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Variational Regularization of 3D Data

Experiments with MATLAB®

  • Book
  • © 2014

Overview

Authors:
  1. Hebert Montegranario

    1. Mathematics Institute, University of Antioquia, Medellín, Colombia

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    You can also search for this author in PubMed   Google Scholar

  2. Jairo Espinosa

    1. National University of Colombia, Medellín, Colombia

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: SpringerBriefs in Computer Science (BRIEFSCOMPUTER)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-x
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  2. 3D Data in Computer Vision and Technology

    • Hebert Montegranario, Jairo Espinosa
    Pages 1-4

  3. Function Spaces and Reconstruction

    • Hebert Montegranario, Jairo Espinosa
    Pages 5-17

  4. Variational Methods

    • Hebert Montegranario, Jairo Espinosa
    Pages 19-29

  5. Interpolation. From One to Several Variables

    • Hebert Montegranario, Jairo Espinosa
    Pages 31-43

  6. Functionals and Their Physical Interpretations

    • Hebert Montegranario, Jairo Espinosa
    Pages 45-49

  7. Regularization and Inverse Theory

    • Hebert Montegranario, Jairo Espinosa
    Pages 51-57

  8. 3D Interpolation and Approximation

    • Hebert Montegranario, Jairo Espinosa
    Pages 59-67

  9. Radial Basis Functions

    • Hebert Montegranario, Jairo Espinosa
    Pages 69-81

  10. Back Matter

    Pages 83-85
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematics Institute, University of Antioquia, Medellín, Colombia

    Hebert Montegranario

  • National University of Colombia, Medellín, Colombia

    Jairo Espinosa

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