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DIGITAL IMAGE PROCESSING

DIGITAL IMAGE PROCESSING. Chapter 9 – Morphological Image Processing ( Part 3 – Gray- S cale Morphology ). J . Shanbehzadeh M. Hosseinajad Shanbehzadeh@gmail.com. Khwarizmi University of Tehran. 9.6 Gray-Scale Morphology. 9.6.1 Erosion and Dilation 9.6.2 Opening and Closing

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DIGITAL IMAGE PROCESSING

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  1. DIGITAL IMAGE PROCESSING Chapter 9 – Morphological Image Processing ( Part 3 – Gray-Scale Morphology ) J. Shanbehzadeh M. Hosseinajad Shanbehzadeh@gmail.com Khwarizmi University of Tehran

  2. 9.6 Gray-Scale Morphology • 9.6.1 Erosion and Dilation • 9.6.2 Opening and Closing • 9.6.3 Some Basic Gray-Scale Morphological Algorithms • 9.6.4 Gray-Scale Morphological Reconstruction

  3. 9.6 Gray-Scale Morphology Structuring elements in gray-scale morphology: • Nonflat • Flat

  4. 9.6 Gray-Scale Morphology • 9.6.1 Erosion and Dilation • 9.6.2 Opening and Closing • 9.6.3 Some Basic Gray-Scale Morphological Algorithms • 9.6.4 Gray-Scale Morphological Reconstruction

  5. 9.6.1 Erosion and Dilation (Flat SEs) Erosion: The minimum value of the image in the region coincident with SE. This is similar to the correlation procedure. Dilation: The maximum value of the image in the window outlined by SE. This is analogous to spatial convolution. Notice: the structuring element is reflected about its origin by using (-s, -t) in the argument of the function.

  6. 9.6.1 Erosion and Dilation (Flat SEs)

  7. 9.6.1 Erosion and Dilation (Flat SEs) Erosion Dilation

  8. 9.6.1 Erosion and Dilation (NonflatSEs) Erosion: Dilation: Notice: As in the binary case, erosion and dilation are duals with respect to function complementation and reflection:

  9. 9.6 Gray-Scale Morphology • 9.6.1 Erosion and Dilation • 9.6.2 Opening and Closing • 9.6.3 Some Basic Gray-Scale Morphological Algorithms • 9.6.4 Gray-Scale Morphological Reconstruction

  10. 9.6.2 Opening and Closing Opening: Closing: Notice: The opening and closing for gray-scale images are duals with respect to complementation and SE reflection.

  11. 9.6.2 Opening and Closing

  12. 9.6.2 Opening and Closing

  13. 9.6.2 Opening and Closing Erosion Opening

  14. 9.6.2 Opening and Closing Dilation Closing

  15. 9.6 Gray-Scale Morphology • 9.6.1 Erosion and Dilation • 9.6.2 Opening and Closing • 9.6.3 Some Basic Gray-Scale Morphological Algorithms • 9.6.4 Gray-Scale Morphological Reconstruction

  16. Morphological Smoothing Opening suppresses bright details smaller than the specified SE and closing suppresses dark details. They are used often in combination as morphological filters for image smoothing and noise removal.

  17. Morphological Smoothing

  18. Morphological Gradient Dilation and erosion can be used in combination with image subtraction to obtain the morphological gradient of an image: The dilation thickens regions in an image and the erosion shrinks them. Their difference emphasizes the boundaries between regions.

  19. Morphological Gradient

  20. Top–hat and Bottom–hat Transformation Combining image subtraction with openings and closings results in top-hat and bottom-hat transformations. Top-hat transformation: Bottom-hat transformation: Notice: The top-hat transform is used for light objects on a dark background, and the bottom-hat transform is used for the converse.

  21. Top–hat and Bottom–hat Transformation

  22. Granulometry Determining the size distribution of particles in an image. Granulometry consists of applying openings with SEs of increasing size. For each opening, the sum of the pixel values in the opening is computed. To emphasize changes between successive openings, we compute the difference between adjacent elements of the 1-D array. The peaks in the plot are an indication of the size distributions of the particles in the image.

  23. Granulometry

  24. Granulometry

  25. Textural Segmentation Finding a boundary between two regions based on their textural content.

  26. 9.6 Gray-Scale Morphology • 9.6.1 Erosion and Dilation • 9.6.2 Opening and Closing • 9.6.3 Some Basic Gray-Scale Morphological Algorithms • 9.6.4 Gray-Scale Morphological Reconstruction

  27. 9.6.4 Gray-Scale Morph. Reconstruction Let f and g denote the marker and mask images. Geodesic dilation of size 1: ^ denotes the point-wise minimum operator. Geodesic dilation of size n: Geodesic erosion of size 1: Geodesic erosion of size n:

  28. 9.6.4 Gray-Scale Morph. Reconstruction Morphological reconstruction by dilation: Morphological reconstruction by erosion:

  29. 9.6.4 Gray-Scale Morph. Reconstruction Opening by reconstruction of size n: Closing by reconstruction of size n:

  30. 9.6.4 Gray-Scale Morph. Reconstruction

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