Threshold Decomposition of Gray-Scale Morphology into Binary Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Threshold Superposition in Morphological Image Analysis Systems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Information Sciences: an International Journal
The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
Why mathematical morphology needs complete lattices
Signal Processing
Theoretical Aspects of Gray-Level Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
An overview of morphological filtering
Circuits, Systems, and Signal Processing - Special issue: median and morphological filters
Theoretical aspects of morphological filters by reconstruction
Signal Processing
Locality and Adjacency Stability Constraints for MorphologicalConnected Operators
Journal of Mathematical Imaging and Vision
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Mathematical morphology on complete semilattices and its applications to image processing
Fundamenta Informaticae - Special issue on mathematical morphology
Fuzzy Mathematical Models in Engineering and Management Science
Fuzzy Mathematical Models in Engineering and Management Science
Inf-Semilattice Approach to Self-Dual Morphology
Journal of Mathematical Imaging and Vision
Digital Video and HDTV Algorithms and Interfaces
Digital Video and HDTV Algorithms and Interfaces
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Idempotent and co-idempotent stack filters and min-max operators
Theoretical Computer Science
Spatio-Temporal Segmentation Using 3D Morphological Tools
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Morphology on Label Images: Flat-Type Operators and Connections
Journal of Mathematical Imaging and Vision
Multiscale Connected Operators
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Flat morphological operators on arbitrary power lattices
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Processors for generalized stack filters
IEEE Transactions on Signal Processing
Annular filters for binary images
IEEE Transactions on Image Processing
Morphological operators on the unit circle
IEEE Transactions on Image Processing
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
Geodesy on label images, and applications to video sequence processing
Journal of Visual Communication and Image Representation
On the role of complete lattices in mathematical morphology: From tool to uncertainty model
Information Sciences: an International Journal
Morphological filtering on graphs
Computer Vision and Image Understanding
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Flat morphological operators, also called stack filters, are the natural extension of increasing set operators to grey-level images. The latter are usually modeled as functions $${E\rightarrow T}$$, where T is a closed subset of $${\boldmath {\rm \bar R}}$$ (for instance, $${\boldmath {\rm {\overline{Z}}}}$$ or [a,b]).We give here a general theory of flat morphological operators for functions defined on a space E of points and taking their values in an arbitrary complete lattice V of values. Several examples of such lattices have been considered in the litterature, and we illustrate our therory with them. Our approach relies on the usual techniques of thresholding and stacking. Some of the usual properties of flat operators for numerical functions extend unconditionally to this general framework. Others do not, unless the lattice V is completely distributive.