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DIGITAL IMAGE PROCESSING . Instructors: Dr J. Shanbehzadeh Shanbehzadeh@gmail.com. Kharazmi University. DIGITAL IMAGE PROCESSING. Chapter 9 – Morphological Image Processing. Instructors: Dr J. Shanbehzadeh Shanbehzadeh@gmail.com. 9.6 - Gray-Scale Morphology. introduction.

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DIGITAL IMAGE PROCESSING

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## DIGITAL IMAGE PROCESSING

Instructors:

Kharazmi University

DIGITAL IMAGE PROCESSING

Chapter 9 – Morphological Image Processing

Instructors:

• 9.6 - Gray-Scale Morphology

### introduction

• 9.6- introduction

• 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

• Structuring elements in gray-scale morphology:

• Non flat

• Flat

• Erosion and Dilation

Some Basic Gray-Scale Morphological Algorithms

### Gray-Scale Morphology

• Opening and Closing

• Gray-Scale Morphological Reconstruction

• Erosionand Dilation

• 9.6- introduction

• 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

### 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

• 9.6- introduction

• 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

### Erosion and Dilation (Flat Ses)

• 9.6- introduction

• 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

### Erosion and Dilation (Flat Ses)

Erosion

• 9.6- introduction

• 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

Dilation

### Erosion and Dilation (Non flat Ses)

Erosion:

• 9.6- introduction

• 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

Dilation :

Notice: As in the binary case, erosion and dilation are duals with respect to function complementation and reflection

• Erosion and Dilation

Some Basic Gray-Scale Morphological Algorithms

### Gray-Scale Morphology

• Opening and Closing

• Gray-Scale Morphological Reconstruction

• Opening and Closing

• 9.6- introduction

• 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

### Opening and Closing

• 9.6- introduction

• 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

• Opening:

• ClosingSeries:

• Notice: The opening and closing for gray-scale images are duals with respect to complementation and SE reflection

Opening and Closing

• 9.6- introduction

• 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

Opening and Closing

• 9.6- introduction

• 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

Opening and Closing

• 9.6- introduction

• 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

Opening

Erosion

Opening and Closing

• 9.6- introduction

• 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

Closing

Dilation

Some Basic Gray-Scale Morphological Algorithms

• Erosion and Dilation

### Gray-Scale Morphology

• Opening and Closing

• Gray-Scale Morphological Reconstruction

Some Basic Gray-Scale Morphological Algorithms

• 9.6- introduction

• 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

### Morphological Smoothing

• 9.6- introduction

• 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

• 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

### Morphological Smoothing

• 9.6- introduction

• 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

• Dilation and erosion can be used in combination with imagesubtraction to obtain the morphologicalgradient of an image:

• The dilation thickens regions in an image and the erosion shrinks them. Their difference emphasizes theboundaries between regions.

• 9.6- introduction

• 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

• 9.6- introduction

• 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

### Top–hat and Bottom–hat Transformation

Combining image subtraction with openings and closings results in top-hat and bottom-hat transformations.

Top-hattransformation:

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.

• 9.6- introduction

• 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

### Top–hat and Bottom–hat Transformation

• 9.6- introduction

• 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

### Granulometry

• 9.6- introduction

• 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

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.

Granulometry

• 9.6- introduction

• 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

### Granulometry

• 9.6- introduction

• 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

### Textural Segmentation

• 9.6- introduction

• 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

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

Some Basic Gray-Scale Morphological Algorithms

• Erosion and Dilation

### Gray-Scale Morphology

• Opening and Closing

• Gray-Scale Morphological Reconstruction

• Gray-Scale Morphological Reconstruction

• 9.6- introduction

• 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

### Gray-Scale Morph. Reconstruction

• 9.6- introduction

• 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

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:

### Gray-Scale Morph. Reconstruction

Morphological reconstruction by dilation:

Morphological reconstruction by erosion:

• 9.6- introduction

• 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

### Gray-Scale Morph. Reconstruction

Opening by reconstruction of size n:

• Closing by reconstruction of size n:

• 9.6- introduction

• 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

### Gray-Scale Morph. Reconstruction

• 9.6- introduction

• 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