(i) Dilation (ii) Erosion (iii) Closing (iv) Opening

Dilation

Dilation is a process in which the binary image is expanded from its original shape. The way the binary image is expanded is determined by the structuring element.

This structuring element is smaller in size as compared to the image itself and normally the size used for the structuring element is 3x3.

The dilation process is similar to the convolution process i.e. the structuring element is reflected and shifted from left to right and from top to bottom and at each shift, the process will look for any overlapping similar pixels with structuring element and that at binary image. If there exists an overlapping then pixels under the centre position of the structuring element will be turned to 1 or black

Let us define X as reference image and B as the structuring element. The dilation operation is defined as
X xor B={Z|[(Ḃ)znx]}

Where Ḃ is the image B rotated about the origin.

Above equation states that when the image X is dilated by the structuring element B, the outcome element Z would be that there will be at least 1 element in B that intersects in X

Erosion

Erosion is the contour-process of dilation. If dilation enlarges on image then erosion shrinks the image.

The way the images shrunk is determined by the structuring element.

The structuring element is normally smaller than the image with a 3x3 size.

Almost similar to dilation process, the erosion process will move the structuring element from left to right and up to bottom.

At the centre position, indicated by the centre of the structuring element, the process will look for whether there is a complete overlap with the structuring element or not. If there is no complete overlapping then centre pixel indicated by the centre of the structuring element will be set white or zero.

Let us define X as the reference binary image and B as the structuring element. Erosion is defined by the equation
X xnor B = { Z | [(Ḃ)z x]

The above equation states that the outcome element Z is considered only when the structuring element is a subset or equal to binary image X

Dilation Erosion Best operation

<1> Opening

1) Opening is based on the morphological operations, erosion and dilation.

2) Opening smoothest the inside of the object contour, brakes narrow strips and eliminates thin portion of the image. It is done by 1st applying erosion and then dilation operations on the image.

3) The opening operation is used to remove noise and CCD detected in the image.

4) The opening filters details and simplifies images by rounding corners from inside objects where the kernel uses fits.

5) The opening process can be mathematically represented as X.B = (X exnor B) exor B Where X is an input image and B is the structuring element.

<2> Closing

1) The closing operation is the opposite of the opening operation. It is a dilation operation followed by an erosion operation.

2) The closing operation fills the small holes and gaps in a single-pixel object.’

3) It is has the same effect of an opening operation, in that it smoothes contours and maintains shapes and sizes of object.

4) The closing process can be mathematically represented as X.B = (X exor B) exnor B Where X is an input image and B is the structuring element.

5) Closing protects coarse structure, closes small gapes and round off concave corners.