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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?