Split-Bregman iteration for framelet based image inpainting ⋮ Image inpainting with energies of linear growth. A collection of proposals ⋮ Self-contact of a flexible loop under uniform hydrostatic pressure ⋮ High-order anisotropic diffusion operators in spaces of variable exponents and application to image inpainting and restoration problems ⋮ Fast algorithm for color texture image inpainting using the non-local CTV model ⋮ Large region inpainting by re-weighted regularized methods ⋮ Fast image inpainting strategy based on the space-fractional modified Cahn-Hilliard equations ⋮ Augmented Lagrangian method for an Euler's elastica based segmentation model that promotes convex contours ⋮ Boundary value problems for Euler-Bernoulli planar elastica. A solution construction procedure ⋮ Denoising and inpainting of images using TV-type energies: theoretical and computational aspects ⋮ Nonlocal elastica model for sparse reconstruction ⋮ Bilevel parameter learning for higher-order total variation regularisation models ⋮ A two-step mixed inpainting method with curvature-based anisotropy and spatial adaptivity ⋮ A framelet-based image inpainting algorithm ⋮ Convex relaxation of a class of vertex penalizing functionals ⋮ Analysis of inpainting via clustered sparsity and microlocal analysis ⋮ A combined first and second order variational approach for image reconstruction ⋮ Association fields via cuspless sub-Riemannian geodesics in SE(2) ⋮ Asymptotic solution of a singularly perturbed optimal control problem related to the reconstruction of a defective curve ⋮ An approximate sparsity model for inpainting ⋮ Analysis of a hyperbolic-parabolic type system for image inpainting ⋮ Discrete variational calculus for B-spline curves ⋮ Total variation with nonlocal FT-Laplacian for patch-based inpainting ⋮ Free gradient discontinuity and image inpainting ⋮ On some perturbations of the total variation image inpainting method. I: Regularity theory ⋮ Approximation of frame based missing data recovery ⋮ On the foundations of vision modeling. III: Noncommutative monoids of occlusive preimages ⋮ Sharp-interface limit of the Allen-Cahn action functional in one space dimension ⋮ On the existence of weak solutions for a curvature driven elliptic system applied to image inpainting ⋮ An elastica-driven digital curve evolution model for image segmentation ⋮ Image reconstruction by minimizing curvatures on image surface ⋮ $C^{1,\alpha }$-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting ⋮ A New Algorithm Framework for Image Inpainting in Transform Domain ⋮ Image inpainting using reproducing kernel Hilbert space and Heaviside functions ⋮ On some perturbations of the total variation image inpainting method. III: Minimization among sets with finite perimeter ⋮ Highly corrupted image inpainting through hypoelliptic diffusion ⋮ Exact solutions for the total variation denoising problem of piecewise constant images in dimension one ⋮ Fast image inpainting based on coherence transport ⋮ Poisson image denoising based on fractional-order total variation ⋮ Nonlocal patches based Gaussian mixture model for image inpainting ⋮ A novel image inpainting technique based on median diffusion ⋮ Color image restoration and inpainting via multi-channel total curvature ⋮ An anisotropic PDE model for image inpainting ⋮ The critical points of the elastic energy among curves pinned at endpoints ⋮ Image segmentation using the Cahn-Hilliard equation ⋮ Image multiplicative denoising using adaptive Euler's elastica as the regularization ⋮ Field of particle filters for image inpainting ⋮ A linear fourth-order PDE-based gray-scale image inpainting model ⋮ Wavelet inpainting by fractional order total variation ⋮ Analysis of iterative methods for solving a Ginzburg-Landau equation ⋮ Fast iterative algorithms for solving the minimization of curvature-related functionals in surface fairing ⋮ Combined first and second order