Digital Image Interpolation in Matlab

5 Transform Domain

We have discussed in Chapter 2 that an image can be represented by the function with two indexing variables that specify the spatial location, while the magnitude of the function at is the light intensity of the image at that spatial location. In this case, the function is said to be defined in the spatial domain. Besides the spatial domain, image can also be represented in other domains. The operation that converts the image representation from one domain to another is known as “transformation.” According to the Oxford dictionary, transform means “change in form or nature.” Mathematically, the word transform has been adopted to mean “to change to different form while having the same value.” A more vigorous definition of image transformation can be given to describe the mathematical process of converting and representing an image into its alternative form that usually means representing the image using an equivalent set of functions in a different domain. For example, an image can be represented as sums of series of 2D sinusoids with varying degree ...