Mathematical Morphology - Inriamaverick.inria.fr/Members/Adrien.Bousseau/morphology/... ·...
Transcript of Mathematical Morphology - Inriamaverick.inria.fr/Members/Adrien.Bousseau/morphology/... ·...
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Mathematical Morphologya non exhaustive overview
Adrien Bousseau
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2Mathematical Morphology
Mathematical Morphology• Shape oriented operations, that “ simplify
image data, preserving their essential shape characteristics and eliminating irrelevancies” [Haralick87]
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3Mathematical Morphology
Overview• Basic morphological operators
• More complex operations
• Conclusion and References
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4Mathematical Morphology
Overview• Basic morphological operators
– Binary
– Grayscale
– Color
– Structuring element
• More complex operations
• Conclusion and References
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5Mathematical Morphology
Basic operators: binary• Dilation , erosion by a structuring element
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6Mathematical Morphology
Basic operators: binary• Opening ° : remove capes, isthmus and
islands smaller than the structuring element
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7Mathematical Morphology
Basic operators: binary• Closing ° : fill gulfs, channels and lakes
smaller than the structuring element
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8Mathematical Morphology
Basic operators: binary• Sequencial filter: open-close or close-open
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9Mathematical Morphology
Overview• Basic morphological operators
– Binary
– Grayscale
– Color
– Structuring element
• More complex operations
• Conclusion and References
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10Mathematical Morphology
Basic operator: grayscale• Dilation : max over the structuring element
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11Mathematical Morphology
Basic operator: grayscale• Erosion : min over the structuring element
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12Mathematical Morphology
Basic operator: grayscale• Opening ° : remove light features smaller
than the structuring element
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13Mathematical Morphology
Basic operator: grayscale• Closing ° : remove dark features smaller
than the structuring element
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14Mathematical Morphology
Basic operator: grayscale• Sequential filter (open-close or close-open):
remove both light and dark features
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15Mathematical Morphology
Overview• Basic morphological operators
– Binary
– Grayscale
– Color
– Structuring element
• More complex operations
• Conclusion and References
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16Mathematical Morphology
Color images• Process each channel separately: color ghosting
with basic operators
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17Mathematical Morphology
Color images• Process each channel separately: color ghosting
unnoticeable with sequential operators
opening
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18Mathematical Morphology
Color images• Several ordering strategy
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19Mathematical Morphology
Overview• Basic morphological operators
– Binary
– Grayscale
– Color
– Structuring element
• More complex operations
• Conclusion and References
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20Mathematical Morphology
Structuring element• Usually, flat element (binary)
• Grayscale element: fuzzy morphology
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21Mathematical Morphology
Structuring element• Shape has an impact!
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22Mathematical Morphology
Structuring element• Choose the structuring element according to
the image structure
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23Mathematical Morphology
Structuring element• Choose the structuring element according to
the image structure
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24Mathematical Morphology
Overview• Basic morphological operators
• More complex operations– Reconstruction operators
– Top hat, sharpening, distance, thinning, segmentation...
• Conclusion and References
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25Mathematical Morphology
Reconstruction operators• Remove features smaller than the structuring
element, without altering the shape
• Reconstruct connected components from the preserved features
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26Mathematical Morphology
Reconstruction operators: binary• Opening by reconstruction:
– Erosion: f'(0) = f
– Iterative reconstruction: f'(t+1) = min(f'(t),I)until stability
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27Mathematical Morphology
Reconstruction operators: binary• Closing by reconstruction:
– Dilation: f'(0) = f
– Iterative reconstruction: f'(t+1) = max(f'(t),I)until stability
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28Mathematical Morphology
Reconstruction operators: grayscale
• Opening by reconstruction: remove unconnected light features
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29Mathematical Morphology
Reconstruction operators: grayscale
• Closing by reconstruction: remove unconnected dark features
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30Mathematical Morphology
Reconstruction operators: grayscale
• Sequential filter by reconstruction: open-close
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31Mathematical Morphology
Overview• Basic morphological operators
• More complex operations– Reconstruction operators
– Top hat, sharpening, distance, thinning, segmentation...
• Conclusion and References
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32Mathematical Morphology
Top Hat• White top-hat: f-opening(f)
Extract light features
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33Mathematical Morphology
Top Hat• Black top-hat: closing(f)-f
Extract dark features
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34Mathematical Morphology
Edge sharpening• Toggle mapping
f f f (f+f)/2
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35Mathematical Morphology
Edge sharpening• Toggle mapping
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36Mathematical Morphology
Distance function• Distance from binary elements
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37Mathematical Morphology
Thinning• Binary (or grayscale ?) skeleton
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38Mathematical Morphology
Segmentation• Watershed:
– Image = heightfield
– Flood the image from its minima
– Lake junctions give the segmentation
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39Mathematical Morphology
Segmentation• Watershed: hierarchical results
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40Mathematical Morphology
Overview• Basic morphological operators
• More complex operations
• Conclusion and References
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41Mathematical Morphology
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!
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42Mathematical Morphology
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)