Foundations of Image Science

Book Description

Winner of the 2006 Joseph W. Goodman Book Writing Award!

A comprehensive treatment of the principles, mathematics, and statistics of image science

In today’s visually oriented society, images play an important role in conveying messages. From seismic imaging to satellite images to medical images, our modern society would be lost without images to enhance our understanding of our health, our culture, and our world.

Foundations of Image Science presents a comprehensive treatment of the principles, mathematics, and statistics needed to understand and evaluate imaging systems. The book is the first to provide a thorough treatment of the continuous-to-discrete, or CD, model of digital imaging. Foundations of Image Science emphasizes the need for meaningful, objective assessment of image quality and presents the necessary tools for this purpose. Approaching the subject within a well-defined theoretical and physical context, this landmark text presents the mathematical underpinnings of image science at a level that is accessible to graduate students and practitioners working with imaging systems, as well as well-motivated undergraduate students.

Destined to become a standard text in the field, Foundations of Image Science covers:

Mathematical Foundations: Examines the essential mathematical foundations of image science

Image Formation–Models and Mechanisms: Presents a comprehensive and unified treatment of the mathematical and statistical principles of imaging, with an emphasis on digital imaging systems and the use of SVD methods

Image Quality: Provides a systematic exposition of the methodology for objective or task-based assessment of image quality

Applications: Presents detailed case studies of specific direct and indirect imaging systems and provides examples of how to apply the various mathematical tools covered in the book

Appendices: Covers the prerequisite material necessary for understanding the material in the main text, including matrix algebra, complex variables, and the basics of probability theory

Customer Reviews:

Tremendous Work and Very Clear.......2006-11-29

This is one of the few books that I will always treasure. Why? Because it is very clear. It has very very good discussions on everything it treats, and it treats a ton of material. In my engineering career, I have read or tried to read many many textbooks and this stands up as one of the absolute best. Barrett and Meyers give exquisite expositions on all of the mathematics necessary to study image science and many other related fields. For example, its treatment on probability, random processes, decision and estimation theory is actually better, more clear and more complete than many standard textbooks on the subject. If I get stuck reading any of them, I refer to this book and am saved.
I only wish they would issue it in two or three volumes. It is so ponderous (yet beautifully put together) if you carry it around you will get big muscles and get a good cardio workout!
I own it and leave it at home and I had the library at work get me a copy which I leave at work. If I want exercise I will go to my health club!
IT IS WORTH EVERY PENNY OF THE 146 BUCKS IT COSTS.
If you want a great textbook to learn this technology from dont hesitate to buy it. You may need two - one for home and one for work, if your company wont buy you one.
Really impressed.

Correction to the quotation from JEI.......2006-08-20

I was the reviewer for this book in the Journal of Electronic Imaging.

The quotation from my review in JEI as it appears on this site should read:

"...a worthwhile addition to the armamentarium of any serious researcher in image science and will be an oft-quoted reference for many years to come." (Journal of Electronic Imaging, April-June 2005)

The corrections pertains to the word, oft-quoted, which has, for some reason, appeared as "opt-quoted" on this site in addition to the reference, "Journal of Electronic Imaging" instead of "Journal of Electrical Imaging"

This book, of course, is outstanding as I have stated in my review in the JEI.

Extremely thorough and rigorous resource.......2006-02-10

This book always amazes me whenever I use it for the absolutely incredible amount of material that it covers in such depth. I had the tremendous good fortune to have taken a Physical Optics course with Prof. Barrett, and it would be impossible to believe that one person can know so much unless you have personally talked with him about science or had a class with him. The rumor in the department is that Dr. Barrett is the only professor to at one time or other have taught ALL of the department's core graduate courses during his career at the College of Optical Sciences. Furthermore, he is one of the rare scientists who is an authority in his field both theoretically and experimentally, so you do not get a one-sided perspective as can often happen with science texts. The book reflects his vast knowledge, expertise, rigor, and thoroughness.

