morphological image processing

Question 1

Explain the morphological operation of erosion and describe their use in image processing.

Answer 1

The erosion of A (image) by set B (structuring element) is defined as A ⊖ B = {x|(x + b) ∈ A for every b ∈ B}
The structuring element B is positioned with its origin at a location in the image and the new pixel value at that location determined as:
- 1 (on) if B fits A
- 0 otherwise

Question 2

Explain the morphological operation of dilation and describe their use in image processing.

Answer 2

The dilation of A (image) by set B (structuring element) is defined as
A ⊕ B = {x|x=a+b for some a ∈A and b∈B}
The structuring element B is positioned with its origin at a location in the image and the new pixel value at that location determined as:
- 1 (on) if B hits A
- 0 otherwise

Question 3

Explain morphological opening.

Answer 3

Morphological opening combines erosion and dilation (compound operator).
Opening is equivalent to erosion followed by dilation with the same structuring element.
A ∘ B = (A⊖B) ⊕ B.
There is morphological shrinking followed by morphological expansion.

Question 4

Explain morphological closing.

Answer 4

Morphological closing combines dilation and erosion (compound operator).
Opening is equivalent to dilation followed by erosion with the same structuring element.
A • B =(A⊕B)⊖B.
There is a morphological expansion followed by morphological shrinking.

Question 5

Closing is not the inverse of…

Answer 5

Opening

Question 6

Opening is not the inverse of…

Answer 6

Closing.