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Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts.   This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp.   It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.

Clifford algebras. --- Fourier analysis. --- Quaternions. --- Wavelets (Mathematics). --- Quaternions --- Clifford algebras --- Fourier analysis --- Wavelets (Mathematics) --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Fourier transformations. --- Wavelet analysis --- Transformations, Fourier --- Transforms, Fourier --- Mathematics. --- Image processing. --- Matrix theory. --- Algebra. --- Numerical analysis. --- Number theory. --- Number Theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Numerical Analysis. --- Fourier Analysis. --- Image Processing and Computer Vision. --- Harmonic analysis --- Transformations (Mathematics) --- Computer vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Analysis, Fourier --- Mathematical analysis --- Number study --- Numbers, Theory of --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment

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This book presents a machine-generated literature overview of quaternion integral transforms from select papers published by Springer Nature, which have been organized and introduced by the book's editor. Each chapter presents summaries of predefined themes and provides the reader with a basis for further exploration of the topic. As one of the experimental projects initiated by Springer Nature for AI book content generation, this book shows the latest developments in the field. It will be a useful reference for students and researchers who are interested in exploring the latest developments in quaternion integral transforms.

Algebra --- Harmonic analysis. Fourier analysis --- Mathematical analysis --- Mathematics --- Fourieranalyse --- algebra --- analyse (wiskunde) --- Fourierreeksen --- mathematische modellen --- wiskunde

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This book constitutes the refereed proceedings of the 36th Computer Graphics International Conference, CGI 2019, held in Calgary, AB, Canada, in June 2019. The 30 revised full papers presented together with 28 short papers were carefully reviewed and selected from 231 submissions. The papers address topics such as: 3D reconstruction and rendering, virtual reality and augmented reality, computer animation, geometric modelling, geometric computing, shape and surface modelling, visual analytics, image processing, pattern recognition, motion planning, gait and activity biometric recognition, machine learning for graphics and applications in security, smart electronics, autonomous navigation systems, robotics, geographical information systems, and medicine and art.

Computer science. --- Computer vision. --- Computer graphics. --- Artificial intelligence. --- Computer network architectures. --- Computer Applications. --- Image Processing and Computer Vision. --- User Interfaces and Human Computer Interaction. --- Computer Graphics. --- Artificial Intelligence. --- Computer Systems Organization and Communication Networks. --- Architectures, Computer network --- Network architectures, Computer --- Computer architecture --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Engineering graphics --- Image processing --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Informatics --- Science --- Digital techniques --- Computer graphics --- Computer vision --- Application software. --- Optical data processing. --- User interfaces (Computer systems). --- Computer organization. --- Organization, Computer --- Electronic digital computers --- Interfaces, User (Computer systems) --- Human-machine systems --- Human-computer interaction --- Optical computing --- Visual data processing --- Integrated optics --- Photonics --- Computers --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software --- Optical equipment --- Human-computer interaction. --- Computer engineering. --- Computer networks. --- Computer and Information Systems Applications. --- Computer Vision. --- Computer Engineering and Networks. --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Computer-human interaction --- Human factors in computing systems --- Interaction, Human-computer --- Human engineering --- User-centered system design --- User interfaces (Computer systems) --- Distributed processing --- Design and construction