J. Shanbehzadeh M. Hosseinajad Khwarizmi University of Tehran

9.6 Gray-Scale Morphology Erosion and Dilation Opening and Closing Some Basic Gray-Scale Morphological Algorithms Gray-Scale Morphological Reconstruction 1

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Gray-Scale Morphology 2 Structuring elements in gray-scale morphology: Nonflat Flat

9.6 Gray-Scale Morphology Erosion and Dilation Opening and Closing Some Basic Gray-Scale Morphological Algorithms Gray-Scale Morphological Reconstruction 3

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Erosion and Dilation (Flat SEs) 4 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.

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

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

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Erosion and Dilation (Nonflat SEs) 7 Erosion: Dilation: Notice: As in the binary case, erosion and dilation are duals with respect to function complementation and reflection:

9.6 Gray-Scale Morphology Erosion and Dilation Opening and Closing Some Basic Gray-Scale Morphological Algorithms Gray-Scale Morphological Reconstruction 8

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Opening and Closing 9 Opening: 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, 3 rd edition, Opening and Closing 10

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Opening and Closing 11

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Opening and Closing 12 Opening Erosion

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Opening and Closing 13 Closing Dilation

9.6 Gray-Scale Morphology Erosion and Dilation Opening and Closing Some Basic Gray-Scale Morphological Algorithms Gray-Scale Morphological Reconstruction 14

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Morphological Smoothing 15 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.

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Morphological Smoothing 16

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Morphological Gradient 17 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.

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Morphological Gradient 18

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Top–hat and Bottom–hat Transformation 19 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.

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Top–hat and Bottom–hat Transformation 20

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Granulometry 21 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.

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Granulometry 22

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Granulometry 23

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Textural Segmentation 24 Finding a boundary between two regions based on their textural content.

9.6 Gray-Scale Morphology Erosion and Dilation Opening and Closing Some Basic Gray-Scale Morphological Algorithms Gray-Scale Morphological Reconstruction 25

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Gray-Scale Morph. Reconstruction 26 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:

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Gray-Scale Morph. Reconstruction 27 Morphological reconstruction by dilation: Morphological reconstruction by erosion:

R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, Gray-Scale Morph. Reconstruction 28 Opening 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, 3 rd edition, Gray-Scale Morph. Reconstruction 29