Part 2. SUBMISSION OF IMAGES IN A DIGITAL FORM Chapter 4. DISCRETIZATION AND RESTORATION OF CONTINUOUS IMAGES

In digital image processing, a continuous (analog) image is converted to an equivalent digital array. In this part of the book we consider the operations of discretization and quantization of the image, with the help of which such a transformation is carried out. Also described is the inverse operation, which allows a continuous image to be obtained from a digital array. Methods of vector representation of images for deterministic and random digital arrays are developed. In conclusion, the question of the quality of discretized images, associated with the introduction of criteria for the fidelity of their reproduction and deciphering, is considered.

Chapter 4. DISCRETIZATION AND RESTORATION OF CONTINUOUS IMAGES

Digital image processing systems usually receive arrays of numbers obtained by sampling a real image by spatial variables. After processing, new numerical arrays are formed, which are used to restore a continuous image, which is considered by a person. Image samples are obtained by measuring some of the physical characteristics of a real image, such as brightness or optical density. Any measuring device works with some kind of error. In order to evaluate the accuracy of the measured values ​​and create error compensation methods, it is important to have a mathematical model of measurement errors. In addition, it is often not possible to directly measure the characteristics of the original image and instead they measure some values ​​related to another image, which is a function of the original image. To determine the characteristics of the original image, this function has to be “reversed”. Similar handling operations are described in the section on image correction (restoration). This chapter discusses the processes of discretization and restoration of continuous images in relation to ideal and real systems.