Morpho math

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One-hour introduction to Morphological Mathematics.

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Morpho math

  1. 1. Mathematical Morphology<br />Christopher Chedeau<br />Gauthier Lemoine<br />1<br />
  2. 2. Algorithms<br />Erosion & Dilation<br />Opening & Closing<br />Gradient<br />Hit & Miss<br />Thinning<br />Top Hat<br />Convolution<br />Reconstruction<br />Watershed<br />Min-Max Tree<br />Overview<br />2<br /><ul><li>Goals
  3. 3. Segmentation
  4. 4. Edge detection
  5. 5. Skeletonization
  6. 6. Image compression
  7. 7. Noise reduction
  8. 8. Feature Detection</li></li></ul><li>Who<br />Ecole des Mines – Paris<br />Georges Matheron<br />Jean Serra<br />Theories<br />Set Theory (Binary) 70’s<br />Lattice Theory (Grayscale) 80’s<br />Topology<br />3<br />Mathematical Morphology<br /><ul><li>http://cmm.ensmp.fr/~serra/pdf/birth_of_mm.pdf</li></li></ul><li>http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf<br />Erosion & Dilation<br />4<br />
  9. 9. http://www.imagemagick.org/Usage/morphology/<br />Structuring Elements<br />5<br />
  10. 10. http://homepages.inf.ed.ac.uk/rbf/HIPR2/erode.htm<br />Erosion – Disconnect Shapes<br />6<br />
  11. 11. http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf<br />Opening & Closing<br />7<br />
  12. 12. http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf<br />Gradient<br />8<br />
  13. 13. http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf<br />Grayscale<br />9<br />
  14. 14. http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf<br />Grayscale - Dilation<br />10<br />
  15. 15. http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf<br />Grayscale - Operations<br />11<br />
  16. 16. http://cmm.ensmp.fr/~serra/cours/pdf/fr/ch3fr.pdf<br />Top Hat<br />12<br />
  17. 17. http://www.slideworld.org/viewslides.aspx/Introduction-to-Mathematical-Morphology-ppt-172551<br />Top Hat<br />13<br />
  18. 18. http://www.imagemagick.org/Usage/morphology/<br />Hit & Miss – Pattern Matching<br />14<br />
  19. 19. http://www.imagemagick.org/Usage/morphology/<br />Structuring Elements<br />15<br />
  20. 20. http://www.fmwconcepts.com/imagemagick/morphology/index.php<br />Thinning - Skeletonization<br />16<br />
  21. 21. http://www.mmorph.com/mxmorph/html/mmdemos/mmdpotatoes.html<br />Skeletonization- Potatoes<br />17<br />
  22. 22. http://www.esiee.fr/~coupriem/Sdi_eng/squel.html<br />Skeletonization 3D<br />18<br />
  23. 23. http://manual.gimp.org/en/plug-in-convmatrix.html<br />Convolution<br /> Emboss Edge Detect Blur<br />19<br />
  24. 24. http://en.wikipedia.org/wiki/Sobel_operator<br />Convolution - Sobel<br />20<br />
  25. 25. http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html<br />Reconstruction<br />21<br />
  26. 26. http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html<br />Reconstruction - Border<br />22<br />
  27. 27. http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html<br />Reconstruction - Grayscale<br />23<br />
  28. 28. http://www.mmorph.com/mxmorph/html/mmdemos/mmdairport.html<br />Airport Runways<br />24<br />
  29. 29. http://cmm.ensmp.fr/~beucher/wtshed.html<br />Watershed<br />25<br />
  30. 30. http://cmm.ensmp.fr/~beucher/wtshed.html<br />Watershed<br />With Markers<br />26<br />
  31. 31. http://www.mmorph.com/mxmorph/html/mmdemos/mmdcalc.html<br />Watershed - Calculator<br />27<br />
  32. 32. http://www.nanobio.dk/assets/edge_detection.pdf<br />Min-Max Tree<br />28<br />
  33. 33. http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf<br />Min-Max Tree Segmentation<br />29<br />
  34. 34. http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf<br />Min-Max Tree Compression<br />30<br />
  35. 35. Simple Algorithms<br />Problem Specific Input<br />Process Chains<br />31<br />Conclusion<br />
  36. 36. 32<br />Questions?<br />

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