Image_Processing--Fundamentals

This book is the result of 11 years of teaching the subject to the students of Surrey

University studying for an MSc degree in Signal Processing and Machine Intelligence.

As the subject of Machine Intelligence has mushroomed in recent years, so it has

attracted the interest of researchers from as diverse fields as Psychology, Physiology,

Engineering and Mathematics. The problems of Machine Intelligence may be tackled

with various tools. However, when we have to perform a task using a computer, we

must have in mind the language a computer understands, and this language is the

language of arithmetic and by extension mathematics. So, the approach to solving

the problems of Machine Intelligence is largely mathematical. Image Processing is the

basic underlying infrastructure of all Vision and Image related Machine Intelligence

topics. Trying to perform Computer Vision and ignoring Image Processing is like

trying to build a house starting from the roof, and trying to do Image Processing

without mathematics is like trying to fly by flapping the arms!

The diversity of people who wish to work and contribute in the general area of

Machine Intelligence led me towards writing this book on two levels. One level should

be easy to follow with a limited amount of mathematics. This is appropriate for newcomers

to thef ield and undergraduate students. Thes econd level, more sophisticated,

going through the mathematical intricacies of the various methods and proofs, is appropriate

for the inquisitive student who wishes to know the “why” and the “how”

and get at the bottom of things in an uncompromising way. At the lower level, the

book can be followed with no reference made at all to the higher level. All material

referring to the higher level is presented inside grey boxes, and may be skipped.

The book contains numerous examples presented inside frames. Examples that refer

to boxed material are clearly marked with a B and they may be ignored alongside

the advanced material if so desired. The basic mathematical background required

by the reader is the knowledge of how to add and subtract matrices. Knowledge of

eigenvalue analysis of matrices is also important. However, there are several fully

worked examples, so that even if somebody is hardly familiar with the subject, they

can easily learn the nuts and boltso f it by working through this book. This approach

is also carried to the stochastic methods presented: one can start learning from the

basic concept of a random variable and reach the level of understanding and using

the concept of ergodicity.

I would like to take this opportunity to thank the numerous MSc students who

over the years helped shape this book, sometimes with their penetrating questions,

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xvi Image Processing: The Fundamentals

and sometimes with their seemingly naive(!) questions. However, there are no naive

questions when one is learning: the naivety is with those who do not ask the questions!

My students’ questions helped formulate the route to learning and gave me the idea

to present the material in the form of questions and answers.

Writing this book was a learning process for Panagiota and me too. We had

a lot of fun working through the example images and discovering the secrets of the

methods. One thing that strucuks as most significant was the divergence betweent he

continuous and the discrete methods. An analytically derived formula appropriate for

the continuous domain often has very little to do with the formula one has to program

into the computer in order to perform the task. This is very clearly exemplified in

Chapter 6 concerned with image restoration. That is the reason we demonstrate all

the methods we present using small, manageable discrete images, that allow us to

manipulate them “manually” and learn what exactly the computer has to do if a real

size image is to be used. When talking about real size images, we would like to thank

Constantinos Boukouvalasw ho helped with the programming of some of the methods

presented.

Finally, I would also like to thank my colleagues in the Centre for Vision, Speech

and Signal Processing of Surrey University, and in particular the directoJro sef Kittler

for all the opportunities and support he gave me, and our systems manager Graeme

Wilford for being always helpful and obliging.

Maria Petrou