We begin with opening operation. Opening: Opening is basically erosion followed by dilation.

D( E(A))= ( A⊖ B )⊕B

Here A is the image and B is the structuring element.

We begin with erosion.

Erosion = minimum { A(x-i, y-j) x B(i, j)}

We now dilate this image eroded image,

Dilation = maximum { A(x-i, y-j) x B(i, j)}

Closing: Closing is basically dilation followed by erosion.

E( D(A) ) = ( A ⊕ B ) ⊝ B

Here A is the image and B is the structuring element.

We begin with erosion.

Dilation = maximum { A(x-i, y-j) x B(i, j)}

We now dilate this image eroded image,

Erosion = minimum { A(x-i, y-j) x B(i, j)}