Erosion:

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Erosion

• Erosion is used for shrinking of element A by
  using element B
• One of the simplest uses of erosion is for
  eliminating irrelevant details from a binary
  image.

Erosion
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Erosion
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Typical Uses of Erosion

• Removes isolated noisy pixels.
• Smoothes object boundary(removes spiky edges).
• Removes the outer layer of object pixels
• - Object becomes slightly smaller.
• - Sets contour pixels of object to
  background value

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Erosion Example
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Erosion explained pixel by pixel
A
B
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Structuring Element in Erosion Example
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How It Works?

• During erosion, a pixel is turned on at the image
  pixel under the structuring element origin only
  when the pixels of the structuring element match
  the pixels in the image
• Both ON and OFF pixels should match.
• This example erodes regions horizontally from the
  right.

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Structuring Element in Erosion Example
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Structuring Element in Erosion Example
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Structuring Element in Erosion Example
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Structuring Element in Erosion Example
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Structuring Element in Erosion Example
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Structuring Element in Erosion Example
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Mathematical Definition of Erosion

1. Erosion is the morphological dual to dilation.
2. It combines two sets using the vector subtraction
   of set elements.
3. Let denotes the erosion of A by B

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Erosion explained pixel by pixel
A
B
(1,1) (0,0) (1,1) (1,2) (0,0) (1,2) (1,3) (0,0) (1,3) (1,4) (0,0) (1,4) (0,4) (0,0) (0,4) (2,4) (0,0) (2,4) (3,4) (0,0) (3,4) (4,4) (0,0) (4,4) (1,1) (1,0) (0,1) (1,2) (1,0) (0,2) (1,3) (1,0) (0,3) (1,4) (1,0) (0,4) (0,4) (1,0) (-1,4) (2,4) (1,0) (1,4) (3,4) (1,0) (2,4) (4,4) (1,0) (3,4)
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Properties of Erosion

• Linearity
• Decomposition of structuring element

• Erosion is not commutative!

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Erosion
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In MATLAB Codes

• strelThis function creates amorphological
  structuring element. SEstrel(shape,parameters)
• Erosion image
• imerode This function erosion the image.
• I2imerode(image,SE)

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

• A imread(Image.tif')
• figure,imshow(A)
• se strel('disk',3)
• A2 imerode(A, se)
• figure,imshow(A2)
• se strel('disk',5)
• A3 imerode(A, se)
• figure,imshow(A3)
• se strel('disk',10)
• A4 imerode(A, se)
• figure,imshow(A4)

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Example of Erosions with various sizes of
structuring elements
Structuring Element
Pablo Picasso, Pass with the Cape, 1960
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Erosion and Dilation summary
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Boundary Extraction
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Boundary Extraction

• First, erode A by B, then make set difference
  between A and the erosion
• The thickness of the contour depends on the size
  of constructing object B

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Boundary Extraction
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Edge detection
Dilate - original
original
Dilate
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Opening Closing

• Opening and Closing are two important operators
  from mathematical morphology
• They are both derived from the fundamental
  operations of erosion and dilation
• They are normally applied to binary images

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OPENING

• Opening of A by B, is simply erosion of A by B,
  followed by dilation of the result by B.
• We use opening for
• Smoothes object boundaries
• Eliminates noise (isolated pixels)
• Maintains object size

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OPENING

• Opening is defined as an erosion followed by a
  dilation using the same structuring element
• The basic effect of an opening is similar to
  erosion but Less destructive than erosion
• Does not significantly change an objects size

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Opening Example

• What combination of erosion and dilation gives
• cleaned binary image
• object is the same size as in original

Original
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Opening Example Cont

• Erode original image.
• Dilate eroded image.
• Smoothes object boundaries, eliminates noise
  (isolated pixels) and maintains object size.

Dilate
Original
Erode
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CLOSING

• Closing of A by B, is dilation followed by
  erosion (opposite to opening).
• We use Closing for
• Smoothes object boundaries
• Eliminates noise (small holes), fills gaps in
  contours and close up cracks in objects.
• Maintains object size.

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Close

• Dilation followed by erosion
• Serves to close up cracks in objects and holes
  due to pepper noise
• Does not significantly change object size

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More examples of Closing

• What combination of erosion and dilation gives
• cleaned binary image
• object is the same size as in original

Original
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More examples of Closing cont

• Dilate original image.
• Erode dilated image.
• Smoothes object boundaries, eliminates noise
  (holes) and maintains object size.

Erode
Dilate
Original
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Open and Close
Close Dilate next Erode Open Erode next Dilate
Original image
eroded
dilated
dilated
eroded
Open
Close
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Spatial Filtering

Closing o Opening Opening o Closing
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Use of opening and closing for morphological
filtering
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Open and Close

• Original image opening opening followed by
  closing

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Codes

• f imread('noisy-fingerprint.tif')
• figure,imshow(f)
• se strel('square', 3)
• fo imopen(f,se)
• figure,imshow(fo)
• foc imclose(fo,se)
• figure,imshow(foc)

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Possible problems with Morphological Operators

• Erosion and dilation clean image but leave
  objects either smaller or larger than their
  original size.
• Opening and closing perform same functions as
  erosion and dilation but object size remains the
  same.