1. 图像处理技术讲座（10） Digital Image Processing (10) 灰度的数学形态学(2) Mathematical morphology in gray scale (2)
顾 力栩
上海交通大学 计算机系
2006.6

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Grayscale Operations
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Grayscale Operations
Dilated by a 7X7 box
Eroded by a 7X7 box
                      
                      
Source
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Grayscale Operations
Opened by a disk 3
Closed by a disk 3
Source
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Edge Detection
Morphological Edge Detection is based on Binary Dilation, Binary Erosion and Image Subtraction.
Morphological Edge Detection Algorithms:
Standard:
External:
Internal:
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Edge Detection
F  K F
F  K K
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Edge Detection
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Edge Detection F
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Edge Detection F
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10. Morphological Gradient
Morphological Gradient is calculated by grayscale dilation and grayscale Erosion.
It is quite similar to the standard edge detection
We also have external and internal gradient
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11. Morphological Gradient
External Gradient:
Internal Gradient:
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12. Morphological Gradient
EG(F)
DG(F)
Gradient(F)S
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13. Morphological Gradient
Standard
External
Internal
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14. Morphological Smoothing
Morphological Smoothing is based on the observation that a grayscale opening smoothes a grayscale image from above the brightness surface and the grayscale closing smoothes from below. So we could get both smooth like:
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15. Morphological Smoothing
OG(F)
Source
CG(F)
Result
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16. Morphological Smoothing
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17. Morphological Smoothing
Morphological Smoothing can also based on the average of gray scale dilation and erosion, which is so called dynamic smooth:
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18. Morphological Smoothing
EG(F)
DG(F)
Source
Result
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Top-hat Transform
Top-hat Transform (TT): An efficient segmentation tool for extracting bright (respectively dark) objects from uneven background.
White Top-hat Transform (WTT):
(ri is the scalar of SE)
Black Top-hat Transform (BTT):
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20. Top-hat Transform tophat + opened = original
tophat: original - opening
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Top-hat Transform
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Top-hat
Transform
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Top-hat Transform
BTT
WTT
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Top-hat Transform
Inspection of a maximal thermometer capillary
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Top-hat Transform
BTT
WTT
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26. Application 1 Detecting runways in satellite airport imagery
Source
WTT
Threshold
Detect long feature
Final result
Reconstruction
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27. Application 2 Detect Filarial Worms
Source
BTT
Remove Noises
Threshold
Skeleton
Eliminate short structures
Reconstruction
Final result
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Differential TT
Difficulties of TT:
Difficult to distinguish ROI for more complicated cases.
Difficult to define the sizes of SE.
Differential Top-hat Transformation (DTT): employ a series of SE (same shape, different sizes) into TT application to find out the difference between Ti and Ti-1:
( | T |B stands for a threshold operation)
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DTT: The Principle
How it works:
Find a series of TT: Ti
Calculate the subtraction between Ti and Ti-1
Threshold the results of 2. by same threshold level.
Put them together by OR
What’s better:
Differentiate the signal slopes in steepness and only pick up the objects with high gradient
Sort the objects by sizes.
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30. DTT: A Model Testing Source testing image and its cross section view
TT result
DTT result
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31. DTT: A Real Image Testing
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Application
Character Extraction From Cover Image
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Application
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Ultimate Erosion
Ultimate Erosion (UE) is based on Recursive Erosion operation.
“Keep aside each connected components just before it is removed throughout the recursive erosion process”.
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Ultimate Erosion
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Geodesic Influence
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”.
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UE and GI
UE: split a connected region (have to be convex) gradually and record the iteration number.
GI: Reconstruct the split regions and get the segments.
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Application
Segment connected organs:
RE: region shrinking to generate all the candidate seeds
GI: region reconstruction to recover separated organs
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Discussion
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