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
Markov random field modeling in computer vision
Markov random field modeling in computer vision
A Variational Method in Image Recovery
SIAM Journal on Numerical Analysis
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
SIAM Journal on Numerical Analysis
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Variational Methods in Imaging
Variational Methods in Imaging
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Total Variation Regularization for Image Denoising, II. Examples
SIAM Journal on Imaging Sciences
Total Variation Regularization for Image Denoising, III. Examples.
SIAM Journal on Imaging Sciences
Fast cartoon + texture image filters
IEEE Transactions on Image Processing
Multiscale Texture Extraction with Hierarchical (BV,Gp,L2) Decomposition
Journal of Mathematical Imaging and Vision
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A novel approach for multiscale image processing based on integro-differential equations (IDEs) was proposed in [E. Tadmor and P. Athavale, Inverse Probl. Imaging, 3 (2009), pp. 693-710]. These IDEs, which stem naturally from multiscale $(BV,L^2)$ hierarchical decompositions, yield inverse scale representations of images in the sense that the $BV$-dual norms of their residuals are inversely proportional to the scaling parameters. Motivated by the fact that $(BV,L^1)$ decomposition is more suitable for extracting local scale-space features than $(BV,L^2)$, we introduce here the IDEs which arise from multiscale $(BV,L^1)$ hierarchical decompositions. We study several variants of this $(BV,L^1)$-based IDE model, depending on modifications to the curvature term.