Morphological filtering on graphs

@article{Cousty2013MorphologicalFO,
  title={Morphological filtering on graphs},
  author={Jean Cousty and Laurent Najman and Fabio Dias and Jean Paul Fr{\'e}d{\'e}ric Serra},
  journal={Computer Vision and Image Understanding},
  year={2013},
  volume={117},
  pages={370-385}
}
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… CONTINUE READING

Citations

Publications citing this paper.
Showing 1-10 of 27 extracted citations

A bi-intuitionistic modal logic: Foundations and automation

J. Log. Algebr. Meth. Program. • 2016
View 6 Excerpts
Highly Influenced

A study of morphological filtering using graph and hypergraphs

2015 IEEE International Advance Computing Conference (IACC) • 2015
View 7 Excerpts
Highly Influenced

A Preprocessing Method for Flutter Signals Based on Morphological Filtering

2018 9th International Conference on Mechanical and Aerospace Engineering (ICMAE) • 2018
View 1 Excerpt

References

Publications referenced by this paper.
Showing 1-10 of 34 references

Micro-viscous morphological operators

F. Meyer, J. Angulo
in: Mathematical Morphology and its Application to Signal and Image Processing • 2007
View 5 Excerpts
Highly Influenced

Algebraic foundations of morphology

C. Ronse, J. Serra
in: Mathematical Morphology: From Theory to Applications, ISTE / J. Wiley & Sons • 2010
View 4 Excerpts
Highly Influenced

Graphs and mathematical morphology

L. Vincent
Signal Processing 16 • 1989
View 4 Excerpts
Highly Influenced

Historical overview of image analysis and mathematical morphology

Pattern Recognition and Image Analysis • 2011
View 3 Excerpts

On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds

Journal of Mathematical Imaging and Vision • 2011
View 1 Excerpt

Watershed Cuts: Thinnings, Shortest Path Forests, and Topological Watersheds

IEEE Transactions on Pattern Analysis and Machine Intelligence • 2010
View 1 Excerpt

Similar Papers

Loading similar papers…