Image Processing

Yujin Zhang, Tsinghua University Press

• Publisher: De Gruyter
• Year: 2017
• ISBN:
  9783110524222
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Signals & Signal Processing
• Index: Technology & Engineering

This graduate textbook explains image geometry, and elaborates on image enhancement in spatial and frequency domain, unconstrained and constrained restoration and restoration from projection, and discusses various coding technologies such as predictive coding and transform coding. Rich in examples and exercises, it prepares electrical engineering and computer science students for further studies on image analysis and understanding.

1Introduction to Image Processing

This book is the first volume of the book set “Image Engineering” and is focused on image processing.

Image processing has been developed for many years. In its broad sense, image processing comprises a number of techniques for treating images to obtain information from image. With the research and application of image technology, a more suitable term used is image engineering. Image engineering refers to a new discipline comprising all subjects relating to images, in which image processing (in its narrow sense) is an important part. This chapter provides an introduction to image processing, an overview of image engineering, and an outline of this book.

The sections of this chapter are arranged as follows:

Section 1.1 introduces the basic concepts and terms of image and its expression (including image representation and display form). A general representation of image is also discussed.

Section 1.2 provides a complete introduction to the field of image engineering. Image engineering currently includes three levels (image processing described in this book is the first level). It has a number of closely related disciplines, and has a wide range of applications. For a comprehensive understanding of the development and current situation of image engineering, some statistical data of image engineering literature, such as the number of papers published each year in a number of journals for the past more than 20 years, the categorization of there papers in 5 classes and further in 23 sub-classes, and the distribution of there papers in these classes and sub-classes, etc. are also presented and analyzed.

Section 1.3 describes the principal modules in the framework and system for image processing. This book mainly focuses on the principles, approaches, and algorithms of image processing. This section summarizes some peripheral knowledge and equipment of image processing, laying the foundation for later chapters to focus purely on image processing techniques.

Section 1.4 overviews the main contents of each chapter in the book and indicates the characteristics of the preparation and some prerequisite knowledge for this book.

1.1Basic Concepts of Images

Images are an important medium by which human beings observe the majority of the information they receive from the real world.

1.1.1Images and Digital Images

Images can be obtained by using different observing and capturing systems from the real world in various forms and manners. They can act, directly and/or indirectly, on human eyes and produce visual perception. The human visual system is a typical example of an observation system, from which humans perceive and recognize objects and scenes by observing and remembering their images.

The real world is three-dimensional (3-D) in space. However, the images obtained from the real word are generally two-dimensional (2-D). Such a 2-D image, in most cases, is a 2-D light intensity function (2-D light pattern). An image can be represented by a 2-D array f(x, y), where x and y are spatial coordinates and f is the amplitude at any pair of coordinates (x, y) representing certain properties of the scene projected on the image at that particular point. For example, in an image recording the brightness of scene, the amplitude f is proportional to the intensity of the image. In general, the amplitude f is proportional to one or several attributes of the image. For a real image, the values of x and y as well as f are real values, which are limited to a certain range.

Mathematically, an image can be explained as a function f(x, y) with two variables. For the purpose of processing by computers, an analog image f(x, y) should be digitalized to a digital image I(r, c), in which r (row) and c (column) refer to the discrete position of any point in the digital image and the amplitude I refers to the discrete magnitude of the image at point (r, c). Since this book mainly discusses digital images, f(x, y) is used to represent a digital image at any point (x, y) and f takes integer values only. A digital image can be considered a matrix whose rows and columns refer to the position of any point in the image and the corresponding matrix value refers to the intensity at that point.

In the early days, an image was called a “picture.” When a picture is digitized, a sampling process is used to extract from the picture a discrete set of real numbers. The picture samples are usually quantized to a set of discrete gray-level values, which are often considered to be equally spaced. The result of sampling and quantizing is a digital picture. It is assumed that a digital picture is a rectangular array of integer values. An element of a digital picture is called a picture element (often abbreviated as “pixel” or “pel”). Although nowadays the term “image” rather than picture is used, because computers store numerical images of a picture or scene, the element of an image is still called a pixel. The element of a 3-D image is called a voxel (volume element). When combined, it is called an imel (2-D/3-D image element).

In its general sense, the word “image” refers to all entities that can be visualized, such as a still picture, a video, an animation, a graphic, a chart, a drawing, and text. These entities can be 2-D, 3-D, or even higher dimensions.

1.1.2Matrix and Vector Representation

A 2-D image of M × N (where M and N are the total number of rows and the total number of columns of the image) can be represented either by a 2-D array f(x, y) or by a 2-D matrix F:

$F=\left[\begin{array}{cccc}{f}_{11}& f_{12}& \cdots & f_{1\mathrm{N}}\\ f_{21}& f_{22}& \cdots & f_{2\mathrm{N}}\\ ⋮& ⋮& \ddots & ⋮\\ f_{\mathrm{M}1}& f_{\mathrm{M}2}& \cdots & f_{\mathrm{M}\mathrm{N}}\end{array}\right]\left(1.1\right)$

The above matrix representation can also be converted to a vector representation. For example, the above equation can be rewritten as

$F=\left[f_1{f}_2\cdots f_{\mathrm{N}}\right]\left(1.2\right)$

where

$f_1={\left[f_{1i}{f}_{2i}\cdots f_{\mathrm{M}i}\right]}^{\text{T}}i=1,2,\cdots ,\mathrm{N}\left(1.3\right)$

Note that the array operation and matrix operations are different. Considering two 2 × 2 images f(x, y) and g(x, y) as an example, the array product is

$f\left(x,y\right)g\left(x,y\right)=\left[\begin{array}{cc}{f}_{11}& f_{12}\\ f_{21}& f_{22}\end{array}\right]\left[\begin{array}{cc}{g}_{11}& g_{12}\\ g_{21}& g_{22}\end{array}\right]=\left[\begin{array}{cc}{f}_{11}{g}_{11}& f_{12}{g}_{12}\\ f_{21}{g}_{21}& f_{22}{g}_{22}\end{array}\right]\left(1.4\right)$

And their matrix product is

$FG=\left[\begin{array}{cc}{f}_{11}& f_{12}\\ f_{21}& f_{22}\end{array}\right]\left[\begin{array}{cc}{g}_{11}& g_{12}\\ g_{21}& g_{22}\end{array}\right]=[\begin{array}{cc}{f}_{11}{g}_{11}+f_{12}{g}_{21}& f_{12}{g}_{12}+...\end{array}$

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• Contents
• 1 Introduction to Image Processing
• 2 Image Acquisition
• 3 Image Enhancement
• 4 Image Restoration
• 5 Image Reconstruction from Projections
• 6 Image Coding
• 7 Image Watermarking
• 8 Color Image Processing
• Answers to Selected Problems and Questions
• References
• Index