Morphological Image Processing
Goal: To implement binary dilation and erosion with a 3x3 structuring element.
I implemented these algorithms in matlab. Neither implementation follows the strict
definitions of dilation and erosion. But they should behave the same as the definitions
as long as the structuring element is smaller than the object. If the object is very small,
erosion will completely remove it. All images are required to be binary (1 - white, 0 black).
And the origin will always be at the center of the structuring element. I ran one erosion
and one dilation on figure 9.14a as a demonstration. I used the following element for both
dilation and erosion.
Structure = [1 1 1
0 1 1
0 0 1]
It is clear where the image has been eroded. It is more difficult to tell what happened with
dilation. But, you should be able to see the extra 'mass' at the end of the nose. And the area
where the hair meets the forehead has filled in some.
Top) The original image with threshold at 1.
Middle) Eroded image.
Bottom) Dilated image.
Below is some more matlab code to perform some routine set functions.
Although, these could in principle be used in dilation and erosion, none
were used in my implementation.