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BOOK

    Symbolic Computing - Signal and Image Processing, Edition 2

    Pentagram Research Publications, 2009, Hyderabad, Andhra Pradesh, India

Authors

 

 E. G. Rajan

 Principal

 Sagar Institute of Technology, Chevella, Hyderabd, India

 Chairman, Pentagram Group of Companies, India

 

 G. Sathya

 Research Engineer

 Pentagram Research Centre Pvt Limited, Hyderabad, India

Preface

Om. Acharya poorva roopam; Anteyvas uttara

roopam; Vidya sandhi; Pravachanam sandhanam

 

(Om. Teacher is like a first syllable; Student is like a second syllable; Education is like the join of the two syllables; Guidance is like the grammar that allows the join of two syllables in order to evolve a meaningful word)

Shikshavalli, Taitiriya Upanishad

The purpose of this book 

This book gives the reader a first-time exposure to certain ideas and concepts related to non-numerical signal and image processing. The material covered here has been the result of many years of fundamental research carried out with the purpose of evolving a logico-mathematical framework for symbolic computing. This book provides certain latest technologies that may serve as a repertoire of tools that are of significant use in formulating DNA computing paradigms. Much care has been taken while preparing the manuscript so that it is useful to a wide spectrum of readers. Consequently, this book has been organized to ensure that the reader understands every concept without the need of any cross-reference. At the same time the scientific rigor has been kept in tact. The content is self-explanatory, covering all the basic fundamentals. Some of the already published research work due to the author has also been inserted at appropriate places in order to give research flair to the readers. The intension of the author is to present this as a reference book. In fact, this book is an outcome of a number of classroom experiments and relevant courses taught by the first author in the department of Electrical Engineering of the Indian Institute of Technology, Kanpur, India and invited seminars and institute lectures offered at various elite universities in the United States of America. Though the book is meant for scientists working in R & D organizations and Academic Institutions, students from universities, people with different background like employees, Researchers and of course a Common Man too can read this book. People working in medical and genetic science also will find this book very useful since the techniques discussed in the book have a direct bearing on certain applications related to medicine and biology like bioinformatics. No prerequisite knowledge is required to go through this book. 

Organization of the book 

This book consists of 27 sections divided into seven parts (i) Symbolic Signal Processing,  (ii) A Language Theoretic Approach to Signal Processing, (iii) Theory of Constructive Signal Processing, (iv) Symbolic Image Processing, (v) Theory of Constructive Image Processing,  (vi) Applications of Cellular Logic Array Processing and (vii) Constructive  Techniques for Machine Vision and Pattern Recognition. The first part deals with certain relevant details about the notion of a normal algorithm and its generalization and the basic techniques involved in implementing non-numerical signal processing operations using normal algorithms. The purpose of the second part is to introduce a formal language and a special automaton for the study of constructive (normal algorithmic) signal processing systems. Part III provides a compressive introduction to symbolic processing of digital images using Cellular Logic Algorithms. A cellular logic algorithm is essentially a realization of a Cellular Automaton by a Generalized Markov Algorithm. With images treated as arrays of symbols, which we refer as Array configurations, from an alphabet A, our concern is to consider the realization of various pattern generating and image processing operations in terms of pattern matching and substitution operations using cellular automata rules. The fourth part of the book describes various application areas and certain important outcomes of our own research in symbolic processing of signals and images. The fifth part describes the notion of geometric filter and its relevance in the processing of digital images. The sixth part of this book provides case studies of solidification process modeling, unidirectional fluid flow modeling, an interactive image processing language for the study of laser scanned data of metal surfaces and modeling of collision processes. The seventh part deals with computationally powerful tools like Rajan Transform and Set Theoretic Rajan Transform. In addition, it provides high throughput video image understanding system and its applications to machine vision based robot control through IP and more specifically to space and security. 

About the contributors 

This book has been brought to this form due to the efforts of a team of students of the first author. Contribution due to the second author has been compiled in five sections of part 7. Many of the undergraduate and graduate students of the first author have been the driving force behind this book-writing project. They were involved in collecting literature from almost all possible sources, in criticizing our lecture notes and in preparing the soft copy of the material.