Of course, the book has several chapters on mathematical formalism, including the linear algebra, dirac delta function, Fourier theory, and group theory. The imaging theory is there, as well as diffraction theory. He covers photon statistics and detection, including the necessary quantum mechanics. He covers several advanced imaging concepts that I haven't any idea about myself. You probably could not find a more comprehensive book in the field of imaging and physical optics. Another benefit is that, at least for the chapters I have used, the individual chapters seem to stand well on their own and you are not forced to study the book in order.

This book is not for the faint of heart in any respect. The material itself is not for the faint of heart: it is extremely rigorous and will require your careful attention, but I believe it is well explained and manageable for someone who is serious about learning it. The size of the book is not for the faint of heart. I would hate to have to carry this thing around much (>1500 pages!!). The price is nothing to sneeze at either, at least for an impoverished graduate student like me, but Dr. Barrett told us that if you calculate the cost per equation, it may be one of the cheapest books on the market. Well, you get what you pay for. As far as anyone in the class found out, there are no typos, either. (Really. We were looking for them). This is certainly a relief for anyone who has much experience shelling out hundreds of dollars for expensive science textbooks.

I do not consider this book to be introductory material, but it is quite likely as close to exhaustive as anything you are apt to encounter in the physical sciences. If you are very serious about imaging or physical optics, this book will be an invaluable resource.

Very good and the most complete of the field!.......2004-02-18

The authors have done a great work. The book is complete and detailed. It is helping me a lot in the beginning of my Ph.D. It's really a must have in the field!

Linear Statistical Models: An Applied Approach (Business Statistics)

Average customer rating:

a good introductory book
a good introductory book

Linear Statistical Models: An Applied Approach (Business Statistics)
Bruce L. Bowerman , and Richard T. O'Connell
Manufacturer: Pws Pub Co
ProductGroup: Book
Binding: Hardcover

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Mathematical Statistics with Applications (Mathematical Statistics (W/ Applications))

ASIN: 0534921779

Book Description

The focus of Linear Statistical Models: An Applied Approach, Second Editon, is on the conceptual, concrete, and applied aspects of model building, data analysis, and interpretaion. Without sacrificing depth and breadth of coverage, Bruce L. Bowerman and Richard T. O'Connell's clear and concise explanantions make the material accessible even to those with limited statistical experience.

Customer Reviews:

a good introductory book.......2000-08-26

I think this book is a good book for those who learnt some basic ideas of statistics, and who wish to improve their understanding in the applied field of statistics. To start this book, some calculus and linear algebra knowledge (one term each is enough)is a prerequisite. This book starts easily, but it'll come to very deep concepts without your noticing it at all.

a good introductory book.......2000-08-26

Weather Derivative Valuation: The Meteorological, Statistical, Financial and Mathematical Foundations

Average customer rating:

An effective introduction

Weather Derivative Valuation: The Meteorological, Statistical, Financial and Mathematical Foundations
Stephen Jewson , and Anders Brix
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521843715

Book Description

Weather Derivative Valuation is the first book to cover all the meteorological, statistical, financial and mathematical issues that arise in the pricing and risk management of weather derivatives. There are chapters on meteorological data and data cleaning, the modelling and pricing of single weather derivatives, the modelling and valuation of portfolios, the use of weather and seasonal forecasts in the pricing of weather derivatives, arbitrage pricing for weather derivatives, risk management, and the modelling of temperature, wind and precipitation. Specific issues covered in detail include the analysis of uncertainty in weather derivative pricing, time-series modelling of daily temperatures, the creation and use of probabilistic meteorological forecasts and the derivation of the weather derivative version of the Black-Scholes equation of mathematical finance. Written by consultants who work within the weather derivative industry, this book is packed with practical information and theoretical insight into the world of weather derivative pricing.

Customer Reviews:

An effective introduction.......2005-12-06

Many businesses, particularly ones that specialize in energy and agriculture, can be subjected to severe financial impact by changes in the weather. Techniques from financial engineering can be used to manage the financial risk involved in these changes, and are structured as swap, call, and put contracts based on `weather indices'. These financial instruments are referred to as `weather derivatives' and are the subject of this book. The weather indices are typically the `heating degree day' (HDD), and the `cooling degree day' (CDD), but could also be such quantities as precipitation, snowfall, and humidity. The HDD (for a particular day) is usually defined as the maximum difference (bounded below by zero) between a chosen baseline temperature and the average temperature. The CDD is the difference between the average temperature and a baseline (again bounded below by zero).

