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Mathematical analysis --- Mathematics --- Math --- Science --- Mathematics.

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Mathematics --- 519.6 --- 681.3*J2 --- Math --- Science --- Computational mathematics. Numerical analysis. Computer programming --- Physical sciences and engineering (Computer applications) --- John, Fritz --- 681.3*J2 Physical sciences and engineering (Computer applications) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- John, Fritz, --- John, F.

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Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences. The first is the mathematical community, to show the contribution of mathematics to this domain and to highlight some unresolved theoretical questions. The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems. The book is divided into five main parts. Chapter 1 is a detailed overview. Chapter 2 describes and illustrates most of the mathematical notions found throughout the work. Chapters 3 and 4 examine how PDEs and variational methods can be successfully applied in image restoration and segmentation processes. Chapter 5, which is more applied, describes some challenging computer vision problems, such as sequence analysis or classification. This book will be useful to researchers and graduate students in mathematics and computer vision.

Image processing --- Mathematics. --- Image processing: image displays image processing software (Computing methododologies) --- 681.3*I4 Image processing: image displays image processing software (Computing methododologies) --- Computers. --- Image processing. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Calculus of variations. --- Analysis. --- Applications of Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Computing Methodologies. --- Image Processing and Computer Vision. --- 681.3*I4 --- 517.97 --- 517.97 Calculus of variations. Mathematical theory of control --- Calculus of variations. Mathematical theory of control --- 681.3*I4 Image processing: image displays; image processing software (Computing methododologies) --- Image processing: image displays; image processing software (Computing methododologies) --- Global analysis (Mathematics). --- Mathematical optimization. --- Systems theory. --- Artificial intelligence. --- Computer vision. --- Artificial Intelligence. --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Systems, Theory of --- Systems science --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis --- Optical equipment --- Philosophy --- Mathematics