Variational Regularization of 3D Data

Experiments with MATLAB®

  • Hebert Montegranario
  • Jairo Espinosa

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

Table of contents

  1. Front Matter
    Pages i-x
  2. Hebert Montegranario, Jairo Espinosa
    Pages 1-4
  3. Hebert Montegranario, Jairo Espinosa
    Pages 5-17
  4. Hebert Montegranario, Jairo Espinosa
    Pages 19-29
  5. Hebert Montegranario, Jairo Espinosa
    Pages 31-43
  6. Hebert Montegranario, Jairo Espinosa
    Pages 45-49
  7. Hebert Montegranario, Jairo Espinosa
    Pages 51-57
  8. Hebert Montegranario, Jairo Espinosa
    Pages 59-67
  9. Hebert Montegranario, Jairo Espinosa
    Pages 69-81
  10. Back Matter
    Pages 83-85

About this book

Introduction

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.

Keywords

MATLAB Tikhonov Regularization computer vision splines surface reconstruction

Authors and affiliations

  • Hebert Montegranario
    • 1
  • Jairo Espinosa
    • 2
  1. 1.Mathematics InstituteUniversity of AntioquiaMedellínColombia
  2. 2.National University of ColombiaMedellínColombia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-0533-1
  • Copyright Information The Author(s) 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Computer Science
  • Print ISBN 978-1-4939-0532-4
  • Online ISBN 978-1-4939-0533-1
  • Series Print ISSN 2191-5768
  • Series Online ISSN 2191-5776
  • About this book