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Matrix-valued data sets - so-called second order tensor fields - have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state-of-the-art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.

Mathematics. --- Radiology. --- Computer graphics. --- Image processing. --- Mathematical analysis. --- Analysis (Mathematics). --- Visualization. --- Differential geometry. --- Analysis. --- Imaging / Radiology. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Image Processing and Computer Vision. --- Differential Geometry. --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Visualisation --- Imagery (Psychology) --- Imagination --- Visual perception --- Differential geometry --- 517.1 Mathematical analysis --- Mathematical analysis --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Radiological physics --- Physics --- Radiation --- Math --- Science --- Digital techniques --- Calculus of tensors --- Graphic methods. --- Data processing. --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Global analysis (Mathematics). --- Radiology, Medical. --- Computer vision. --- Global differential geometry. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Clinical radiology --- Radiology, Medical --- Radiology (Medicine) --- Medical physics --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Optical equipment --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions

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This book constitutes the refereed proceedings of the 35th German Conference on Pattern Recognition, GCPR 2013, held in Saarbrücken, Germany, in September 2013. The 22 revised full papers and 18 revised poster papers were carefully reviewed and selected from 79 submissions. The papers covers topics such as image processing and computer vision, machine learning and pattern recognition, mathematical foundations, statistical data analysis and models, computational photography and confluence of vision and graphics, and applications in natural sciences, engineering, biomedical data analysis, imaging, and industry.

Engineering & Applied Sciences --- Electrical & Computer Engineering --- Computer Science --- Electrical Engineering --- Computer science. --- Artificial intelligence. --- Computer simulation. --- Computer graphics. --- Image processing. --- Pattern recognition. --- Computer Science. --- Pattern Recognition. --- Image Processing and Computer Vision. --- Artificial Intelligence (incl. Robotics). --- Computer Graphics. --- Simulation and Modeling. --- Pattern recognition systems --- Optical pattern recognition. --- Computer vision. --- Artificial Intelligence. --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Fifth generation computers --- Neural computers --- Machine vision --- Vision, Computer --- Artificial intelligence --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- Digital techniques --- Optical data processing. --- Optical computing --- Visual data processing --- Integrated optics --- Photonics --- Computers --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Optical equipment

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With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents:Part ISecond-order decomposition model for image processing: numerical experimentationOptimizing spatial and tonal data for PDE-based inpaintingImage registration using phase・amplitude separationRotation invariance in exemplar-based image inpaintingConvective regularization for optical flowA variational method for quantitative photoacoustic tomography with piecewise constant coefficientsOn optical flow models for variational motion estimationBilevel approaches for learning of variational imaging modelsPart IINon-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problemsThe Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controlsControllability of Keplerian motion with low-thrust control systemsHigher variational equation techniques for the integrability of homogeneous potentialsIntroduction to KAM theory with a view to celestial mechanicsInvariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometryTime-optimal control for a perturbed Brockett integratorTwist maps and Arnold diffusion for diffeomorphismsA Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part IIndex

Image processing --- Image analysis --- Analysis of images --- Image interpretation --- Photographs --- Forensic sciences --- Imaging systems --- Pictorial data processing --- Picture processing --- Processing, Image --- Optical data processing --- Mathematical models. --- Inspection