erosion: erosion is used for shrinking of element a by using element b one of the simplest uses of...
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Erosion:
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
Typical Uses of Erosion
1. Removes isolated noisy pixels.
2. Smoothes object boundary(removes spiky edges).
3. Removes the outer layer of object pixels:
- Object becomes slightly smaller.
- Sets contour pixels of object to background value
Erosion Example
Erosion explained pixel by pixel
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B
A BA
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Structuring Element in Erosion Example
Image Structuring Element Result
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.
Image Structuring Element Result
Structuring Element in Erosion Structuring Element in Erosion ExampleExample
Image Structuring Element Result
Structuring Element in Erosion Structuring Element in Erosion ExampleExample
Image Structuring Element Result
Structuring Element in Erosion Structuring Element in Erosion ExampleExample
Image Structuring Element Result
Structuring Element in Erosion Structuring Element in Erosion ExampleExample
Image Structuring Element Result
Structuring Element in Erosion Structuring Element in Erosion ExampleExample
Image Structuring Element Result
Structuring Element in Erosion Structuring Element in Erosion ExampleExample
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 BBA
){
},,{
BbeveryforAbxxx
baxAaanexistBbeveryforxBA
Erosion explained pixel by pixel
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BA BA
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(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)
Properties of Erosion
Erosion is not commutative!
Linearity
Decomposition of structuring element
)()()( CBCACBA
)()()( CABACBA
ABBA
Erosion
In MATLAB Codesstrel:This function creates amorphological structuring element.
SE=strel(‘shape’,parameters)
Erosion image:
imerode: This function erosion the image.
I2=imerode(‘image’,SE)
shape parameters
‘disk’ R
‘line’ Len,deg
‘square’ w
‘rectangle’ [m n]
CodesA = 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);
Pablo Picasso, Pass with the Cape, 1960
Structuring
Element
Example of Erosions Example of Erosions with various sizes of with various sizes of structuring elementsstructuring elements
Erosion and Dilation summary
Boundary Extraction
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
Boundary Extraction
Edge detectionDilate - originaloriginal Dilate
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
OPENINGOPENING•Opening of A by B, is simply erosion of A by B, followed by dilation of the result by B.
•We use opening for: o Smoothes object boundarieso Eliminates noise (isolated pixels) o Maintains object size
BBABA )(
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 object’s size
OPENINGOPENING
Opening Example
Original What combination of
erosion and dilation gives:o cleaned binary image
o object is the same size as in original
Opening Example Cont
Erode original image.
Dilate eroded image.
Smoothes object boundaries, eliminates noise (isolated pixels) and maintains object size.
DilateOriginal Erode
•Closing of A by B, is dilation followed by erosion (opposite to opening).
•We use Closing for: oSmoothes object boundaries oEliminates noise (small holes), fills gaps in contours and close up cracks in objects. o Maintains object size.
CLOSINGCLOSING
BBABA )(
Close Dilation followed by erosion Serves to close up cracks in objects and holes
due to pepper noise Does not significantly change object size
More examples of Closing
Original What combination of
erosion and dilation gives:o cleaned binary image
o object is the same size as in original
More examples of Closing cont
Dilate original image.
Erode dilated image.
Smoothes object boundaries, eliminates noise (holes) and maintains object size.
ErodeDilateOriginal
Open and CloseClose = Dilate next ErodeOpen = Erode next Dilate
OpenClose
Original image dilated
eroded
dilated
eroded
Spatial Filtering
Closing o Opening & Opening o Closing
Use of opening and closing for morphological filtering
Open and Close
Original image; opening; opening followed by closing
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);
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.