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Mathematical Morphology
Christopher ChedeauGauthier Lemoine
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Algorithms◦ Erosion & Dilation◦ Opening & Closing◦ Gradient◦ Hit & Miss◦ Thinning◦ Top Hat◦ Convolution◦ Reconstruction◦ Watershed◦ Min-Max Tree
Overview 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
Mathematical Morphology
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
Erosion & Dilation
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http://www.imagemagick.org/Usage/morphology/
Structuring Elements
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http://homepages.inf.ed.ac.uk/rbf/HIPR2/erode.htm
Erosion – Disconnect Shapes
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http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf
Opening & Closing
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http://www2.ifi.auf.org/personnel/Alain.Boucher/cours/traitement_images/07-Images_binaires.pdf
Gradient
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http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf
Grayscale
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http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf
Grayscale - Dilation
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http://ia700307.us.archive.org/7/items/Lectures_on_Image_Processing/EECE253_18_GrayMorphology.pdf
Grayscale - Operations
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http://cmm.ensmp.fr/~serra/cours/pdf/fr/ch3fr.pdf
Top Hat
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http://www.slideworld.org/viewslides.aspx/Introduction-to-Mathematical-Morphology-ppt-172551
Top Hat
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http://www.imagemagick.org/Usage/morphology/
Hit & Miss – Pattern Matching
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http://www.imagemagick.org/Usage/morphology/
Structuring Elements
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http://www.fmwconcepts.com/imagemagick/morphology/index.php
Thinning - Skeletonization
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http://www.mmorph.com/mxmorph/html/mmdemos/mmdpotatoes.html
Skeletonization - Potatoes
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http://www.esiee.fr/~coupriem/Sdi_eng/squel.html
Skeletonization 3D
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http://manual.gimp.org/en/plug-in-convmatrix.html
Convolution Emboss Edge Detect Blur
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http://en.wikipedia.org/wiki/Sobel_operator
Convolution - Sobel
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http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html
Reconstruction
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http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html
Reconstruction - Border
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http://www.mmorph.com/mmtutor1.0/html/mmtutor/mm060reconstruction.html
Reconstruction - Grayscale
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http://www.mmorph.com/mxmorph/html/mmdemos/mmdairport.html
Airport Runways
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http://cmm.ensmp.fr/~beucher/wtshed.html
Watershed
With Markers
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http://www.mmorph.com/mxmorph/html/mmdemos/mmdcalc.html
Watershed - Calculator
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http://www.nanobio.dk/assets/edge_detection.pdf
Min-Max Tree
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http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf
Min-Max Tree Segmentation
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http://gps-tsc.upc.es/imatge/pub/ps/IEEE_IP00_Salembier_Garrido.pdf
Min-Max Tree Compression
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Simple Algorithms Problem Specific Input Process Chains
Conclusion
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Questions?
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