Activity 8: Morphological Transforms

July 15, 2008 at 9:04 pm (Uncategorized)

Dilation and Erosion are morphological transform where we have a binary image (white/1 foreground and black/0 background). Dilation is mathematical defined as

where A is the image and B is called the structuring element where the dilation is based. In lay terms (or in more comprehensible terms), Is the set that involves all z’s which are translations of a reflected B that when intersected with A is not the empty set. This can be illustrated as

On the other hand, erosion is mathematically defined as

or in more comprehensible terms,  is  the set  of 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. This can be illustrated as

(based on Dr Soriano’s lecture)

In this activity, we used different images (circle, square, hollow square, triangle and cross) and varying structuring elements shown here:

The results of the morphological transform are shown below. The code is

se1=ones(4,4); //square
se2=ones(2,4); //rectangle
se3=ones(4,2); //rectangle
se4=[0 0 1 0 0; 0 0 1 0 0; 1 1 1 1 1; 0 0 1 0 0; 0 0 1 0 0]; //cross

im=imread(‘cross.PNG’);
im=im(:,:,1);
er1=erode(im, se1, [1,1]);
er2=erode(im, se2, [1,1]);
er3=erode(im, se3, [1,1]);
er4=erode(im, se4, [3,3]);

di1=dilate(im, se1, [1,1]);
di2=dilate(im, se2, [1,1]);
di3=dilate(im, se3, [1,1]);
di4=dilate(im, se4, [3,3]);

scf(1);
subplot(2,2,1);
imshow(se1);
subplot(2,2,2);
imshow(se2);
subplot(2,2,3);
imshow(se3);
subplot(2,2,4);
imshow(se4);

scf(2);
subplot(2,2,1);
imshow(er1);
subplot(2,2,2);
imshow(er2);
subplot(2,2,3);
imshow(er3);
subplot(2,2,4);
imshow(er4);

scf(3);
subplot(2,2,1);
imshow(di1);
subplot(2,2,2);
imshow(di2);
subplot(2,2,3);
imshow(di3);
subplot(2,2,4);
imshow(di4);

Circle Dilation

Circle Erosion

Cross

Cross Dilate

Cross Erode

hollow

Hollow Dilate

Hollow Erode

Square

Square Dilate

Square Erode

Triangle

triangle dilate

triangle erode

I will give my self 10 pts here since the actual and predicted are in good correspondence.

Thanks to Julie and JC for the help. 🙂