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Variational Regularization of 3D Data [electronic resource] : Experiments with MATLAB� / by Hebert Montegranario, Jairo Espinosa.

By: Montegranario, Hebert [author.].
Contributor(s): Espinosa, Jairo [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: SpringerBriefs in Computer Science: Publisher: New York, NY : Springer New York : Imprint: Springer, 2014Description: X, 85 p. 21 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781493905331.Subject(s): Computer science | Computer science -- Mathematics | Computer simulation | Image processing | Computer Science | Image Processing and Computer Vision | Math Applications in Computer Science | Simulation and ModelingAdditional physical formats: Printed edition:: No titleDDC classification: 006.6 | 006.37 Online resources: Click here to access online
Contents:
3D Data in Computer vision and technology -- Function Spaces and Reconstruction -- Variational methods -- Interpolation: From one to several variables -- Functionals and their physical interpretations -- Regularization and inverse theory -- 3D Interpolation and approximation -- Radial basis functions.
In: Springer eBooksSummary: Variational Regularization of 3D Data provides an introduction to variational methods for data modelling and its application in computer vision. In this book, the authors identify interpolation as an inverse problem that can be solved by Tikhonov regularization. The proposed solutions are generalizations of one-dimensional splines, applicable to n-dimensional data and the central idea is that these splines can be obtained by regularization theory using a trade-off between the fidelity of the data and smoothness properties. As a foundation, the authors present a comprehensive guide to the necessary fundamentals of functional analysis and variational calculus, as well as splines. The implementation and numerical experiments are illustrated using MATLAB�. The book also includes the necessary theoretical background for approximation methods and some details of the computer implementation of the algorithms. A working knowledge of multivariable calculus and basic vector and matrix methods should serve as an adequate prerequisite.
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3D Data in Computer vision and technology -- Function Spaces and Reconstruction -- Variational methods -- Interpolation: From one to several variables -- Functionals and their physical interpretations -- Regularization and inverse theory -- 3D Interpolation and approximation -- Radial basis functions.

Variational Regularization of 3D Data provides an introduction to variational methods for data modelling and its application in computer vision. In this book, the authors identify interpolation as an inverse problem that can be solved by Tikhonov regularization. The proposed solutions are generalizations of one-dimensional splines, applicable to n-dimensional data and the central idea is that these splines can be obtained by regularization theory using a trade-off between the fidelity of the data and smoothness properties. As a foundation, the authors present a comprehensive guide to the necessary fundamentals of functional analysis and variational calculus, as well as splines. The implementation and numerical experiments are illustrated using MATLAB�. The book also includes the necessary theoretical background for approximation methods and some details of the computer implementation of the algorithms. A working knowledge of multivariable calculus and basic vector and matrix methods should serve as an adequate prerequisite.

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