What is an image and how it is stored on a computer

Conceptually, an image in its simplest form (single-channel; for example, binary or mono-chrome, grayscale or black and white images) is a two-dimensional function f(x,y) that maps a coordinate-pair to an integer/real value, which is related to the intensity/color of the point. Each point is called a pixel or pel (picture element). An image can have multiple channels too (for example, colored RGB images, where a color can be represented using three channels—red, green, and blue). For a colored RGB image, each pixel at the (x,y) coordinate can be represented by a three-tuple (r_x,y, g_x,y, b_x,y).

In order to be able to process it on a computer, an image f(x,y) needs to be digitalized both spatially and in amplitude. Digitization of the spatial coordinates (x,y) is called image sampling. Amplitude digitization is called gray-level quantization. In a computer, a pixel value corresponding to a channel is generally represented as an integer value between (0-255) or a floating-point value between (0-1). An image is stored as a file, and there can be many different types (formats) of files. Each file generally has some metadata and some data that can be extracted as multi-dimensional arrays (for example, 2-D arrays for binary or gray-level images and 3D arrays for RGB and YUV colored images). The following figure shows how the image data is stored as matrices for different types of image. As shown, for a grayscale image, a matrix (2-D array) of width x height suffices to store the image, whereas an RGB image requires a 3-D array of a dimension of width x height x 3:

The next figure shows example binary, grayscale, and RGB images:

In this book, we shall focus on processing image data and will use Python libraries to extract the data from images for us, as well as run different algorithms for different image processing tasks on the image data. Sample images are taken from the internet, from the Berkeley Segmentation Dataset and Benchmark (https://www2.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/BSDS300/html/dataset/images.html), and the USC-SIPI Image Database (http://sipi.usc.edu/database/), and many of them are standard images used for image processing.