A nonlinear laplace operator as edge detector in noisy images
Computer Vision, Graphics, and Image Processing
Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
An overview of morphological filtering
Circuits, Systems, and Signal Processing - Special issue: median and morphological filters
Signal and image restoration using shock filters and anisotropic diffusion
SIAM Journal on Numerical Analysis
Local Scale Control for Edge Detection and Blur Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Adjunctions in Pyramids, Curve Evolution and Scale-Spaces
International Journal of Computer Vision
Regularized Shock Filters and Complex Diffusion
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Adaptive fuzzy switching filter for images corrupted by impulse noise
Pattern Recognition Letters
Lattice Image Processing: A Unification of Morphological and Fuzzy Algebraic Systems
Journal of Mathematical Imaging and Vision
Digital Image Processing (3rd Edition)
Digital Image Processing (3rd Edition)
Theoretical foundations for spatially discrete 1-D shock filtering
Image and Vision Computing
Constrained Connectivity for Hierarchical Image Decomposition and Simplification
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Constrained Connectivity and Transition Regions
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Beyond self-duality in morphological image analysis
Image and Vision Computing
Journal of Visual Communication and Image Representation
Adaptivity and group invariance in mathematical morphology
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
IEEE Transactions on Image Processing
Constrained connectivity for the processing of very-high-resolution satellite images
International Journal of Remote Sensing - Spatial Information Retrieval, Analysis, Reasoning and Modelling
Preventing chaining through transitions while favouring it within homogeneous regions
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Image enhancement and denoising by complex diffusion processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Composing morphological filters
IEEE Transactions on Image Processing
Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization
IEEE Transactions on Image Processing
Kernel Regression for Image Processing and Reconstruction
IEEE Transactions on Image Processing
The iDUDE Framework for Grayscale Image Denoising
IEEE Transactions on Image Processing
Adaptive median filters: new algorithms and results
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
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We study a class of mathematical morphology filters to operate conditionally according to a set of pixels marked by a binary mask. The main contribution of this paper is to provide a general framework for several applications including edge enhancement and image denoising, when it is affected by salt-and-pepper noise. We achieve this goal by revisiting shock filters based on erosions and dilations and extending their definition to take into account the prior definition of a mask of pixels that should not be altered. New definitions for conditional erosions and dilations leading to the concept of conditional toggle mapping. We also investigate algebraic properties as well as the convergence of the associate shock filter. Experiments show how the selection of appropriate methods to generate the masks lead to either edge enhancement or salt-and-pepper denoising. A quantitative evaluation of the results demonstrates the effectiveness of the proposed methods. Additionally, we analyse the application of conditional toggle mapping in remote sensing as pre-filtering for hierarchical segmentation.