variational approaches for image processing ⋮ The Cauchy problem for a nonlinear elliptic equation: Nash-game approach and application to image inpainting ⋮ On some perturbations of the total variation image inpainting method. II: Relaxation and dual variational formulation ⋮ An Optimized Dynamic Mode Decomposition Model Robust to Multiplicative Noise ⋮ Partial differential equation transform-Variational formulation and Fourier analysis ⋮ Analysis and Application of a Nonlocal Hessian ⋮ A Fractional Inpainting Model Based on the Vector-Valued Cahn--Hilliard Equation ⋮ A Total Fractional-Order Variation Model for Image Restoration with Nonhomogeneous Boundary Conditions and Its Numerical Solution ⋮ Existence, regularity and structure of confined elasticae ⋮ A Fast Relaxed Normal Two Split Method and an Effective Weighted TV Approach for Euler's Elastica Image Inpainting ⋮ The pre-image problem for Laplacian Eigenmaps utilizing L 1 regularization with applications to data fusion ⋮ A Nested Variational Time Discretization for Parametric Anisotropic Willmore Flow ⋮ Cuspless Sub-Riemannian Geodesics within the Euclidean Motion Group SE(d) ⋮ Applications of PDEs inpainting to magnetic particle imaging and corneal topography ⋮ Image inpainting using non-convex low rank decomposition and multidirectional search ⋮ Piecewise constant reconstruction of damaged color images ⋮ Minimizing acceleration on the group of diffeomorphisms and its relaxation ⋮ A Ginzburg-Landau-\({H}^{-1}\) model and its SAV algorithm for image inpainting ⋮ A denoising model based on the fractional Beltrami regularization and its numerical solution ⋮ Multi-component separation, inpainting and denoising with recovery guarantees ⋮ A New Operator Splitting Method for the Euler Elastica Model for Image Smoothing ⋮ A Fast Minimization Algorithm for the Euler Elastica Model Based on a Bilinear Decomposition ⋮ An Obstacle Problem for Elastic Graphs ⋮ Nonlocal Cahn-Hilliard type model for image inpainting ⋮ Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion ⋮ Numerical analysis of elastica with obstacle and adhesion effects ⋮ Curvature Regularized Surface Reconstruction from Point Clouds ⋮ A Nonlocal Feature-Driven Exemplar-Based Approach for Image Inpainting ⋮ CURE: Curvature Regularization for Missing Data Recovery ⋮ Alternating Direction Method of Multiplier for Euler’s Elastica-Based Denoising ⋮ Convex Lifting-Type Methods for Curvature Regularization ⋮ Shape programming of a magnetic elastica ⋮ A Complex Version of the Cahn--Hilliard Equation for Grayscale Image Inpainting ⋮ Parameter Estimation in Image Processing and Computer Vision ⋮ Partial Differential Equations for Interpolation and Compression of Surfaces ⋮ Fast numerical schemes related to curvature minimization: a brief and elementary review ⋮ Weak solutions of a parabolic-elliptic type system for image inpainting ⋮ Guidefill: GPU Accelerated, Artist Guided Geometric Inpainting for 3D Conversion of Film ⋮ A Nonlocal Image Inpainting Problem Using the Linear Allen–Cahn Equation ⋮ A multiscale fourth‐order model for the image inpainting and low‐dimensional sets recovery ⋮ Locally Parallel Textures Modeling with Adapted Hilbert Spaces ⋮ Cahn--Hilliard Inpainting with the Double Obstacle Potential ⋮ Variational Image Regularization with Euler's Elastica Using a Discrete Gradient Scheme ⋮ Three-Dimensional Volume Reconstruction Using Two-Dimensional Parallel Slices ⋮ A Penalty Relaxation Method for Image Processing Using Euler's Elastica Model ⋮ A Color Elastica Model for Vector-Valued Image Regularization ⋮ Sparse Inpainting with Smoothed Particle Hydrodynamics ⋮ F-Transform Representation of Nonlocal Operators with Applications to Image Restoration ⋮ The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising ⋮ Nonconvex Total Generalized Variation Model for Image Inpainting ⋮ Nonlocal Difference Operators on Graphs for Interpolation on Point Clouds