1. 图像处理技术讲座（11） Digital Image Processing (11) 灰度的数学形态学(3) Mathematical morphology in gray scale (3)
顾 力栩
上海交通大学 计算机系
2006.6

2. Lixu Gu @ 2005 copyright reserved
Conditional Dilation
Conditional Dilation : a special recursive dilation operation. It is also known as Geodesic Dilation or Morphological Reconstruction used for restoring destroyed objective regions.
Let M and V (M  V) be two binary images defined as “marker” and “mask”, respectively.
Conditional dilation Ri(M,V) is defined as:
Marker M is only allowed to grow in the region restricted by mask V.
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3. Lixu Gu @ 2005 copyright reserved
How it works
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4. Morphological Reconstruction
Algorithm for binary reconstruction:
1. M = V o K , where K is any SE.
2. T = M,
3. M= M  Ki , where i=4 or i=8,
4. M = M ∩ V, [Take only those pixels from M that are also in V .]
5. if M  T then go to 2,
6. else stop;
Original (V)
Opened (M)
Reconstructed (T)
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5. Lixu Gu @ 2005 copyright reserved
Conditional Dilation
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6. Grayscale Reconstruction
Step1: perform grayscale dilation on marker g.
Step2: check every gray value in dilated result is not exceed the restriction of mask f.
Step3: repeat step1 and 2, until g getting stable.
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7. Grayscale Reconstruction
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8. Grayscale Reconstruction
Grayscale Opening by Reconstruction (OBR):
Smooth image or detect seeds by grayscale opening operation
Recover the objective regions by grayscale reconstruction f
f °g r30X1Kline
OBR
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9. Grayscale Reconstruction
Grayscale Closing by Reconstruction(CBR):
Smooth image by grayscale closing operation
Recover the objective regions by grayscale reconstruction
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10. Grayscale Reconstruction
OBR
CBR
Source
r10Kdisk
r20Kdisk
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11. Grayscale Reconstruction
OBR
CBR
r5Kdisk
r10Kdisk
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12. Grayscale Reconstruction
Source
OBR by r10Kdisk
CBR by r10Kdisk
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13. Grayscale Reconstruction
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14. Lixu Gu @ 2005 copyright reserved
Geodesic Distance
Geodesic Distance: Let Fa be a connected region. The geodesic distance dFa(x,y) between two pixels x and y in Fa is the infimum of the length of the paths P which join x and y and are totally included in Fa:
where, “” stands for the infimum and l(P) is the length of the path P.
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15. Geodesic Distance vs. Euclidean Distance
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16. Geodesic Influence Zone
Geodesic Influence Zone (IZ): Suppose a region A contains a set B made of several connected components B1,B2,…, Bk. IZ is denoted by izA(Bi) and defined as:
izA(Bi) is the locus of the points of A whose geodesic distance to Bi is smaller than the distances to any other components of B.
SKIZ
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17. Lixu Gu @ 2005 copyright reserved
SKIZ
Skeleton by Influence Zone (SKIZ): the points of A which do not belong to any IZ, constitute the SKIZ of B inside A, denoted as SKIZA(B) :
“A/B” means all members in A except those in B (BA)
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Watershed
The Great Divide
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19. Watershed – Catchment Basin
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Watershed - Dam
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Watershed
How it works:
Sort all the pixels in an image by their intensities
Find the minimum intensity pixel as the start point (it’s gray level as the initial threshold level)
Increase threshold level by 1:
If find another local minimum point, add it to minimum list, and calculate the SKIZ with other existing minimum points
Otherwise, calculate SKIZ within existing minimum list.
Repeat 3., until all the pixels are sorted to basins or threshold exceed maximum intensity.
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Watershed Demo
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23. Marked Watershed - Demo
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Watershed - Example
Source Image
Watershed
Over-segmented
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25. Watershed - Example Merged by increase flood level Final Result
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Application
Extract blood cells and separate them:
Source
Smoothed
Binary
Smoothed
SKIZ
Watershed
Distance Transform
Maximum points
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27. Application The cell binary image overlay with watershed lines
Cells separated by watershed lines
The Cells that touch the frames are removed
Final
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Exercise
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29. Lixu Gu @ 2005 copyright reserved
Grayscale Operations
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Grayscale Operations
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Grayscale Operations
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32. Lixu Gu @ 2005 copyright reserved
Grayscale Operations
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33. Lixu Gu @ 2005 copyright reserved
Projects
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34. Lixu Gu @ 2005 copyright reserved
Project1
Write your own code to realize dilation, erosion,opening and closing operations in grayscale.
Requirement:
Design your own UI and display I/O images
Try to apply fast operations in case
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35. Lixu Gu @ 2005 copyright reserved
Project2
Write code to realize the next functions:
Morphological edge detection
Morphological Reconstruction
Conditional dilation in binary image
Gray scale Reconstruction
Morphological gradient
Requirement:
Design your own UI and display I/O images
Try to apply fast operations in case
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36. Lixu Gu @ 2005 copyright reserved
Discussion
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