A perfect weather derivative would be designed so as to eliminate all risk due to the weather. For example, if the temperature is to be the index of choice, then one would like to be able to `hedge' so successfully so as to make, as far as the affected industry is concerned, the weather effectively irrelevant. This of course is not possible, due to the unavailability of perfect forecasts. However, one can enter into weather derivative contracts that will enable the affected industry to manage their weather risk in a manner that that makes use of what can actually be predicted in weather forecasts, with the remaining uncertainty being hedged. Possible lost revenue due to adverse weather can be hedged for example by a weather derivative that will give a revenue stream that is based on the forecast error.

Like all other financial instruments, there will be a cost associated with weather derivative contracts. Within the scope of propriety, the authors have given an excellent introduction to the methodologies used to price weather derivatives, and how to perform risk management of portfolios based on weather derivatives. Since the underlying weather indices are not traded, pricing based on arbitrage is more involved for the case of weather derivatives. The authors though show how arbitrage pricing can be done, and also give in-depth discussion on other pricing strategies, these being classified as `actuarial' and `market-based' pricing. Actuarial pricing, as the name implies, involves calculating the probabilities of all future outcomes of a contract or portfolio of contracts, while market-based pricing is based on the actual prices that are observed in the market. Arbitrage pricing can be done in locations where the option is actively traded. Otherwise, the authors show how a swap contract defined on the index can be used to obtain dynamic hedging. However, they remark that this pricing strategy is not widely done at the time of writing. Actuarial pricing thus dominates the discussions in the book.

The mathematical modeling involved in weather derivatives can be difficult, due in part to the fact that the underlying weather indices are nonstationary, i.e. they are characterized by variations and trends with scales greater than the length of the historical record. In addition, the weather indices exhibit a high degree of autocorrelation. Also, the actual measurement of volatility can be problematic, due to sparse data sets or even the unavailability of data. Further, arriving at a general method for estimating volatility is difficult since the exposure to weather risk is highly variable between different companies.

One method of valuing single contracts discussed early on in the book is called `burn analysis', and can be viewed as a step above a quick back-of-the-envelope calculation. It attempts to value a contract based on how it would have performed in the past. The authors estimate the fair strike for a swap, i.e. the strike that gives an expected value of zero, using burn analysis. This involves using the (detrended) historical index values and the calculation of the mean of this data to estimate the expected index. The authors show how to incorporate `risk loading' to model more closely what is actually going on in the trading of swaps. They also show how to apply the burn analysis to options, calculating the `fair premium' by using the historical pay-offs, with the mean of this data being the expected pay-off.

The most interesting part of the book is the one on arbitrage pricing models. The price charged for a weather contract will be influenced by the possibility of hedging, which is different from actuarial pricing, which is based on diversification. The arbitrage pricing mechanism that the authors discuss is restricted to weather swaps, and they review arbitrage theory both from the standpoint of partial stochastic differential equations and from measure theory. The swaps are all assumed to be linear and based on linear degree days. The authors derive the stochastic differential equations for the swap price to obtain a version of the Black-Scholes equation for weather swaps trading with a premium. They also derive, using a hedging strategy based on forward contracts, the partial differential equation satisfied by the price of the weather option. The solution of this equation gives the arbitrage price, which interestingly turns out to be the same as the actuarial fair price without risk loading. This is due to the absence of drift in the discounted swap price and also the fact that there is no expected loss on the swaps. The authors' algorithm for calculating the arbitrage price for options consists of taking the market swap price to be the expected index, using this to calculate the expected pay-off, and then discounting this quantity to give the arbitrage price. This algorithm is done assuming knowledge of the standard deviation of the settlement index. Their algorithm is interesting, but its validation is not discussed in the book. Readers will have to consult the references for further discussion on this important issue. To gain confidence in the efficacy of the algorithm will of course require it be used in real-life trading or risk management.

