Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
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
International Journal of Computer Vision
A Variational Method in Image Recovery
SIAM Journal on Numerical Analysis
LCIS: a boundary hierarchy for detail-preserving contrast reduction
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Gradient domain high dynamic range compression
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
A Review of Nonlinear Diffusion Filtering
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Behavioral analysis of anisotropic diffusion in image processing
IEEE Transactions on Image Processing
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Noise removal using smoothed normals and surface fitting
IEEE Transactions on Image Processing
The staircasing effect in neighborhood filters and its solution
IEEE Transactions on Image Processing
Ramp preserving Perona-Malik model
Signal Processing
Comments on "Staircase effect alleviation by coupling gradient fidelity term"
Image and Vision Computing
Image variational denoising using gradient fidelity on curvelet shrinkage
EURASIP Journal on Advances in Signal Processing - Special issue on robust processing of nonstationary signals
A coupled variational model for image denoising using a duality strategy and split Bregman
Multidimensional Systems and Signal Processing
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Image denoising with second order nonlinear PDEs often leads to an undesirable staircase effect, namely, the transformation of smooth regions into piecewise constant ones. In this paper, the similarity in gradient between the noisy images and the restored ones is described and preserved by the gradient fidelity term during the noise removal. The introduction of the Euler equation derived from the gradient fidelity term into nonlinear diffusion PDEs helps to alleviate staircase effect efficiently, while preserving sharp discontinuities in images. The gradient fidelity term is integrable in bounded variation function space, which makes our models outperform fourth order nonlinear PDE-based denoising methods in the preservation of edges and textures. In addition, the necessity of introducing spatial regularization into gradient estimation is theoretically analyzed and experimentally emphasized.