Digital Image Representation

An image can be defined as f(x,y) where x,y is the spatial co-ordinatess and amplitude is the intensity of the image at that point. The term gray level is used often to refer to the intensity of the monochrome images. Color images are formed by a combination of individual 2-D images. For eg in the RGB color system, a color image consists of three (red, green, blue) individual component images. For this reason, many of the techniques developed for monochrome images can be extended to color images by processing the the three component images individually.

Digitizing the corordinate values is called as sampling, digitizing the amplitude values is called quantization. When x,y and the amplitude values of f are all finite, discrete quantities we call the image a digital image.

The result of sampling and quantization is a matrix of real numbers. Assume that an image f(x,y) is sampled so that the resulting image has M rows and N columns. We say that the image is of size M * N. The values of the coordinates (x, y) are discrete quantities.


A 1*N matrix is called as row vector, where as M*1 matrix is called a column vector. A 1*1 matrix is scalar.