Dilation
A dilation fills holes and smoothens the contour lines. The dilation of image A with a structuring element B blows up the objects in the image.
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 union of the mask with the image:
D(A, B) = {x | x = a + b, for a in A and b in B}
This is the formulation according to the Minkowski notation. The formulation according to Serra is similar, but the structuring element will have to be reflected in order to get the same result. If the structuring element is symmetric, then the two methods are the same.
For grayscale images the union operation is replaced by a maximum operation.
An example:
The first image is the original Lena image.
The second image is the result of a dilation
with a square structuring element with side five.
The third image is the result of a dilation with a square structuring element
with side eleven.
Notice the square artifacts due to the used structuring element. After dilation
the number of light gray values has increased.
The eyes for instance are interpreted as holes, and are filled by the dilation
with the maximum gray values of the surrounding pixels. The contour lines
have been smoothened and Lena appears a little bit more fat.
To view the full-size figures before and after dilation with a square structuring element with size three, five, seven, nine and eleven, or after dilation with a disk-like structuring element with radius one, two, three, four or five, click on the respective links.
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