Entry 15: Morphological Operations

Morphological operations are methods in transforming an image by using a specific structuring element to yield desired formation in the image.  This technique is widely used in image processing to produce a more easy-to-handle image.

Two main morphological operations are used in this activity which are the dilate and the erode operations.

The erode operation is defined mathematically as,

this means that every points in B must be contained in A so that the value in A where the origin of B is located will attain a value, else, a zero value will be assigned to that B location.

Graphically it can be illustrated by the image below.

The dilate operation on the other hand is defined mathematically as,

the implication of this equation is that when B covers a location in the background, provided that the origin of B is contained in A, then the background region covered by B will take the value of the foreground.

An illustration is shown by the image below.

Below (Fig. 1) are the images to be structured and (Fig. 2) are the structuring elements used.

Figure 1:  Images to be structured.

Figure 2:  Structuring elements used in the process.

In the succeeding images, we show the results of dilating the original images (Fig. 1) with the strels (Fig. 2).

Figure 3:  Dilated images using a 1x2 strel.

Figure 4:  Dilated images using a decreasing diagonal strel.

Figure 5:  Dilated images using a 2x1 strel.

Figure 6:  Dilated images using an increasing diagonal strel.

Figure 7:  Dilated images using a 2x2 strel.

Figure 8:  Dilated images using a cross strel.

After determining the dilated images, we tried another morphological operation which is erosion.  The images below are the eroded original (Fig. 1) images using the strels in Fig. 2.

Figure 9:  Eroded images using a 1x2 strel.

Figure 10:  Eroded images using a decreasing diagonal strel.

Figure 11:  Eroded images using a 2x1 strel.

Figure 12:  Eroded images using an increasing diagonal strel.

Figure 13:  Eroded images using a 2x2 strel.

Figure 14:  Eroded images using a cross strel.

Morphological operations can be applied to different image processing problems to simplify them.  The usefulness of these operations depend on the user.

In this activity I would rate myself a grade of 10/10.

Source:
    Activity Sheet for Activity 9 - Dr. Maricor Soriano