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Mathematical Morphology

Mathematical Morphology. Christopher Chedeau Gauthier Lemoine. Overview. Goals Segmentation Edge detection Skeletonization Image compression Noise reduction Feature Detection. Algorithms Erosion & Dilation Opening & Closing Gradient Hit & Miss Thinning Top Hat Convolution

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Mathematical Morphology

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  1. Mathematical Morphology Christopher Chedeau Gauthier Lemoine

  2. Overview • Goals • Segmentation • Edge detection • Skeletonization • Image compression • Noise reduction • Feature Detection • Algorithms • Erosion & Dilation • Opening & Closing • Gradient • Hit & Miss • Thinning • Top Hat • Convolution • Reconstruction • Watershed • Min-Max Tree

  3. Mathematical Morphology • Who • Ecole des Mines – Paris • Georges Matheron • Jean Serra • Theories • Set Theory (Binary) 70’s • Lattice Theory (Grayscale) 80’s • Topology • http://cmm.ensmp.fr/~serra/pdf/birth_of_mm.pdf

  4. Erosion & Dilation • http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf

  5. Structuring Elements • http://www.imagemagick.org/Usage/morphology/

  6. Erosion – Disconnect Shapes • http://homepages.inf.ed.ac.uk/rbf/HIPR2/erode.htm

  7. Opening & Closing • http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf

  8. Gradient • http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf

  9. Grayscale • http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf

  10. Grayscale - Dilation • http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf

  11. Grayscale - Operations • http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf

  12. Top Hat • http://cmm.ensmp.fr/~serra/cours/pdf/fr/ch3fr.pdf

  13. Top Hat • http://www.slideworld.org/viewslides.aspx/Introduction-to-Mathematical-Morphology-ppt-172551

  14. Hit & Miss – Pattern Matching • http://www.imagemagick.org/Usage/morphology/

  15. Structuring Elements • http://www.imagemagick.org/Usage/morphology/

  16. Thinning - Skeletonization • http://www.fmwconcepts.com/imagemagick/morphology/index.php

  17. Skeletonization- Potatoes • http://www.mmorph.com/mxmorph/html/mmdemos/mmdpotatoes.html

  18. Skeletonization 3D • http://www.esiee.fr/~coupriem/Sdi_eng/squel.html

  19. Convolution • http://manual.gimp.org/en/plug-in-convmatrix.html Emboss Edge Detect Blur

  20. Convolution - Sobel • http://en.wikipedia.org/wiki/Sobel_operator

  21. Reconstruction • http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html

  22. Reconstruction - Border • http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html

  23. Reconstruction - Grayscale • http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html

  24. Airport Runways • http://www.mmorph.com/mxmorph/html/mmdemos/mmdairport.html

  25. Watershed • http://cmm.ensmp.fr/~beucher/wtshed.html With Markers

  26. Watershed - Calculator • http://www.mmorph.com/mxmorph/html/mmdemos/mmdcalc.html

  27. Min-Max Tree • http://www.nanobio.dk/assets/edge_detection.pdf

  28. Min-Max Tree Segmentation • http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf

  29. Min-Max Tree Compression • http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf

  30. Conclusion • Simple Algorithms • Problem Specific Input • Process Chains

  31. Questions?

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