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DIGITAL IMAGE PROCESSING J. Shanbehzadeh M. Hosseinajad [email protected] Khwarizmi University of Tehran Chapter 9 – Morphological Image Processing ( Part 3 – Gray-Scale Morphology )
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DIGITAL IMAGE PROCESSING

Feb 15, 2016

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DIGITAL IMAGE PROCESSING. Chapter 9 – Morphological Image Processing ( Part 3 – Gray- S cale Morphology ). J . Shanbehzadeh M. Hosseinajad [email protected]. Khwarizmi University of Tehran. 9.6 Gray-Scale Morphology. 9.6.1 Erosion and Dilation 9.6.2 Opening and Closing - PowerPoint PPT Presentation
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Chapter 7 - Wavelet and Multiresolution Processing

DIGITAL IMAGE PROCESSING

J. Shanbehzadeh M. [email protected]

Khwarizmi University of TehranChapter 9 Morphological Image Processing( Part 3 Gray-Scale Morphology )

9.6 Gray-Scale Morphology9.6.1 Erosion and Dilation9.6.2 Opening and Closing9.6.3 Some Basic Gray-Scale Morphological Algorithms9.6.4 Gray-Scale Morphological Reconstruction

119.6 Gray-Scale Morphology2Structuring elements in gray-scale morphology:NonflatFlat

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6 Gray-Scale Morphology9.6.1 Erosion and Dilation9.6.2 Opening and Closing9.6.3 Some Basic Gray-Scale Morphological Algorithms9.6.4 Gray-Scale Morphological Reconstruction

339.6.1 Erosion and Dilation (Flat SEs)4Erosion: 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.

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6.1 Erosion and Dilation (Flat SEs)5

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6.1 Erosion and Dilation (Flat SEs)6

ErosionDilationR. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6.1 Erosion and Dilation (Nonflat SEs)7Erosion:

Dilation:

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

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6 Gray-Scale Morphology9.6.1 Erosion and Dilation9.6.2 Opening and Closing9.6.3 Some Basic Gray-Scale Morphological Algorithms9.6.4 Gray-Scale Morphological Reconstruction

889.6.2 Opening and Closing9Opening:

Closing:

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

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6.2 Opening and Closing10

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6.2 Opening and Closing11

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6.2 Opening and Closing12

OpeningErosionR. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6.2 Opening and Closing13ClosingDilation

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6 Gray-Scale Morphology9.6.1 Erosion and Dilation9.6.2 Opening and Closing9.6.3 Some Basic Gray-Scale Morphological Algorithms9.6.4 Gray-Scale Morphological Reconstruction

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Morphological Smoothing15Opening 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.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.Morphological Smoothing16

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.Morphological Gradient17Dilation 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.

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.Morphological Gradient18

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.Tophat and Bottomhat Transformation19Combining 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.

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.Tophat and Bottomhat Transformation20

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.Granulometry21Determining 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.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.Granulometry22

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.Granulometry23

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.

Textural Segmentation24Finding a boundary between two regions based on their textural content.

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6 Gray-Scale Morphology9.6.1 Erosion and Dilation9.6.2 Opening and Closing9.6.3 Some Basic Gray-Scale Morphological Algorithms9.6.4 Gray-Scale Morphological Reconstruction

25259.6.4 Gray-Scale Morph. Reconstruction26Let 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:

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6.4 Gray-Scale Morph. Reconstruction27Morphological reconstruction by dilation:

Morphological reconstruction by erosion:

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6.4 Gray-Scale Morph. Reconstruction28Opening by reconstruction of size n:

Closing by reconstruction of size n:

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.9.6.4 Gray-Scale Morph. Reconstruction29

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3rd edition, 2008.