Morpho math

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    27-Jun-2015
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One-hour introduction to Morphological Mathematics.

Transcript of Morpho math

  • 1. Mathematical Morphology
    Christopher Chedeau
    Gauthier Lemoine
    1

2. Algorithms
Erosion & Dilation
Opening & Closing
Gradient
Hit & Miss
Thinning
Top Hat
Convolution
Reconstruction
Watershed
Min-Max Tree
Overview
2

  • Goals 3. Segmentation 4. Edge detection 5. Skeletonization 6. Image compression 7. Noise reduction 8. Feature Detection

Who
Ecole des Mines Paris
Georges Matheron
Jean Serra
Theories
Set Theory (Binary) 70s
Lattice Theory (Grayscale) 80s
Topology
3
Mathematical Morphology

  • http://cmm.ensmp.fr/~serra/pdf/birth_of_mm.pdf

http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf
Erosion & Dilation
4
9. http://www.imagemagick.org/Usage/morphology/
Structuring Elements
5
10. http://homepages.inf.ed.ac.uk/rbf/HIPR2/erode.htm
Erosion Disconnect Shapes
6
11. http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf
Opening & Closing
7
12. http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf
Gradient
8
13. http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf
Grayscale
9
14. http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf
Grayscale - Dilation
10
15. http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf
Grayscale - Operations
11
16. http://cmm.ensmp.fr/~serra/cours/pdf/fr/ch3fr.pdf
Top Hat
12
17. http://www.slideworld.org/viewslides.aspx/Introduction-to-Mathematical-Morphology-ppt-172551
Top Hat
13
18. http://www.imagemagick.org/Usage/morphology/
Hit & Miss Pattern Matching
14
19. http://www.imagemagick.org/Usage/morphology/
Structuring Elements
15
20. http://www.fmwconcepts.com/imagemagick/morphology/index.php
Thinning - Skeletonization
16
21. http://www.mmorph.com/mxmorph/html/mmdemos/mmdpotatoes.html
Skeletonization- Potatoes
17
22. http://www.esiee.fr/~coupriem/Sdi_eng/squel.html
Skeletonization 3D
18
23. http://manual.gimp.org/en/plug-in-convmatrix.html
Convolution
EmbossEdge DetectBlur
19
24. http://en.wikipedia.org/wiki/Sobel_operator
Convolution - Sobel
20
25. http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html
Reconstruction
21
26. http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html
Reconstruction - Border
22
27. http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html
Reconstruction - Grayscale
23
28. http://www.mmorph.com/mxmorph/html/mmdemos/mmdairport.html
Airport Runways
24
29. http://cmm.ensmp.fr/~beucher/wtshed.html
Watershed
25
30. http://cmm.ensmp.fr/~beucher/wtshed.html
Watershed
With Markers
26
31. http://www.mmorph.com/mxmorph/html/mmdemos/mmdcalc.html
Watershed - Calculator
27
32. http://www.nanobio.dk/assets/edge_detection.pdf
Min-Max Tree
28
33. http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf
Min-Max Tree Segmentation
29
34. http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf
Min-Max Tree Compression
30
35. Simple Algorithms
Problem Specific Input
Process Chains
31
Conclusion
36. 32
Questions?