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Erosion Operation on Binary &Graylevel images in C#

Overview

Erosion is one of the two basic operators in the area of mathematical morphology. The basic effect of the operator on a

set of coordinates associated with the input image is derived. In addition, these coordinates are 3-D rather than 2-D. The

brief procedure for implementing the erosion in the binary image, and in the graylevel image are explained below.

The erosion is applied on the binary image in a single pass. During the pass, if the pixel in hand is equal to binary 0, then

apply the structuring element on the image by starting from that particular pixel as the origin. The sample project supposes

that, in the threshold image, the background is white and the foreground is black. If the sample image is not so, then you

have to adjust accordingly.

The erosion can also be applied on the graylevel images also in a single pass. During the passing through the image, the

structuring element is applied on each pixel of the image, such that the origin of the structuring element is applied on that

particular pixel. In this case the corresponding pixel of the output image contains the minimum of the pixels surrounding it.

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The following image shows the effect of it on the above image:

In the above images, the boxes shows the pixels, and the white colored boxes shows that the binary pixel contains 1,

while the black box shows that the corresponding pixel contains 0. It can be seen that only the pixels in the only input

image that were surrounded by the white pixels are left, other have vanished. This erosion effect can be seen in the

example below. Erosion can be made directional by using less symmetrical structuring elements. e.g. a structuring

and the following be the structuring element:

now, the eroded image pixel setup is as:

In order to understand the working, take the example of the pixel in the 3rd row, and in the 4th column. Its intensity is 56.

Now, the pixel in the images are compared in the image where the structuring element has one. The intensity values of

those pixels are 198 , 32 , 56 , 16 , 78. The minimum of these is 16 intensity value, thus it is the intensity value of the pixel