Morphological Operations

Morphology refers to the study of shapes, forms and structures. Classically, morphological operations are done on binarized images. By applying different morphological operations, the images were modified. The were a lot of possible outcome on the image, may be narrowed, widened, hole may be filled or connected blobs may be separated.

Some of the morphological operations were erosion and dilation.

Erosion operator is defined by

The product of the erosion is to reduce the image A by the shape of B. The image should obviously be narrower or thinner.

Dilation operator is defined by

The product of the dilation is to expand the image A by the shape of B. The image should obviously be thicker or wider.

The images to be applied with morphological operations are as follows:

1. A 5×5 square
2. A triangle, base=4 boxes, height=3 boxes
3. A hollow 10×10 square, 2 boxes thick
4. A plus sign, one box thick, 5 boxes along each line

The structuring elements to be used, on the other hand, were the following

1. 2×2 ones
2. 2×1 ones
3. 1×2 ones
4. cross, 3 pixels long, one pixel thick
5. A diagonal line, two boxes long

Erosion and Dilation results

The set of erosion and dilation results includes the one done by hand (graphing paper images) and the other using Scilab functions.

Erosion and dilation of a 5×5 square by the set of structuring elements

Erosion and dilation of a triangle, base=4 boxes, height=3 boxes by the set of structuring elements

Erosion and dilation of a hollow 10×10 square, 2 boxes thick by the set of structuring elements

Erosion and dilation of a plus sign, one box thick, 5 boxes along each line by the set of structuring elements

The predicted result were all matched with the code-simulated result. With this I give myself a grade of 10/10 by accomplishing all the required output.

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[1] Soriano, M. "Morphological Operations." AP 186 Laboratory Manual. National Institute of Physics, University of the Philippines, Diliman. 2013.