The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
Theoretical Aspects of Gray-Level Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
Journal of Mathematical Imaging and Vision
A Statistical, Nonparametric Methodology for Document Degradation Model Validation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Connectivity on complete lattices: new results
Computer Vision and Image Understanding
Journal of Mathematical Imaging and Vision
Flat Morphology on Power Lattices
Journal of Mathematical Imaging and Vision
Image filtering using morphological amoebas
Image and Vision Computing
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
Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
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
Spatially-Variant Anisotropic Morphological Filters Driven by Gradient Fields
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Spatially-Variant Morpho-Hessian Filter: Efficient Implementation and Application
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Some Morphological Operators in Graph Spaces
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Collapses and Watersheds in Pseudomanifolds
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
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
Minimum spanning tree adaptive image filtering
ICIP'09 Proceedings of the 16th IEEE international conference on 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
Composing morphological filters
IEEE Transactions on Image Processing
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
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We study some basic morphological operators acting on the lattice of all subgraphs of an arbitrary (unweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of G and (ii) to extend it to subgraphs of G. Afterward, we propose several new openings, closings, granulometries and alternate filters acting (i) on the subsets of the edge and vertex set of G and (ii) on the subgraphs of G. The proposed framework is then extended to functions that weight the vertices and edges of a graph. We illustrate with applications to binary and grayscale image denoising, for which, on the provided images, the proposed approach outperforms the usual one based on structuring elements.