A little forewarning before we dive into the figures down below. If you’re a loyal reader of this blog, you might notice later on that figure numbers aren’t present here. Forgive me for that but I really wasn’t in the mood to keep track of such a large number. I also thought it wouldn’t be pretty to have a Figure 24 (hypothetically). Also, I’m not including a copy of my Scilab codes for this report because (i) there are too many figures as it is and (ii) it’s quite simple and not an object of awe.
The morphology of an object refers to its shape or structure. From the name itself, morphological operations are operations that vary the structure of an object. Binary images are composed of pixels that may only have two possible values – 0 and 1. The former refers to the background of an image while the latter refers to the foreground.
For this activity, we first give an extensive look into the dilate and erode morphological operations. These two, mathematically, can be stated as:
Equations for Dilation and Erosion, respectively.
Basically, the results of a dilation is an image that is the union of two images with respect to the origin of the second image. On the other hand, the erosion is looks similar to the first image just with the intersections (again with respect to the second image’s origin) removed. Four images were to be dilated and eroded by five different structuring elements. For each pairing, we were tasked to give a prediction before using the corresponding Scilab functions.
Four binary images to be dilated and eroded. A (A1) 5x5 square, (A2) a triangle with base 4 and height 3, (A3) a hollow 10x10 square with a 2 pixel thickness and (A4) a 5x5 cross
Four structuring elements to be used in the dilation and erosion process.
From left to right, a (B1) 2x2, (B2) 2x1, (B3) 1x2, (B4) 3x3 cross and (B5) diagonal matrix of 1’s.
Before you get confused, the two rows of structuring elements represent the two methods I used in my predictions. I’d like to call the first a non-origin-based prediction and the second, an origin-based prediction. The non-origin based prediction allows any of the structuring element’s points to interact with the binary image whilst the opposite was set for the origin-based prediction. I have two methods because the first was taught by Mr. Timothy Joseph Abregana which I followed for a while. Upon seeing that my results varied from Ms. Eloise Anguluan’s, I asked her to explain her process to me. Because these two methods gave different results, I wanted to see which one gave the right (or at least closest to the right) results. From the results below the non-origin based prediction (a.k.a. Method 1) is less accurate as compared to the origin-based prediction (a.k.a. Method 2).
For the predictions, the light blue represents the original image while the purple pixels represent the areas changed by the morphological operation. In the case of dilation, the purple pixels are added to the image as a whole and thus, the final image a person should see was the combination of the two color pixels. On the other hand, the erosion predictions are quite different. The person should only see the light blue pixels as the purple pixels – the ones changed by the said morphological operation – are removed from the image itself. I attempted to aid the visibility for the Scilab results by placing them all in front of a light blue background (because it goes with the colors for the prediction and we can’t have clashing colors now, can we?).
From top to bottom, predictions using Method 1 and 2 and the results of the Scilab simulation.
From left to right, the original image A1 and the corresponding results for the dilation with B1, B2, B3, B4 and B5, respectively.
From top to bottom, predictions using Method 1 and 2 and the results of the Scilab simulation.
From left to right, the original image A2 and the corresponding results for the dilation with B1, B2, B3, B4 and B5, respectively.
From top to bottom, predictions using Method 1 and 2 and the results of the Scilab simulation.
From left to right, the original image A3 and the corresponding results for the dilation with B1, B2, B3, B4 and B5, respectively.
From top to bottom, predictions using Method 1 and 2 and the results of the Scilab simulation.
From left to right, the original image A4 and the corresponding results for the dilation with B1, B2, B3, B4 and B5, respectively.
From top to bottom, predictions using Method 1 and 2 and the results of the Scilab simulation.
From left to right, the original image A1 and the corresponding results for the erosion with B1, B2, B3, B4 and B5, respectively.
From top to bottom, predictions using Method 1 and 2 and the results of the Scilab simulation.
From left to right, the original image A2 and the corresponding results for the erosion with B1, B2, B3, B4 and B5, respectively.
From top to bottom, predictions using Method 1 and 2 and the results of the Scilab simulation.
From left to right, the original image A3 and the corresponding results for the erosion with B1, B2, B3, B4 and B5, respectively.
From top to bottom, predictions using Method 1 and 2 and the results of the Scilab simulation.
From left to right, the original image A3 and the corresponding results for the erosion with B1, B2, B3, B4 and B5, respectively.
I mentioned earlier that there were two other morphological operations that this activity asked us to look into. If you ask me, the skel function makes things more groovy and the thin function makes things look like they were drawn by a two-year-old. Kidding! Those morphological operations don’t really do that. As you can see below, the skel function draws the skeleton of an image using numerous lines and the thin function reduces an image to minimally connected strokes.
Image to undergo skel and thin morphological operations.
From top to bottom and left to right, Result of skel morphological operation – exterior, interior and both.
Result of thin morphological operation.
I honestly spent most of yesterday (July 27) on this and even though I had the whole day to finish it, I wasn’t able to do so. Most of that had to do with my complete shading of my predictions for both methods and with that, I have to thank Ms. Aven Perez (Hi, roommate!) for volunteering to shade. With all the effort I placed into this activity, I think I deserve an eleven out of a ten, yes?
SOURCES:
A9 – Morphological Operations 2011, Applied Physics 186 Manual
Scilab Help
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