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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

Mathematical Morphology

Christopher Chedeau

Gauthier Lemoine

overview
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
mathematical morphology1
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
erosion dilation
Erosion & Dilation
  • http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf
structuring elements
Structuring Elements
  • http://www.imagemagick.org/Usage/morphology/
erosion disconnect shapes
Erosion – Disconnect Shapes
  • http://homepages.inf.ed.ac.uk/rbf/HIPR2/erode.htm
opening closing
Opening & Closing
  • http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf
gradient
Gradient
  • http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf
grayscale
Grayscale
  • http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf
grayscale dilation
Grayscale - Dilation
  • http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf
grayscale operations
Grayscale - Operations
  • http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf
top hat
Top Hat
  • http://cmm.ensmp.fr/~serra/cours/pdf/fr/ch3fr.pdf
top hat1
Top Hat
  • http://www.slideworld.org/viewslides.aspx/Introduction-to-Mathematical-Morphology-ppt-172551
hit miss pattern matching
Hit & Miss – Pattern Matching
  • http://www.imagemagick.org/Usage/morphology/
structuring elements1
Structuring Elements
  • http://www.imagemagick.org/Usage/morphology/
thinning skeletonization
Thinning - Skeletonization
  • http://www.fmwconcepts.com/imagemagick/morphology/index.php
skeletonization potatoes
Skeletonization- Potatoes
  • http://www.mmorph.com/mxmorph/html/mmdemos/mmdpotatoes.html
skeletonization 3d
Skeletonization 3D
  • http://www.esiee.fr/~coupriem/Sdi_eng/squel.html
convolution
Convolution
  • http://manual.gimp.org/en/plug-in-convmatrix.html

Emboss Edge Detect Blur

convolution sobel
Convolution - Sobel
  • http://en.wikipedia.org/wiki/Sobel_operator
reconstruction
Reconstruction
  • http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html
reconstruction border
Reconstruction - Border
  • http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html
reconstruction grayscale
Reconstruction - Grayscale
  • http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html
airport runways
Airport Runways
  • http://www.mmorph.com/mxmorph/html/mmdemos/mmdairport.html
watershed
Watershed
  • http://cmm.ensmp.fr/~beucher/wtshed.html
watershed1
Watershed
  • http://cmm.ensmp.fr/~beucher/wtshed.html

With Markers

watershed calculator
Watershed - Calculator
  • http://www.mmorph.com/mxmorph/html/mmdemos/mmdcalc.html
min max tree
Min-Max Tree
  • http://www.nanobio.dk/assets/edge_detection.pdf
min max tree segmentation
Min-Max Tree Segmentation
  • http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf
min max tree compression
Min-Max Tree Compression
  • http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf
conclusion
Conclusion
  • Simple Algorithms
  • Problem Specific Input
  • Process Chains