There are two different types of operations that are widely used in image processing especially in image morphology.

Arithmetic Operations

Arithmetic operations between two pixels a and b are denoted as follows:

i) Addition: a + b

Image addition is used in image averaging to reduce noise. This kind of operation was performed in image enhancement.

ii) Subtracting: a - b

Image subtraction is widely used in medical imaging. A very common example is the Digital Subtraction Angiography (DSA).

Image Subtraction is basically used to get rid of background information.

iii) Image multiplication: a × b

iv) Image division: a/b

Both, Image Multiplication and Image Division are used to correct grey level shading that result from non-uniformities in illumination or in the sensor used.

One thing that needs to be understood in arithmetic operations is that these are carried out on an entire image, pixel by pixel. Arithmetic operations involve only one spatial pixel location at a time and hence can be done in place. Arithmetic operations are applied to multi-valued pixels.

Logical Operations

Logical operations commonly used are as follows:

a) AND : a AND b

b) OR : a OR b

c) COMPLEMENT : NOT a

These operations can be combined to form other logic operations. Logic operations actually apply only to binary images. (Image having only two values, 0 and 1).

The AND operator gives out 1 only when both ‘a’ and ‘b’ are equal to 1.

Figure 37

The OR operator gives out 1 if either ‘a’ or ‘b’ or both are equal to 1.

Figure 38

The COMPLEMENT (NOT) operator gives out 1 when a = 0

Figure 39

The AND operator applied on sets A and B is also denoted in the jargon of set theory as

C = A $\bigcap$ B

i.e., C is the intersection of A and B. Similarly, the OR operator applied on sets A and B is denoted as

C = A $\bigcup$ B

i.e., C is the union of A and B.