Erosion
An erosion removes small objects and disconnects objects connected by a small bridge. The erosion of image A with a structuring element B lets the objects in the image shrink.
Mathematically this means we scan the image with the structuring element and on every object pixel we put the mask of the structuring element and take the intersection of the mask with the image:
E(A, B) = {x | x + b in A, for all b in B}
The formulation according to the Minkowski notation and the formulation according to Serra are the same for the erosion, but not for the dilation.
For grayscale images the intersection operation is replaced by a minimum operation.
An example:
The first image is the original Lena image.
The second image is the result of a erosion with a square structuring element
with side five.
The third image is the result of a erosion with a square structuring element
with side eleven.
Notice the square artifacts due to the used structuring element. After erosion
the number of dark gray values has increased.
Some of the feathers disappear because they are too small and the structuring
element doesn't fit in them. After an erosion it looks like Lena lost some
weight.
To view the full-size figures before and after erosion with a square structuring element with size three, five, seven, nine and eleven, or after erosion with a disk-like structuring element with radius one, two, three, four or five, click on the respective links.
[ Mathematical Morphology ] -- [ Basics ] -- [ Dilation ] -- [ Opening ] -- [ Closing ]