Mathematical Morphology

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Christopher Chedeau Gauthier Lemoine 1

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

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

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 http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf 4

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 http://www.imagemagick.org/Usage/morphology/ 5

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 http://homepages.inf.ed.ac.uk/rbf/HIPR2/erode.htm 6

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 http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf 7

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

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

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 http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf 10

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 http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf 11

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 http://cmm.ensmp.fr/~serra/cours/pdf/fr/ch3fr.pdf 12

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

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 http://www.imagemagick.org/Usage/morphology/ 14

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 http://www.imagemagick.org/Usage/morphology/ 15

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 http://www.fmwconcepts.com/imagemagick/morphology/index.php 16

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 http://www.mmorph.com/mxmorph/html/mmdemos/mmdpotatoes.html 17

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 http://www.esiee.fr/~coupriem/Sdi_eng/squel.html 18

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

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 http://en.wikipedia.org/wiki/Sobel_operator 20

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

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 http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html 22

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 http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html 23

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 http://www.mmorph.com/mxmorph/html/mmdemos/mmdairport.html 24

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

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 http://www.mmorph.com/mxmorph/html/mmdemos/mmdcalc.html 26

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 http://www.nanobio.dk/assets/edge_detection.pdf 27

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 http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf 28

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 http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf 29