Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
Journal of Mathematical Imaging and Vision
Connectivity on complete lattices: new results
Computer Vision and Image Understanding
Mask-Based Second-Generation Connectivity and Attribute Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological mesh filtering and α-objects
Pattern Recognition Letters
New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Watershed Cuts: Minimum Spanning Forests and the Drop of Water Principle
IEEE Transactions on Pattern Analysis and Machine Intelligence
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Watershed Cuts: Thinnings, Shortest Path Forests, and Topological Watersheds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological operators for flooding, leveling and filtering images using graphs
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Milena: Write Generic Morphological Algorithms Once, Run on Many Kinds of Images
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds
Journal of Mathematical Imaging and Vision
Mathematical morphology on hypergraphs: preliminary definitions and results
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Some morphological operators on simplicial complex spaces
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Incremental algorithm for hierarchical minimum spanning forests and saliency of watershed cuts
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Mathematical morphology on hypergraphs, application to similarity and positive kernel
Computer Vision and Image Understanding
Morphological filtering on graphs
Computer Vision and Image Understanding
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We study some basic morphological operators acting on the lattice of all subgraphs of a (non-weighted) graph $\mathbb{G}$. To this end, we consider two dual adjunctions between the edge set and the vertex set of $\mathbb{G}$. This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of $\mathbb{G}$ and (ii) to extend it to subgraphs of $\mathbb{G}$. Afterward, we propose several new erosions, dilations, granulometries and alternate filters acting (i) on the subsets of the edge and vertex set of $\mathbb{G}$ and (ii) on the subgraphs of $\mathbb{G}$.