Introduction au traitement mathématique des images : méthodes déterministes / Maïtine Bergounioux

Bibliogr. p. 233-237. Index

As a textbook, this work is organized as an introductory course on mathematical treatment of images. The methods described are both deterministic and probability-statistics. The book is organized in 7 chapters and two appendices. Chapter 1 (introduction) makes a brief presentation of the basic facts about numerical (discretized) images, and various types of images (classical and digital photos, medical images – scanning procedures). Chapter 2 describes the contrast, histogram and digitization of an image. In chapters 3 and 4 the author is concerned with the noise and denoising procedures of images. He describes several types of filters, deconvolution procedures, Tikhonov regularization, Wiener filter, variational method of Rudin-Osher-Fatemi. Chapter 5 is dedicated to segmentation of images. The author presents segmentation procedures based on filters, the Mumford-Shah model, as well as variational techniques for segmentation. Chapter 6 is concerned with the mathematical morphology of images. The author firstly describes the set based morphology, which can be used for denoising and segmentation; then he presents the functional mathematical morphology, which applies to gray images, based on transformations as dilatation, erosion, opening, closing. In the last chapter 7, the author considers applications in the fields of steganography (information hiding), wavelets compression, inpainting by regularization. The book also contains two appendices; the first one is containing the basic definitions, notations and results related to Fourier analysis, wavelets, functional and convex analysis, Sobolev spaces. The second one is a brief replay of the main techniques and procedures presented in the book. The book is intended for master and engineering students, as well as researchers wanting to comprehend or deepen their background and understanding of the basic mathematical techniques in processing and image analysis (zbMath)