image algebra

There are two primary categories of algebraic operations applied to image:
1. Arithmetic operation.
2. Logic operations.
Addition, subtraction, division and multiplications comprise the arithmetic operations, while AND, OR and NOT makeup the logic operations. These operations are done on a pixel –by-pixel basis.
To apply the arithmetic operations to two images, we simply operate on corresponding pixel values. For example to add image I1 and I2 to create I3:
• Addition is used to combine the information in two images. Applications include development of image restoration algorithm for molding additive noise and special effects, such as image morphing in motion pictures.
• Subtraction of two images is often used to detect motion consider the case where nothing has changed in a sense; the image resulting from subtraction of two sequential image is filled with zero-a black image. If something has moved in the scene, subtraction produces a nonzero result at the location of movement. Applications include Object tracking.
• Multiplication and Division are used to adjust the brightness of an image. One image typically consists of a constant number greater than one. Multiplication of the pixel values by a number grater than one will darken the image (Brightness adjustment is often used as a processing step in image enhancement).

• The logic operations AND, OR and NOT form a complete set, meaning that any other logic operation (XOR, NOR, NAND) can be created by a combination of these basic elements. They operate in a bit-wise fashion on pixel data.