Morphological Filtering

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Morphological Filtering
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Morphological Filtering
Spatial Filtering

• Morphological operators are used to change image
  data to reflect new geometric structure.
• Basics of Morphological Filtering
• To kinds
• Binary Morphology
• Grey Level Morphology

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Libraries of Structuring Elements

• Application specific structuring elements created
  by the user

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Binary Morphology

• Binary images often suffer from noise
  (specifically salt-and-pepper noise)
• Binary regions also suffer from noise (isolated
  black pixels in a white region). Can also have
  cracks, picket fence , etc.
• Dilation and erosion are two binary morphological
  operations that can assist with these problems.

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Dilation

• Dilation is used for expanding an element A by
  using structuring element B.
• The dilation operator takes two pieces of data as
  input
• A binary image, which is to be dilated
• A structuring element (or kernel), which
  determines the behavior of the morphological
  operation

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Main Applications of Dilation

• Expand shapes
• Fills in holes, crack, valleys between spiky
  regions
• Smoothes object boundaries.
• Adds an extra outer ring of pixels onto object
  boundary, ie, object becomes slightly larger.
• (sets background pixels adjacent to object's
  contour to object's value)
• smoothes small negative grey level regions

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Main Applications of Dilation
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Dilation A More interesting Example cracks
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Dilation
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Dilation fills holes

• Fills in holes.
• Smoothes object boundaries.
• Adds an extra outer ring of pixels onto object
  boundary, ie, object becomes slightly larger.

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Dilation example
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Dilation explained pixed by pixel
B
A
Denotes origin of B i.e. its (0,0)
Denotes origin of A i.e. its (0,0)
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Dilation explained by shape of A
Shape of A repeated without shift
B
Shape of A repeated with shift
A
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Structuring Element for Dilation
Length 6
Length 5
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Structuring Element for Dilation
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Structuring Element for Dilation
Single point in Image replaced with this in
the Result
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Structuring Element for Dilation
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Illustration of Extensitivity of Dilation
A
B
Replaced with
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Definition of Dilation Mathematically

• Let A and B are subsets in 2-D space. A image
  undergoing analysis, B Structuring element,
  denotes dilation

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Dilation explained pixed by pixel
B
A
(0,1) (0,0) (0,1) (1,2) (0,0) (1,2) (1,3) (0,0) (1,3) (1,4) (0,0) (1,4) (2,2) (0,0) (2,2) (0,1) (1,0) (1,1) (1,2) (1,0) (2,2) (1,3) (1,0) (2,3) (1,4) (1,0) (2,4) (2,2) (1,0) (3,2)
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Mathematical Properties of Dilation

• Commutative
• Associative
• Linearity
• Containment
• Decomposition of structuring element

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More Properties of Dilation

• Translation Invariance
• Linearity
• Containment
• Decomposition of structuring element

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Dilation
Question Suppose that the structuring element
is a 3x3 square with the origin at its center
evaluate the new image
(-1,-1), (0,-1), (1,-1), (-1,0), (0,0),
(1,0), ( 1,1), (0,1), (1,1)
B
A
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Dilation
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In MATLAB Codes

• strelThis function creates amorphological
  structuring element. SEstrel(shape,parameters)
• Dilation image
• imdilate This function Dilate the image.
• I2imerode(image,SE)

shape parameters
disk R
line Len,deg
square w
rectangle m n
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Codes

• Example1
• A imread(Image.tif')
• figure,imshow(A)
• se strel('disk',3)
• A2 imdilate(A, se)
• imshow(A), figure,imshow(A2)
• Example 2
• A imread('broken-text.tif')
• B 0 1 0 1 1 1 0 1 0
• A2 imdilate(A,B)
• imshow(A),figure,imshow(A2)

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Example of Dilation with various sizes of
structuring elements
Pablo Picasso, Pass with the Cape, 1960