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Our understanding of nature is often through nonuniform observations in space or time. In space, one normally observes the important features of an object, such as edges. The less important features are interpolated. History is a collection of important events that are nonuniformly spaced in time. Historians infer between events (interpolation) and politicians and stock market analysts forecast the future from past and present events (extrapolation). The 20 chapters of Nonuniform Sampling: Theory and Practice contain contributions by leading researchers in nonuniform and Shannon sampling, zero crossing, and interpolation theory. Its practical applications include NMR, seismology, speech and image coding, modulation and coding, optimal content, array processing, and digital filter design. It has a tutorial outlook for practising engineers and advanced students in science, engineering, and mathematics. It is also a useful reference for scientists and engineers working in the areas of medical imaging, geophysics, astronomy, biomedical engineering, computer graphics, digital filter design, speech and video processing, and phased array radar.

Sampling. --- Signal theory (Telecommunication) --- Time-series analysis. --- Mathematics. --- Electronics. --- Microelectronics. --- Electrical engineering. --- Signal processing. --- Image processing. --- Speech processing systems. --- Optical data processing. --- Electronics and Microelectronics, Instrumentation. --- Electrical Engineering. --- Signal, Image and Speech Processing. --- Image Processing and Computer Vision. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Electric engineering --- Engineering --- Microminiature electronic equipment --- Microminiaturization (Electronics) --- Electronics --- Microtechnology --- Semiconductors --- Miniature electronic equipment --- Electrical engineering --- Physical sciences --- Optical equipment

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Computer science --- Computer Science --- Engineering & Applied Sciences --- Computer science. --- Data structures (Computer science). --- Computers. --- Image processing. --- Computer Science. --- Theory of Computation. --- Data Structures, Cryptology and Information Theory. --- Image Processing and Computer Vision. --- Data Structures. --- Mathematics of Computing. --- Mathematics. --- Information theory. --- Data structures (Computer scienc. --- Computer vision. --- Data Structures and Information Theory. --- Informatics --- Science --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Communication theory --- Communication --- Cybernetics --- Optical data processing. --- Computer science—Mathematics. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- File organization (Computer science) --- Abstract data types (Computer science) --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Machine theory --- Calculators --- Cyberspace --- Optical equipment --- Computer science - Congresses --- Data structures (Computer science)

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The purpose of this book is to develop a generative theory of shape that has two properties we regard as fundamental to intelligence –(1) maximization of transfer: whenever possible, new structure should be described as the transfer of existing structure; and (2) maximization of recoverability: the generative operations in the theory must allow maximal inferentiability from data sets. We shall show that, if generativity satis?es these two basic criteria of - telligence, then it has a powerful mathematical structure and considerable applicability to the computational disciplines. The requirement of intelligence is particularly important in the gene- tion of complex shape. There are plenty of theories of shape that make the generation of complex shape unintelligible. However, our theory takes the opposite direction: we are concerned with the conversion of complexity into understandability. In this, we will develop a mathematical theory of und- standability. The issue of understandability comes down to the two basic principles of intelligence - maximization of transfer and maximization of recoverability. We shall show how to formulate these conditions group-theoretically. (1) Ma- mization of transfer will be formulated in terms of wreath products. Wreath products are groups in which there is an upper subgroup (which we will call a control group) that transfers a lower subgroup (which we will call a ?ber group) onto copies of itself. (2) maximization of recoverability is insured when the control group is symmetry-breaking with respect to the ?ber group.

Geometric programming --- Shape theory (Topology) --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Geometric programming. --- Computer science. --- Computer graphics. --- Image processing. --- Application software. --- Computer-aided engineering. --- Group theory. --- Geometry. --- Computer Science. --- Image Processing and Computer Vision. --- Computer Applications. --- Computer Graphics. --- Group Theory and Generalizations. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces --- Programming (Mathematics) --- Computer vision. --- Computer aided design. --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Informatics --- Science --- Mathematics --- Euclid's Elements --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Digital techniques --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software --- CAE --- Engineering --- Optical equipment --- Data processing

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Evolutionary programming (Computer science) --- Evolutionary computation --- Computer Science --- Engineering & Applied Sciences --- Computer science. --- Information technology. --- Business --- Algorithms. --- Computer science --- Artificial intelligence. --- Image processing. --- Complexity, Computational. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Algorithm Analysis and Problem Complexity. --- Mathematics of Computing. --- Image Processing and Computer Vision. --- Complexity. --- IT in Business. --- Data processing. --- Mathematics. --- Computer software. --- Computer vision. --- Engineering. --- Artificial Intelligence. --- IT (Information technology) --- Technology --- Telematics --- Information superhighway --- Knowledge management --- Construction --- Industrial arts --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Informatics --- Science --- Software, Computer --- Computer systems --- 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 --- Computer science—Mathematics. --- Optical data processing. --- Computational complexity. --- Business—Data processing. --- Complexity, Computational --- Optical computing --- Visual data processing --- Integrated optics --- Photonics --- Computers --- Algorism --- Algebra --- Arithmetic --- Optical equipment --- Foundations

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Wavelets (Mathematics) --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Computer science. --- Coding theory. --- Multimedia information systems. --- Image processing. --- Application software. --- Mathematical analysis. --- Analysis (Mathematics). --- Computer Science. --- Coding and Information Theory. --- Analysis. --- Computer Applications. --- Multimedia Information Systems. --- Information Systems Applications (incl. Internet). --- Image Processing and Computer Vision. --- Global analysis (Mathematics). --- Multimedia systems. --- Computer vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Computer-based multimedia information systems --- Multimedia computing --- Multimedia information systems --- Multimedia knowledge systems --- Information storage and retrieval systems --- Informatics --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Information theory. --- Optical data processing. --- 517.1 Mathematical analysis --- Mathematical analysis --- Communication theory --- Communication --- Cybernetics --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software --- Optical equipment