Mathematical Models in Photographic Science

Avner Friedman, David Ross (Autoren)

Buch | Hardcover

VIII, 184 Seiten

2002 | 2003
Springer Berlin (Verlag)
978-3-540-44219-6 (ISBN)

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th Although photography has its beginning in the 17 century, it was only in the 1920's that photography emerged as a science. And as with other s- ences, mathematics began to play an increasing role in the development of photography. The mathematical models and problems encountered in p- tography span a very broad spectrum, from the molecular level such as the interaction between photons and silver halide grains in image formation, to chemical processing in ?lm development and issues in manufacturing and quality control. In this book we present mathematical models that arise in today's p- tographic science. The book contains seventeen chapters, each dealing with oneareaofphotographicscience.Eachchapter,exceptthetwointroductory chapters, begins with general background information at a level understa- able by graduate and undergraduate students. It then proceeds to develop a mathematical model, using mathematical tools such as Ordinary Di?erential Equations, Partial Di?erential Equations, and Stochastic Processes. Next, some mathematical results are mentioned, often providing a partial solution to problemsraisedby the model.Finally,mostchaptersinclude problems.By the nature of the subject, there is quite a bit ofdisparity in the mathematical level of the various chapters.

1. History of Photography.- References.- I. The Components of a Film.- 2. An Overview.- 3. Crystal Growth - Ostwald Ripening.- 4. Crystal Growth-Sidearm Precipitation.- 5. Gelatin Swelling.- 6. Gelation.- 7. Polymeric Base.- II. The Role of Surfactants.- 8. Limited Coalescence.- 9. Measuring Coalescence.- III. Coating.- 10. Newtonian Coating Flows.- 11. Coating Configurations.- 12. Curtain Coating.- 13. Shear Thinning.- IV. Image Capture.- 14. Latent Image Formation.- 15. Granularity.- V. Development.- 16. A Reaction-Diffusion System.- 17. Parameter Identification.

This book provides an interesting and well documented presentation of mathematical topics related to photographic sciences. [...] This is an attractive and easy to read book, which is characterized by a valuable (in the reviewer¿s opinion) feature: each chapter covers the whole path from the phenomenological analysis and interpretation of the real system, to modeling, statement of problems related to the application of models, an outline of qualitative analysis, and finally to perspectives and open problems.

This book is recommended to applied mathematicians interested in industrial mathematics and is intended for applications and the development of mathematical methods for problems generated from technology. It is also a good text for advanced university courses on mathematical modeling to be joined to courses on computational methods.

Applied mathematicians will find a description of open problems which are definitely challenging even for experienced mathematicians.

MathSciNet 2004. Nicola Bellomo (I-TRNP)

Erscheint lt. Verlag	11.12.2002
Reihe/Serie	Mathematics in Industry
Zusatzinfo	VIII, 184 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	484 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	action • coating flows • crystal growth • Design • Diffusion • Dispersion • Fotoindustrie • gelation • Image Formation • Mathematisches Modell • partial differential equation • Partial differential equations • photography • reaction diffusion systems • Transmission
ISBN-10	3-540-44219-7 / 3540442197
ISBN-13	978-3-540-44219-6 / 9783540442196
Zustand	Neuware