Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Variational methods in image segmentation
Variational methods in image segmentation
Image processing: flows under min/max curvature and mean curvature
Graphical Models and Image Processing
Level set methods for curvature flow, image enhancement, and shape recovery in medical images
Visualization and mathematics
A Variational Method in Image Recovery
SIAM Journal on Numerical Analysis
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Filtering, Segmentation, and Depth
Filtering, Segmentation, and Depth
SIAM Journal on Scientific Computing
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Image Processing via the Beltrami Operator
ACCV '98 Proceedings of the Third Asian Conference on Computer Vision-Volume I - Volume I
Fair Triangle Mesh Generation with Discrete Elastica
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
Journal of Scientific Computing
Geometric surface processing via normal maps
ACM Transactions on Graphics (TOG)
Fourth order partial differential equations on general geometries
Journal of Computational Physics
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
A Variational Model for Capturing Illusory Contours Using Curvature
Journal of Mathematical Imaging and Vision
Segmentation with Depth: A Level Set Approach
SIAM Journal on Scientific Computing
A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
SIAM Journal on Imaging Sciences
A general framework for low level vision
IEEE Transactions on Image Processing
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
Disocclusion: a variational approach using level lines
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Noise removal using smoothed normals and surface fitting
IEEE Transactions on Image Processing
Homotopy method for a mean curvature-based denoising model
Applied Numerical Mathematics
Non-convex hybrid total variation for image denoising
Journal of Visual Communication and Image Representation
Nonlinear multigrid method for solving the anisotropic image denoising models
Numerical Algorithms
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We propose a new variational model for image denoising, which employs the $L^{1}$-norm of the mean curvature of the image surface $(x,f(x))$ of a given image $f:\Omega\rightarrow\mathbb{R}$. Besides eliminating noise and preserving edges of objects efficiently, our model can keep corners of objects and greyscale intensity contrasts of images and also remove the staircase effect. In this paper, we analytically study the proposed model and justify why our model can preserve object corners and image contrasts. We apply the proposed model to the denoising of curves and plane images, and also compare the results with those obtained by using the classical Rudin-Osher-Fatemi model [Phys. D, 60 (1992), pp. 259-268].