Mathematical image processing. Translated from the German
In these days imaging is an element of everyday life. Efficient image processing techniques involve modern high level mathematics. This book reveals the base theory which is applied in such image processing tasks as denoising, inpainting, deblurring, feature detection, etc. This book consists of six chapters. The first chapter introduces the reader into the world of image processing. In the second chapter there are preliminaries -- the basic theorems and definitions which are used in the following chapters. From chapter three the clue of the book starts -- mathematical image processing. In more details, in chapter three the basic tools are described like image representations, histograms or linear and morphological filters. Chapter four is devoted to frequency mono- and multiscaled methods. So, the Fourier Transform, Fourier series and the continuous and discrete wavelet transforms are presented. In the next chapter the partial differential equations are described together with their stability, regularity, locality, monotonicity, etc., followed by their applications to image denoising, and edge and feature detection. The final chapter deals with variational methods and their applications to denoising, deblurring and resolution enlarging. This book has a strong theoretical character with definitions, lemmas, and theorems with the proofs. However, it is written in very accessible manner with many examples and figures. There is also a number of still images (some of them are in color), so the reader can see the real applications of the presented theory to image processing. This book is devoted to researches in image processing and can be used for courses of applied mathematics. This book can be treated as a good starting point, since it introduces the reader into the base theory of mathematical image processing and shows the wide spectrum of approaches to typical image processing tasks. However, the lack of some of the recent approaches causes that this book is not complete as such. See the review of the German edition in [Zbl 1220.68001].
scientific article; zbMATH DE number 6967813