Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Lattice Boltzmann Models for Anisotropic Diffusion of Images
Journal of Mathematical Imaging and Vision
Orthonormal ridgelets and linear singularities
SIAM Journal on Mathematical Analysis
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Diffusions and Confusions in Signal and Image Processing
Journal of Mathematical Imaging and Vision
New Methods of Controlled Total Variation Reduction for Digital Functions
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
On the Design of Optimal Derivative Filters for Coherence-Enhancing Diffusion Filtering
CGIV '04 Proceedings of the International Conference on Computer Graphics, Imaging and Visualization
Diffusion-Inspired Shrinkage Functions and Stability Results for Wavelet Denoising
International Journal of Computer Vision
A four-pixel scheme for singular differential equations
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space
IEEE Transactions on Image Processing
From two-dimensional nonlinear diffusion to coupled Haar wavelet shrinkage
Journal of Visual Communication and Image Representation
On the Relation between Anisotropic Diffusion and Iterated Adaptive Filtering
Proceedings of the 30th DAGM symposium on Pattern Recognition
Crossing-Preserving Coherence-Enhancing Diffusion on Invertible Orientation Scores
International Journal of Computer Vision
Nonlinear diffusion on the 2D Euclidean motion group
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
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Diffusion processes driven by anisotropic diffusion tensors are known to be well-suited for structure-preserving denoising. However, numerical implementations based on finite differences introduce unwanted blurring artifacts that deteriorate these favourable filtering properties. In this paper we introduce a novel discretisation of a fairly general class of anisotropic diffusion processes on a 2-D grid. It leads to a locally semi-analytic scheme (LSAS) that is absolutely stable, simple to implement and offers an outstanding sharpness of filtered images. By showing that this scheme can be translated into a 2-D Haar wavelet shrinkage procedure, we establish a connection between tensor-driven diffusion and anisotropic wavelet shrinkage for the first time. This result leads to coupled shrinkage rules that allow to perform highly anisotropic filtering even with the simplest wavelets.