1. Mathematical Morphology
Christopher Chedeau
Gauthier Lemoine

2. Overview Goals Algorithms Segmentation 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

3. Mathematical Morphology
Who
Ecole des Mines – Paris
Georges Matheron
Jean Serra
Theories
Set Theory (Binary) 70’s
Lattice Theory (Grayscale) 80’s
Topology

4. Erosion & Dilation

5. Structuring Elements

6. Erosion – Disconnect Shapes

7. Opening & Closing

8. Gradient

9. Grayscale

10. Grayscale - Dilation

11. Grayscale - Operations

12. Top Hat

13. Top Hat

14. Hit & Miss – Pattern Matching

15. Structuring Elements

16. Thinning - Skeletonization

17. Skeletonization - Potatoes

18. Skeletonization 3D

19. Convolution Emboss Edge Detect Blur

20. Convolution - Sobel

21. Reconstruction

22. Reconstruction - Border

23. Reconstruction - Grayscale

24. Airport Runways

25. Watershed

26. Watershed
With Markers

27. Watershed - Calculator

28. Min-Max Tree

29. Min-Max Tree Segmentation

30. Min-Max Tree Compression

31. Conclusion
Simple Algorithms
Problem Specific Input
Process Chains

32. Questions?