Random Iterative Models (Stochastic Modelling and Applied Probability)

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Random Iterative Models (Stochastic Modelling and Applied Probability)
Marie Duflo
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540571000

Book Description

The recent development of computation and automation has lead to quick advances in the theory and practice of recursive methods for stabilization, identification and control of complex stochastic models (guiding a rocket or a plane, organizing multiaccess broadcast channels, self-learning of neural networks ...). This book provides an up-to-date view of a wide range of those methods: stochastic approximation, linear and non-linear models, controlled Markov chains, estimation and adaptive control, learning ...Mathematicians (researchers and also students) and engineers will find here a self-contained account of many approaches to those theories.

Design Theory (Encyclopedia of Mathematics and its Applications)

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Design Theory (Encyclopedia of Mathematics and its Applications)
Thomas Beth , D. Jungnickel , and H. Lenz
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521772311

Book Description

This volume concludes the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to reflect this. In particular, the growing importance of discrete mathematics to many parts of engineering and science have made designs a useful tool for applications, a fact that has been acknowledged here with the inclusion of an additional chapter on applications. The volume is suitable for advanced courses and for reference use, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. Features include exercises and an extensive, updated bibliography of well over 1800 citations.

Structural Equation Modeling: Foundations and Extensions (Advanced Quantitative Techniques in the Social Sciences)

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exposition but not explanation
A good reference, once you know something about SEM

Structural Equation Modeling: Foundations and Extensions (Advanced Quantitative Techniques in the Social Sciences)
David W. Kaplan
Manufacturer: Sage Publications, Inc
ProductGroup: Book
Binding: Hardcover

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ASIN: 0761914072

Book Description

"This is a thorough and sophisticated treatment of structural equation modeling (SEM). The book assumes a strong background in statistics and matrix algebra. The author clearly is knowledgeable and has put much thought into the pros and cons of standard applications of SEM. The chapters on multilevel and growth modeling are an excellent feature of the book."

--Rick H. Hoyle, University of Kentucky

Through the use of detailed, empirical examples, this exciting book presents an advanced treatment of the foundations of structural equation modeling (SEM) and demonstrates how SEM can provide a unique lens on problems in the social and behavioral sciences.

The author begins with an introduction to recursive and non-recursive models, estimation, testing, and the problem of measurement in observed variables. Kaplan then explores the issue of group differences in structural models, statistical assumptions in structural modeling (from sampling to missing data and specification error), the assessment of statistical power and model modification in the context of model evaluation, and SEM applied to complex data structures such as those obtained from clustered random sampling. The book concludes with a discussion of recent developments in latent variable growth curve modeling and a critique of the conventional practice of structural modeling in light of recent developments in econometric modeling.

Features/Benefits:

- Shows how SEM can be used to answer substantive questions by weaving a small set of substantive examples throughout the book

- Explains recent developments in structural equation modeling applied to complex sampling, such as multilevel SEM and latent variable growth

- Provides a critique of the standard practice of structural equation modeling throughout the book and discusses an alternative approach in light of recent developments in econometric modeling.

Customer Reviews:

exposition but not explanation.......2007-10-04

This book is almost useless if you don't know the mathematics and logic of structural equation modelling. Tragically if you know the mathematics and logic of structural equation modelling and seeking a deeper discussion this book would not help you either. Therefore it is hard to understand the target public and purpose of the author. In fact this book is a good application of a particular (and annoying) formula for pseudo-writing about mathematical concepts: whenever there is a need for rigour point out a reference, talk about concepts without any depth and without appealing to intuition and present computer outputs instead of solutions.
You may wish to have this (kind of) book only if you want to have a kind of tourist guide for the realm of structural equation modelling.

A good reference, once you know something about SEM.......2004-11-08

As a student of Dr. Kaplan's, we used this book as a way to remind us what the loads of greek symbols scrawled across our notes actually meant. While not written to be used with any specific program, I find the book to be a great reference when I haven't used SEM for a while and need to be reminded of some of its nuances. If you are trying to learn SEM, I suggest you get a book specifically written for the program you plan on using first. Once you understand the basics, this book comes in handy. Also useful if you have a burning desire to understand the barebones behind what SEM is and the math involved.