About the supporting organizations           

Pentagram Research Centre (P) Ltd. Hyderabad was the major supporter for this project in extending technical, materialistic and logistic support to us in a very big way. The International School For Information Technology of Dr. Swaminadhan Research foundation, National Institute of Research and Social Action, Hyderabad was kind enough to support us in every possible way. Surya Academy, Chennai played a great role in extending various technical information related to Information Technology. M/s Pentagram Research Publications, Hyderabad was solely responsible in extending materialistic and financial support in brining out this book in this form.

 About individuals           

Thanks are due to Mrs. G. Chitra, the Managing Director of Pentagram Research Centre Private Limited, Hyderabad for her untiring support in the form of infrastructure, funding and constant encouragement. Thanks are due to Dr. T. D. Bhatt, Dr. M. Ekambaram Naidu, Dr. Md. Yusuf Mulge, Dr. Ramesh Chandra, Dr. E. Nagabhooshanam, Dr. Satyanarayana Sarma, Dr. Claudio Moraga, Dr. Klaus Dieter Lukoschus, Dr. Manish Prateek, Dr. Ajay Shankar Singh, Dr. Alexander Ya Kaplan, Dr. G. Ramamurthy, Dr. Anthony Constantinides, Dr. S. C. Dutta Roy, Dr. Virendra Pratap Sinha, Dr. Himanshu Agrawal, Dr. Walter Murray Wonham, and Dr. Dirk van Dalen for their very valuable criticism on part or whole of the material covered in this book. The whole manuscript was edited by a big team and the role played by Dr. K. Promod Sankar is highly commendable.

E. G. Rajan

Chairman, Pentagram Group of Companies, Hyderabad , India

Fellow, Institution of Engineers, India

Director, International School of Information Technology, NIRSA, Hyderabad

Principal, Sagar Institute of Technology, Chevella, Hyderabad, India

G. Sathya

Research Engineer, Pentagram Research Centre (P) Limited, Hyderabad, India

Place: Hyderabad

Date:  June 2009

Contents 

Sections

Topics

Page

 

Part I

 

 

Symbolic Signal Processing

 

1

Non-numerical Representation and Processing of Signals and Images

001

2

Normal Algorithms

011

3

Normal Algorithms for Implementing Non-numerical Signal Processing Operations

025

4

Realization of Certain Normal Algorithmic Signal Processing Operations

037

 

Part II

 

 

A Language Theoretic Approach to Signal Processing

 

5

Study of Normal Algorithmic Signal Processing Systems in Terms of Formal Languages

Generated by a Grammar

077

6

Special Automata for Normal Algorithms and Their Transcriptions

099

 

Part III

 

 

Theory of Constructive Signal Processing

 

7

The Logic of Constructive Signal Processing

125

8

Homomorphisms in the Theory of

Constructive Signal Processing

137

9

A Constructive Reformulation of Extended Topological Filters

147

10

Quantifiable Measures of Constructive Extended Filters in Terms of Normal Algorithmic Operators

175

 

 Part IV

 

 

Symbolic Image Processing

 

11

Cellular Automata and Their Realizations

183

12

Normal Algorithmic Realization of Cellular Automata

211

13

Pattern Generation

231

14

Image Processing

245

15

Cellular Logic Array Processing of Digital Images on a Hexagonal Grid

287

 

Part V

 

 

Theory of Constructive Image Processing

 

16

On the Notion of a Geometric Filter and Its Relevance in the Neighborhood Processing of Digital Images

297

17

Pextral Coding of Digital Images

313

 

Part VI

 

 

Applications of Cellular Logic Array Processing

 

18

Research Areas  Related to Symbolic Processing of Signals and Images

319

19

Thinning Lattice Gas Automaton Model for Solidification Process

345

20

Cellular Automata Modeling of Unidirectional Fluid Flow

351

21

Cellular Logic Array Processing of  Laser Scanned

365

22

Modeling of Collision Processes

371

 

Part VII

 

 

Constructive Techniques for Machine Vision and Pattern Recognition

 

23

Rajan Transform and Its Applications to Computer Vision and Pattern Recognition

387

24

Set Theoretic Rajan Transform and Its Applications to the Study of Constructive Extended Filters

398

25

Machine Vision Based Control of Autonomous Mobile Systems over IP

417

26

High Throughput Video Image Understanding Systems Using Cellular Logic Array Processing

427

27

Space and Security Applications of Video Image Understanding Systems

449

 

References

457

 

Index

461

 

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