ABSTRACT
According to the Merriam-Webster dictionary, transform in its broadest sense means “change in the external form or in the inner nature.” Continuing, mathematical transform means: “to change to a different form having the same value.” In this chapter, we are focusing on the image transforms. Usually, an image is represented as a function of two spatial variables x y( , ) and represented as f x y( , ). The intensity at a particular point in an image is the value taken by the function f x y( , ) at that spatial location. This domain of representation is most common for image storage and display. Since an image is a representation in space through spatial coordinates, domain is termed as the spatial domain. The term image transform refers to the mathematical process of converting and representing an image into its alternative form. For example, an image can be represented as a series summation of sinusoids with varying degree of magnitude and frequencies by the cosine transform. This alternative representation of an image is known as frequency domain. A typical transformation process between spatial and frequency domain is shown in Figure 3.1.
