Mathematical Morphology Christopher Chedeau Gauthier Lemoine 1 Overview

Mathematical Morphology Christopher Chedeau Gauthier Lemoine 1

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

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 3

Erosion & Dilation � http: //www 2. ifi. auf. org/personnel/Alain. Boucher/cours/traitement_images/07 -Images_binaires. pdf 4

Structuring Elements � http: //www. imagemagick. org/Usage/morphology/ 5

Erosion – Disconnect Shapes � http: //homepages. inf. ed. ac. uk/rbf/HIPR 2/erode. htm 6

Opening & Closing � http: //www 2. ifi. auf. org/personnel/Alain. Boucher/cours/traitement_images/07 -Images_binaires. pdf 7

Gradient � http: //www 2. ifi. auf. org/personnel/Alain. Boucher/cours/traitement_images/07 -Images_binaires. pdf 8

Grayscale � http: //ia 700307. us. archive. org/7/items/Lectures_on_Image_Processing/EECE 253_18_Gray. Morphology. pdf 9

Grayscale - Dilation � http: //ia 700307. us. archive. org/7/items/Lectures_on_Image_Processing/EECE 253_18_Gray. Morphology. pdf 10

Grayscale - Operations � http: //ia 700307. us. archive. org/7/items/Lectures_on_Image_Processing/EECE 253_18_Gray. Morphology. pdf 11

Top Hat � http: //cmm. ensmp. fr/~serra/cours/pdf/fr/ch 3 fr. pdf 12

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

Hit & Miss – Pattern Matching � http: //www. imagemagick. org/Usage/morphology/ 14

Structuring Elements � http: //www. imagemagick. org/Usage/morphology/ 15

Thinning - Skeletonization � http: //www. fmwconcepts. com/imagemagick/morphology/index. php 16

Skeletonization - Potatoes � http: //www. mmorph. com/mxmorph/html/mmdemos/mmdpotatoes. html 17

Skeletonization 3 D � http: //www. esiee. fr/~coupriem/Sdi_eng/squel. html 18

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

Convolution - Sobel � http: //en. wikipedia. org/wiki/Sobel_operator 20

Reconstruction � http: //www. mmorph. com/mmtutor 1. 0/html/mmtutor/mm 060 reconstruction. html 21

Reconstruction - Border � http: //www. mmorph. com/mmtutor 1. 0/html/mmtutor/mm 060 reconstruction. html 22

Reconstruction - Grayscale � http: //www. mmorph. com/mmtutor 1. 0/html/mmtutor/mm 060 reconstruction. html 23

Airport Runways � http: //www. mmorph. com/mxmorph/html/mmdemos/mmdairport. html 24

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

Watershed - Calculator � http: //www. mmorph. com/mxmorph/html/mmdemos/mmdcalc. html 26

Min-Max Tree � http: //www. nanobio. dk/assets/edge_detection. pdf 27

Min-Max Tree Segmentation � http: //gps-tsc. upc. es/imatge/pub/ps/IEEE_IP 00_Salembier_Garrido. pdf 28

Min-Max Tree Compression � http: //gps-tsc. upc. es/imatge/pub/ps/IEEE_IP 00_Salembier_Garrido. pdf 29

Conclusion � Simple Algorithms � Problem Specific Input � Process Chains 30

Questions? 31