Mathematical Morphology a non exhaustive overview Adrien Bousseau - - PowerPoint PPT Presentation

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Mathematical Morphology a non exhaustive overview Adrien Bousseau - - PowerPoint PPT Presentation

Sep 19, 2022 326 likes •767 views

Mathematical Morphology a non exhaustive overview Adrien Bousseau Mathematical Morphology Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies

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Mathematical Morphology

a non exhaustive overview

Adrien Bousseau

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2 Mathematical Morphology

Mathematical Morphology

  • Shape oriented operations, that “simplify

image data, preserving their essential shape characteristics and eliminating irrelevancies” [Haralick87]

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3 Mathematical Morphology

Overview

  • Basic morphological operators
  • More complex operations
  • Conclusion and References
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4 Mathematical Morphology

Overview

  • Basic morphological operators

– Binary – Grayscale – Color – Structuring element

  • More complex operations
  • Conclusion and References
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5 Mathematical Morphology

Basic operators: binary

  • Dilation , erosion  by a structuring element
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6 Mathematical Morphology

Basic operators: binary

  • Opening ° : remove capes, isthmus and

islands smaller than the structuring element

 

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7 Mathematical Morphology

Basic operators: binary

  • Closing ° : fill gulfs, channels and lakes

smaller than the structuring element

 

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8 Mathematical Morphology

Basic operators: binary

  • Sequencial filter: open-close or close-open
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9 Mathematical Morphology

Overview

  • Basic morphological operators

– Binary – Grayscale – Color – Structuring element

  • More complex operations
  • Conclusion and References
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10 Mathematical Morphology

Basic operator: grayscale

  • Dilation : max over the structuring element
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11 Mathematical Morphology

Basic operator: grayscale

  • Erosion : min over the structuring element
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12 Mathematical Morphology

Basic operator: grayscale

  • Opening ° : remove light features smaller

than the structuring element

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13 Mathematical Morphology

Basic operator: grayscale

  • Closing ° : remove dark features smaller

than the structuring element

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14 Mathematical Morphology

Basic operator: grayscale

  • Sequential filter (open-close or close-open):

remove both light and dark features

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15 Mathematical Morphology

Overview

  • Basic morphological operators

– Binary – Grayscale – Color – Structuring element

  • More complex operations
  • Conclusion and References
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16 Mathematical Morphology

Color images

  • Process each channel separately: color ghosting

with basic operators

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17 Mathematical Morphology

Color images

  • Process each channel separately: color ghosting

unnoticeable with sequential operators

  • pening
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18 Mathematical Morphology

Color images

  • Several ordering strategy
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19 Mathematical Morphology

Overview

  • Basic morphological operators

– Binary – Grayscale – Color – Structuring element

  • More complex operations
  • Conclusion and References
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20 Mathematical Morphology

Structuring element

  • Usually, flat element (binary)
  • Grayscale element: fuzzy morphology
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21 Mathematical Morphology

Structuring element

  • Shape has an impact!
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22 Mathematical Morphology

Structuring element

  • Choose the structuring element according to

the image structure

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23 Mathematical Morphology

Structuring element

  • Choose the structuring element according to

the image structure

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24 Mathematical Morphology

Overview

  • Basic morphological operators
  • More complex operations

– Reconstruction operators – Top hat, sharpening, distance, thinning, segmentation...

  • Conclusion and References
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25 Mathematical 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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26 Mathematical 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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27 Mathematical 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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28 Mathematical Morphology

Reconstruction operators: grayscale

  • Opening by reconstruction: remove

unconnected light features

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29 Mathematical Morphology

Reconstruction operators: grayscale

  • Closing by reconstruction: remove

unconnected dark features

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30 Mathematical Morphology

Reconstruction operators: grayscale

  • Sequential filter by reconstruction: open-close
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31 Mathematical Morphology

Overview

  • Basic morphological operators
  • More complex operations

– Reconstruction operators – Top hat, sharpening, distance, thinning, segmentation...

  • Conclusion and References
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32 Mathematical Morphology

Top Hat

  • White top-hat: f-opening(f)

Extract light features

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33 Mathematical Morphology

Top Hat

  • Black top-hat: closing(f)-f

Extract dark features

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34 Mathematical Morphology

Edge sharpening

  • Toggle mapping

f f f (f+f)/2

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35 Mathematical Morphology

Edge sharpening

  • Toggle mapping
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36 Mathematical Morphology

Distance function

  • Distance from binary elements
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37 Mathematical Morphology

Thinning

  • Binary (or grayscale ?) skeleton
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38 Mathematical Morphology

Segmentation

  • Watershed:

– Image = heightfield – Flood the image from its minima – Lake junctions give the segmentation

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39 Mathematical Morphology

Segmentation

  • Watershed: hierarchical results
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40 Mathematical Morphology

Overview

  • Basic morphological operators
  • More complex operations
  • Conclusion and References
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41 Mathematical 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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42 Mathematical 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)