Foundations of Potential Theory (Dover Books on Advanced Mathematics)

Average customer rating:

Beautiful mathematics
THE book on classical potential theory

Foundations of Potential Theory (Dover Books on Advanced Mathematics)
Oliver D. Kellogg
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486601447

Book Description

Introduction to fundamentals of potential functions covers: the force of gravity, fields of force, potentials, harmonic functions, electric images and Green’s function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential and much more. Detailed proofs rigorously worked out. 1929 ed.

Customer Reviews:

Beautiful mathematics.......2000-04-11

A beautiful presentation which I much enjoyed in grad school. Now I need to return to the subject, but I can't find it in my lib. So I'm ordering another copy and looking forward to reading it again!

THE book on classical potential theory.......1999-05-06

There are few books left in print on this captivating subject from theoretical mechanics. Kellogg's presentation is clear and mathematically formal. This is an excellent reprint from Dover.

Now, if Dover would only bring back into print MacMillan's "The Theory of the Potential" and maybe try to reprint Sternberg & Smith's U. of Toronto Press published (and out of print) "The Theory of the Potential and Spherical Harmonics", they would have themselves a trilogy to corner the science book market for the classical treatment of potential theory.

Book Description

This Växjö conference was devoted to the reconsideration of quantum foundations. Due to increasing research in quantum information theory, especially on quantum computing and cryptography, many questions regarding the foundations of quantum mechanics, which have long been considered to be exclusively of philosophical interest, nowadays play an important role in theoretical and experimental quantum physics.

Mathematical Foundations of Statistical Mechanics

Average customer rating:

The best on classical statistical mechanics
A beautiful work by a great writer and mathematician.

Mathematical Foundations of Statistical Mechanics
A. I. Khinchin
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486601471

Customer Reviews:

The best on classical statistical mechanics.......2005-01-23

To read this book one needs some fundamental knowledge of mechanics and probability theory. The great author builds the foundations of statistical mechanics on these two pillars. Throughout the book the author develops the statistical theory of mechanics using an axiomatic approach and tries to invoke as few assumptions as possible.
If you like the language of mathematics, this is the most elegant and concise book on classical equilibrium statistical mechanics. J.W.Gibbs's pioneering book, elementary principles of statistical mechanics, is not as readable as this one, in my opinion.
In the appendix there is author's extension of the central limit theorem as a bonus!

A beautiful work by a great writer and mathematician........2001-02-25

A Y Khinchin was one of the great mathematicians of the first half of the twentieth century. His name is is already well-known to students of probability theory along with A N Kolmogorov and others from the host of important theorems, inequalites, constants named after them. He was also famous as a teacher and communicator. The books he wrote on Mathematical Foundations of Information Theory, Statistical Mechanics and Quantum Statistics are still in print in English translations, published by Dover. Like William Feller and Richard Feynman he combines a complete mastery of his subject with an ability to explain clearly without sacrificing mathematical rigour.

In his "Mathematical Foundations" books Khinchin develops a sound mathematical structure for the subject under discussion based on the modern theory of probability. His primary reason for doing this is the lack of mathematically rigorous presentation in many textbooks on these subjects. I can remember the vague feeling of dissatisfaction I felt as a student with some of the mathematics in Frederick Reif's "Fundamentals of Statistical and Thermal Physics" and other texts. Khinchin's little book puts everything on a firm mathematical foundation and yet is very readble.

Book Description

The expression of uncertainty in measurement is a challenging aspect for researchers and engineers working in instrumentation and measurement because it involves physical, mathematical and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (GUM).

This text is the first to make full use of the mathematical theory of evidence to express the uncertainty in measurements. It gives an overview of the current standard, then pinpoints and constructively resolves its limitations through its unique approach. The text presents various tools for evaluating uncertainty, beginning with the probabilistic approach and concluding with the expression of uncertainty using random-fuzzy variables. The exposition is driven by numerous examples. The book is designed for immediate use and application in research and laboratory work.

Apart from a classroom setting, this book can be used by practitioners in a variety of fields (including applied mathematics, applied probability, electrical and computer engineering, and experimental physics), and by such institutions as the IEEE, ISA, and National Institute of Standards and Technology.

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