Activity 7: Morphological Operations

In preparation for an extreme ultra-CSI episode that’ll be up next after this activity, we have to familiarize ourselves with another technique in image processing that will be handy in future use.

The word Morphology already gives you a faint idea that it deals with shapes and structures. Morphological operations are commonly used on images to enhance, isolate, and improve its details. However, these operations are carried out only on binary images with its elements lying on a 2-dimensional space.

A quick review of the set-theory is needed as this serves as the main rules of our operations. The image below will serve as our reference point. The following elements can be seen:

Set A – pink box, Set B – purple box, C – region within the green blue outline, Set D – yellow box, and the elements butterfly and running man.

• The butterfly is an element of Set A whereas the running man is not.
• The complement of D are all the elements outside it (Set A, butterfly, doorman and the whole region of B that is not within D).
• Set D is a subset of Set B.
• C is the intersection of Sets A and B.
• The union of Set A and B is the whole pink and purple regions together.
• The difference of Set A and B is the whole pink region excluding those within the blue green outline.

In addition, translation is simply the shifting of the element to another point.

For the morphological operations to work, two images or sets are required. The main pattern will serve as the image we hope to increase/decrease its size. The structuring element on the other hand will serve as our basis on how much will the original pattern change and as to how it will change.

Dilation – Super Size Me!

With your structuring element having a set origin (where this is where we will be placing an element if certain cases are met), this is translated to every point of the main pattern. The points at which at least a single element of your structuring element intersects with your main pattern, the origin will turn into an element of the dilated set.

A larger structuring element will then result to a larger output. If in case a single pixel is considered as your structuring element, we will end up with the exact image as our main pattern.

Erode – The Biggest Loser!

As for the case of the erode operation, the resulting image will be smaller as compared to the original image. This is because this operation considers the points at which your structuring element fit inside your main pattern.

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To start of with the activity, we first have to determine the images we want to apply the operations. As indicated earlier, there should be two inputs involved: the main pattern by which we will be eroding / dilating and the structuring element which will be the basis as to how much will the original pattern be eroded/dilated.

For the main pattern, four different shapes were used as drawn below:

(L-R): A 5×5 square, a triangle with 4 units as its base and 3 units as its height, a cross that has a length of 5 units for each strip and lastly a hollow 10×10 square that has a width of 2 units.

The structuring elements on the other hand are as shown below:

(L-R): A 2×2 square, 1×2 square, 2×1 sqaure, 1’s at the diagonal of 2×2

Going old-school:

Before taking advantage of the gifts of technology, we are to test if we have really understood the concepts behind the dilate and erode morphological operations by going old-school. Through the use of a graphing paper and a marker, the resulting shape as our main patterns are eroded for a chosen structuring element is predicted and drawn.

Starting with erode, we are to expect that the shapes would be smaller as compared to the original pattern. The matrix of images below shows that I have managed to get shapes that are indeed smaller. In fact, there are instances wherein the original pattern is totally removed! This is expected for certain shapes as the erode operation deals with points at which your structuring element perfectly fits the main pattern. Take for example the case of cross main pattern where the 2×2 box structuring element is impossible to embed as the width of the cross is only 1 unit! Hence, the resulting eroded shape is nothing.

Erode Matrix of Images (Theoretical)

In contrast, dilating the shape results to a relatively larger pattern which I have managed to observe from my predictions. With the dilate function considering the points at which the structuring element still overlaps on the main pattern even if the overlap is only a single pixel.

Dilate Matrix of Images (Theoretical)

Consistency please?

Knowing what we are to expect upon dilating and eroding all our patterns and structuring elements together, it’s time to find out if my predictions are correct.  The operations can be carried out in Scilab as readily available functions for morphological operations are present in the SIP and IPD toolbox.

With the sudden death of my Ubuntu system, I have finally accepted defeat and opted to download the Scilab 4.1.2.. This version of Scilab matches the last version of the SIP toolbox amidst having lots of flaws such as being unable to run .sce’s so I usually end up typing my codes in notepad and pasting them on the prompt.

Through the use of Photoshop, I recreated the main patterns as well as the structuring elements as observed below:

Main Patterns

Structural elements

The important thing to take note in creating these patterns is the consistency of the scale of your units. Initially, I downloaded a graphing paper page from the internet and used this as the basis in creating my patterns. However, upon eroding and dilating them, the results produced images that seemed to not fit the units that I have! I had to redo my patterns again using  3×3 pixels as a single unit.

Now after calling all our patterns into scilab through the imread() function, it is best to ensure that the matrix of your patterns is strictly binary and not in grayscale (afterall, we are talking about binary operations!). This can be easily done by the im2bw() function with my threshold point set to be at 0.7.

The erode() function calls for two inputs: the matrix of the image you wish to erode and the structuring element. Using this through all our patterns gives rise to the matrix of images below:

Eroded Images through Scilab

Comparing this matrix to my matrix of images of old-school eroded patterns, I am glad to say that they are exactly the same! The only difference between the two are their scaling.

Similarly, the matrix of image for the dilated images show that the digitally dilated images as well as my predictions are the same.

Dilated images through Scilab

Personal Note:

Despite getting the right results from my predictions, it took quite awhile before I managed to fully understand and master the art of eroding and dilating. I had the hardest time taking to heart the process of dilation and it was all thanks to Mr. Xavier Tarcelo that I finally figured it out through the use of an acetate in which I had to move box per box on my graphing paper.  For this activity, I would like to give myself a grade of 10/10 as I have managed to accomplish all the requirements in the activity as well as understand the techniques and concepts.

 

References:

1. Soriano, Jing. Applied Physics 186  Activity 7 – Morphological Operations. NIP, UP Diliman. 2012.