# Digital Image Representation in Image Processing

An image can be defined as a 2D signal that varies over the spatial coordinates x and y and can be written mathematically a f(x,y).

In general, the image can be written as a mathematical function f(x,y) as a matrix of values, comprising of rows and columns.

The image f(x,y) is divided into X rows and Y columns. Thus, the coordinate ranges are x = {0, 1,......, X-1} and y = {0, 1,......, Y-1}.

The value of the function f(x,y) at every point indexed by a row and a column is called the **gray value** or intensity of the image. Generally, the value of the pixel is the intensity value of the image at that point.

The number of rows in the digital image is called **vertical resolution**. The number of columns in the digital image is called **horizontal resolution**. The number of rows and columns describes the dimensions of the image.

The number of bits necessary to encode the pixel value is called **bit depth**.

The set of all colors that can be represented by the bit depth is called the **gamut** or **palette**.

So, the total number of bits necessary to represent the image is equal to Number of rows x Number of columns x Bit depth.