Mathematical Morphology a non exhaustive overview. Adrien Bousseau

Transcription

1 a non exhaustive overview Adrien Bousseau

2 Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies [Haralick87] 2

3 Overview Basic morphological operators More complex operations Conclusion and References 3

4 Overview Basic morphological operators Binary Grayscale Color Structuring element More complex operations Conclusion and References 4

5 Basic operators: binary Dilation, erosion by a structuring element 5

6 Basic operators: binary Opening : remove capes, isthmus and islands smaller than the structuring element 6

7 Basic operators: binary Closing : fill gulfs, channels and lakes smaller than the structuring element 7

8 Basic operators: binary Sequencial filter: open-close or close-open 8

9 Overview Basic morphological operators Binary Grayscale Color Structuring element More complex operations Conclusion and References 9

10 Basic operator: grayscale Dilation : max over the structuring element 10

11 Basic operator: grayscale Erosion : min over the structuring element 11

12 Basic operator: grayscale Opening : remove light features smaller than the structuring element 12

13 Basic operator: grayscale Closing : remove dark features smaller than the structuring element 13

14 Basic operator: grayscale Sequential filter (open-close or close-open): remove both light and dark features 14

15 Overview Basic morphological operators Binary Grayscale Color Structuring element More complex operations Conclusion and References 15

16 Color images Process each channel separately: color ghosting with basic operators 16

17 Color images Process each channel separately: color ghosting unnoticeable with sequential operators opening 17

18 Color images Several ordering strategy 18

19 Overview Basic morphological operators Binary Grayscale Color Structuring element More complex operations Conclusion and References 19

20 Structuring element Usually, flat element (binary) Grayscale element: fuzzy morphology 20

21 Structuring element Shape has an impact! 21

22 Structuring element Choose the structuring element according to the image structure 22

23 Structuring element Choose the structuring element according to the image structure 23

24 Overview Basic morphological operators More complex operations Reconstruction operators Top hat, sharpening, distance, thinning, segmentation... Conclusion and References 24

25 Reconstruction operators Remove features smaller than the structuring element, without altering the shape Reconstruct connected components from the preserved features 25

26 Reconstruction operators: binary Opening by reconstruction: Erosion: f'(0) = f Iterative reconstruction: f'(t+1) = min( f'(t),i) until stability 26

27 Reconstruction operators: binary Closing by reconstruction: Dilation: f'(0) = f Iterative reconstruction: f'(t+1) = max( f'(t),i) until stability 27

28 Reconstruction operators: grayscale Opening by reconstruction: remove unconnected light features 28

29 Reconstruction operators: grayscale Closing by reconstruction: remove unconnected dark features 29

30 Reconstruction operators: grayscale Sequential filter by reconstruction: open-close 30

31 Overview Basic morphological operators More complex operations Reconstruction operators Top hat, sharpening, distance, thinning, segmentation... Conclusion and References 31

32 Top Hat White top-hat: f-opening(f) Extract light features 32

33 Top Hat Black top-hat: closing(f)-f Extract dark features 33

34 Edge sharpening Toggle mapping f f f ( f+ f)/2 34

35 Edge sharpening Toggle mapping 35

36 Distance function Distance from binary elements 36

37 Thinning Binary (or grayscale?) skeleton 37

38 Segmentation Watershed: Image = heightfield Flood the image from its minima Lake junctions give the segmentation 38

39 Segmentation Watershed: hierarchical results 39

40 Overview Basic morphological operators More complex operations Conclusion and References 40

41 Conclusion Powerful toolbox for many image analysis tasks Not famous because not useful? Not used because not famous? Based on a whole mathematical theory But can be very practical (maybe too much?) French! 41

42 References Pierre Soille, 2003: Morphological Image Analysis, Principles and Applications. (Practical approach) Jean Serra and Luc Vincent, 1992: An Overview of Morphological Filtering. (Mathematical approach) 42