A8 - Morphological Operations

This activity demonstrates how morphological operations, particularly dilation and erosion, can change the shape and structure of a binary image.

Let A be our image and define B as a structuring element. The dilation operation gives all the z's which are translations of a reflected B that when intersected with A is not the empty set. The effect of a dilation is to expand or elongate A in the shape of B.

On the other hand, the erosion operation results to all points z such that B translated by z is contained in A. The effect of erosion is to reduce the image by the shape of B.

To illustrate the definitions given above, consider the following sample images:

Figure1. Square (50x50 pixels)

Figure 2. Triangle ( B = 50 pixels, H = 30 pixels)

Figure 3. Circle (R = 25 pixels)

Figure 4. Hollow Square (60x60 pixels , 4 pixels thick)

Figure 5. Plus Sign ( 50 pixels long, 8 pixels thick)

And the structure elements that will be used are below:

Figure 6. Structure elements

Before doing the said operations in scilab, we first predicted the output of the operations.


We then perform the said operations in scilab. For the dilation operation, the codes are below:

A = imread('shape.jpg');

B = imread('structureelement.jpg');

im = im2bw(A, 0.5); // converts the shape to a binary image

se = im2bw(B, 0.5); // converts the structure element to binary

imse = dilate(im,se,[1,1]); //dilation operation

imshow(imse,[]);

The [1,1] written above is the chosen position of the origin for the all the structure elements except the plus sign, which has its origin at (3,3).

The results are summarized below. Note that the resulting image is also binary. The colors were added so that one can easily see the differences among them. Also, below each dilated images are their corresponding structure elements.

Figure 7. Dilated images of the square.

Figure 8. Dilated images of the triangle

Figure 9. Dilated images of the circle

Figure 10. Dilated images of the hollow square

Figure 11. Dilated images of the plus sign

For the erosion operation:

A = imread('shape.jpg');

B = imread('structureelement.jpg');

im = im2bw(A, 0.5); // converts the shape to a binary image

se = im2bw(B, 0.5); // converts the structure element to binary

imse = erode(im,se,[1,1]); //dilation operation

imshow(imse,[]);

And the results are also summarized below:

Figure 12. Eroded images of the square.


Figure 13. Eroded images of the triangle.



Figure 14. Eroded images of the circle.

Figure 15. Eroded images of the hollow square.


Figure 16. Eroded images of the plus sign.

I rate myself 10/10 for this activity because it took me half my day to do the predicted images and the other half for checking my results in scilab. Also because I had a hard time convincing other people and myself that some of my predicted images are correct. ;)

I want to thank April, Beth and Rica for helping me in this activity,

Reference:

A8 - Morphological Operations hand-out