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Tensor fields are the natural representation for many physical quantities; they can describe how water moves around in the brain, how gravity varies around the earth, or how materials are stressed and deformed. This book provides researchers a look at how to process and visualize complicated 2D and 3D images known as tensor fields.

Calculus of tensors. --- Visualization. --- Image processing. --- Mathematics. --- Computer science --- Computer graphics. --- Computer mathematics. --- Computational Mathematics and Numerical Analysis. --- Mathematics of Computing. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Image Processing and Computer Vision. --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Visualisation --- Imagery (Psychology) --- Imagination --- Visual perception --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Computer science. --- Computer vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Informatics --- Science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Computer science—Mathematics. --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Optical equipment

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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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ThisbookattemptstocapturesomeoftheexcitementofaninspiringDagstuhl SeminarinJanuary2007. Theauthorsreportonrecentresearchresultsaswell as opining on future directions for the analysis and visualization of tensor ?elds. Topics range from applications of the analysis of tensor ?elds to purer researchintotheirmathematical andanalytical properties. Oneofthegoalsof thisseminarwastobringtogetherresearchersfromalongthatpure-to-applied disciplinary axis with the hope of fostering new collaborations and research. This book, we hope, will continue to further that goal in a broader context. Providence, Rhode Island, USA David H. Laidlaw Saarbruc ¨ ken, Saarland, Germany Joachim Weickert August 2008 Contents Part I Models for Di?usion MRI Modelling, Fitting and Sampling in Di?usion MRI Daniel C. Alexander. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Tensors, Polynomials and Models for Directional Data P. G. Batchelor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 A Mixture of Wisharts (MOW) Model for Multi?ber Reconstruction ¨ Bing Jian, Baba C. Vemuri, and Evren Ozarslan. . . . . . . . . . . . . . . . . . . . . 39 The Algebra of Fourth-Order Tensors with Application to Di?usion MRI Maher Moakher. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Part II Higher-Level Analysis of Di?usion Images Structure-Speci?c StatisticalMappingofWhiteMatterTracts Paul A. Yushkevich, Hui Zhang, Tony J. Simon, and James C. Gee. . . . 83 Analysis of Distance/Similarity Measures for Di?usion Tensor Imaging T. H. J. M. Peeters, P. R. Rodrigues, A. Vilanova, and B. M. ter Haar Romeny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 XContents Part III Tensor Field Visualization Tensor Glyph Warping: Visualizing Metric Tensor Fields using Riemannian Exponential Maps Anders Brun and Hans Knutsson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Interactive Volume Rendering of Di?usion Tensor Data Mario Hlawitschka, Gunther H. Weber, Alfred Anwander, Owen T. Carmichael, Bernd Hamann, and Gerik Scheuermann. . . . . . . . 161 Dense Glyph Sampling for Visualization Louis Feng, Ingrid Hotz, Bernd Hamann, and Kenneth Joy. . . . . . . . . . . .

Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- beeldverwerking --- grafische vormgeving --- informatica --- wiskunde

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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.

Mathematical statistics --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- computervisie --- patroonherkenning --- beeldverwerking --- factoranalyse --- machine learning --- vormgeving --- computers --- grafische vormgeving --- mineralen (chemie) --- simulaties --- mijnbouw --- KI (kunstmatige intelligentie) --- computerkunde --- robots --- optica --- AI (artificiële intelligentie)