Variational Regularization of 3D Data: Experiments with MATLAB® - Brossura

Montegranario, Hebert; Espinosa, Jairo

Brossura

ISBN 10: 1493905325 ISBN 13: 9781493905324

Casa editrice: Springer, 2014

Riassunto

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.

Su questo libro

Informazioni sull'autore

Hebert Montegranario is an applied mathematician and computational scientist, currently serving as a professor at the Antioquia University, Medellín, Colombia. He holds a Ph.D. in Engineering from Universidad Nacional de Colombia, with a research focus on image processing, computer vision, and machine learning. Dr. Montegranario has extensive expertise in numerical analysis, scientific computing, and software design. He has authored several academic papers and a book on variational regularization of 3D data, showcasing his contributions to the field.

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 1493905325
• ISBN 13: 9781493905324
• Rilegatura: Copertina flessibile
• Numero di pagine: 85
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania