A gentle introduction to bilateral filtering and its applications
ACM SIGGRAPH 2007 courses
Edge-preserving decompositions for multi-scale tone and detail manipulation
ACM SIGGRAPH 2008 papers
Staircase effect alleviation by coupling gradient fidelity term
Image and Vision Computing
A gentle introduction to bilateral filtering and its applications
ACM SIGGRAPH 2008 classes
A Nonlinear Structure Tensor with the Diffusivity Matrix Composed of the Image Gradient
Journal of Mathematical Imaging and Vision
An Edge-Preserving Multilevel Method for Deblurring, Denoising, and Segmentation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Clustering-based denoising with locally learned dictionaries
IEEE Transactions on Image Processing
Adaptive total variation denoising based on difference curvature
Image and Vision Computing
From Local Kernel to Nonlocal Multiple-Model Image Denoising
International Journal of Computer Vision
Analysis of Non Local Image Denoising Methods
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Edge-Preserving Laplacian Pyramid
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Ramp preserving Perona-Malik model
Signal Processing
Cascadic multilevel methods for fast nonsymmetric blur- and noise-removal
Applied Numerical Mathematics
Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Hierarchical region-based representation for segmentation and filtering with depth in single images
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Morphological sharpening and denoising using a novel shock filter model
ICISP'10 Proceedings of the 4th international conference on Image and signal processing
Self-similarity-based image denoising
Communications of the ACM
Non local image denoising using image adapted neighborhoods
CIARP'10 Proceedings of the 15th Iberoamerican congress conference on Progress in pattern recognition, image analysis, computer vision, and applications
SIAM Journal on Imaging Sciences
Local Laplacian filters: edge-aware image processing with a Laplacian pyramid
ACM SIGGRAPH 2011 papers
Analysis of non-local image denoising methods
Pattern Recognition Letters
Total Variation as a Local Filter
SIAM Journal on Imaging Sciences
Adaptive guided image filtering for sharpness enhancement and noise reduction
PSIVT'11 Proceedings of the 5th Pacific Rim conference on Advances in Image and Video Technology - Volume Part I
A local variance-based bilateral filtering for artifact-free detail- and edge-preserving smoothing
PSIVT'11 Proceedings of the 5th Pacific Rim conference on Advances in Image and Video Technology - Volume Part II
Robust reconstruction of 2D curves from scattered noisy point data
Computer-Aided Design
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Many classical image denoising methods are based on a local averaging of the color, which increases the signal/noise ratio. One of the most used algorithms is the neighborhood filter by Yaroslavsky or sigma filter by Lee, also called in a variant "SUSAN" by Smith and Brady or "Bilateral filter" by Tomasi and Manduchi. These filters replace the actual value of the color at a point by an average of all values of points which are simultaneously close in space and in color. Unfortunately, these filters show a "staircase effect," that is, the creation in the image of flat regions separated by artifact boundaries. In this paper, we first explain the staircase effect by finding the subjacent partial differential equation (PDE) of the filter. We show that this ill-posed PDE is a variant of another famous image processing model, the Perona-Malik equation, which suffers the same artifacts. As we prove, a simple variant of the neighborhood filter solves the problem. We find the subjacent stable PDE of this variant. Finally, we apply the same correction to the recently introduced NL-means algorithm which had the same staircase effect, for the same reason.