1. Application 2 Detect Filarial Worms SourceBTTRemove NoisesThreshold Skeleton Eliminate short structures ReconstructionFinal result

2. Ultimate Erosion Ultimate Erosion (UE) is based on Recursive Erosion operation. Ultimate Erosion (UE) is based on Recursive Erosion operation. “Keep aside each connected components just before it is removed throughout the recursive erosion process”. “Keep aside each connected components just before it is removed throughout the recursive erosion process”.

3. Geodesic Influence Geodesic Influence (GI) is based on Recursive Dilation operation with mask which also called conditional dilation. Geodesic Influence (GI) is based on Recursive Dilation operation with mask which also called conditional dilation. Reconstruct the seeds by the restriction of the mask, and distribute the pixels on the interface by means of “first come first serve”. Reconstruct the seeds by the restriction of the mask, and distribute the pixels on the interface by means of “first come first serve”.

4. UE and GI UE: split a connected region (have to be convex) gradually and record the iteration number. UE: split a connected region (have to be convex) gradually and record the iteration number. GI: Reconstruct the split regions and get the segments. GI: Reconstruct the split regions and get the segments.

5. Application Segment connected organs: Segment connected organs: 1.RE: region shrinking to generate all the candidate seeds 2.GI: region reconstruction to recover separated organs

7. Figure 4.22: Region filling: (a) boundary of an object; (b) complement of the boundary; (c) structuring element(d) initial point inside the boundary; (e)-(h) various steps of the algorithm; (i) final result, obtained by forming the set union of (a) and (h).

8. A grey-level image may be seen as a topographic relief,topographic where the grey level of a pixel is interpreted as its altitude in the relief. A drop of water falling on a topographic relief flows along a path to finally reach a local minimum. Intuitively, the watershed of a relief correspond to the limits of the adjacent catchment basins of the drops of water. Watershed transform Watershed of the gradient Watershed of the gradient (relief) Relief of the gradient Gradient image Cardiac MRI image

11. GENERAL DEFINITION 11 A drainage basin or watershed is an extent or an area of land where surface water from rain melting snow or ice converges to a single point at a lower elevation, usually the exit of the basin, where the waters join another waterbody, such as a river, lake, wetland, sea, or ocean

12. INTRODUCTION 12  The watershed concept was first applied by Beucher and Lantuejoul at 1979, they used it to segment images of bubbles and SEM metallographic pictures  The Watershed transformation is a powerful tool for image segmentation, it uses the region-based approach and searches for pixel and region similarities.

13. IMAGE REPRESENTATION 13

14. REMINDER-IMAGE GRADIENT 14 An image gradient is a directional change in the intensity or color in an image. Image gradients may be used to extract information from images.

15. IMAGE GRADIENT 15 an intensity image a gradient image in the x direction measuring horizontal change in intensity a gradient image in the y direction measuring vertical change in intensity

16. IMAGE GRADIENT 16

17. GEODESIC DISTANCE 17

18. GEODESIC ZONE OF INFLUENCE 18

19. GEODESIC SKELETON BY ZONES OF INFLUENCE 19

20. MINIMA AND MAXIMA 20

21. MINIMA AND MAXIMA 21

22. 22 ASCENDING PATH

23. 23 NON-ASCENDING PATH

24. THE WATERSHED TRANSFORMATION 24

25. 25 THE WATERSHED TRANSFORMATIO N

26. 26  http://cmm.ensmp.fr/~beucher/lpe1.gif http://cmm.ensmp.fr/~beucher/lpe1.gif THE WATERSHED TRANSFORMATIO N

27. BUILDING THE WATERSHED 27

28. BUILDING THE WATERSHED 28

29. BUILDING THE WATERSHED 29  Visual illustration Visual illustration

39. Skeletonization

40. Skeleton by distance transforms Maxima of distance transform

48. Distance Transform

49. Skeleton Reconstruction: the original object can be reconstructed by given knowledge of the skeleton subsets S i (F), the SE K, and i : Examples of skeleton:

59. The Distance Transform on Curved Space (DTOCS)

61. Distance Transform on Curved Space (DTOCS) Calculates minimal distances between 2 points along a curved surface Calculates minimal distances between areas and areas/points on curved surface Uses a 3x3 calculation kernel with different metrics: Chessboard City block Is a gray-level extension to the Rosenfeldt-Pfaltz-Lay algorithm (which calculates a distance transform for binary images) Presented by Toivanen and Vepsäläinen in 1991 and 1993. Applications: Texture feature extraction and classification (e.g. paper roughness) (Kuparinen and Toivanen 2006, 2007) Shortest distance calculations (Ikonen and Toivanen 2006) Image compression

62. Weighted Distance Transform on Curved Space (WDTOCS) Calculates minimal distances between 2 points along a curved surface Calculates minimal distances between areas and areas/points on curved surface Uses a 3x3 calculation kernel with different metrics: Chessboard City block Measures the differences between adjacent pixels by their Euclidean distance + (1 or 1,4 for the xy-surface displacement) Presented by Toivanen and Vepsäläinen in 1991 and 1993. Applications: Texture feature extraction and classification (e.g. paper roughness) (Kuparinen and Toivanen 2006, 2007) Shortest distance calculations (Ikonen and Toivanen 2006) Image compression

63. Definition of the Distance Transform On Curved Space (DTOCS)

64. p ne pnpn pwpw pcpc pepe p sw psps p se The 3x3 kernel used in DTOCS algorithm

65. p ne pnpn pwpw pcpc pepe p sw psps p se The 3x3 kernel used in DTOCS algorithm

66. The Distance Transform on Curved Space (DTOCS)

68. Original imageDistance image after forward pass

69. Distance image after backward pass Distance image after 2nd iteration (= forward+backward pass second time)

71. Original Lena image 521 x 521 x 8 bits Curves in which DTOCS distance > binary distance Control points chosen along the curves

73. (a) LWC(b) SC(c) Cardboard (d) LWC(e) SC(f) Cardboard

75. Shortest route calculation with Route DTOCS.

76. Original image a b

77. a b Shortest route between a and b

78. Fig. 2. a) Original image, b) distance from source point, c) distance from destination point, d) sum of distance images, e) route by DTOCS, f) route by WDTOCS.

79. Original labyrinth Shortest routes by DTOCS

80. Original labyrinth Shortest routes by DTOCS

81. The End