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Optimization Techniques in Computer Vision

Ill-Posed Problems and Regularization

  • Mongi A. Abidi
  • Andrei V. Gribok
  • Joonki Paik

Part of the Advances in Computer Vision and Pattern Recognition book series (ACVPR)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Part I

    1. Front Matter
      Pages 1-1
    2. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 3-27
    3. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 29-50
  3. Part II

    1. Front Matter
      Pages 51-51
    2. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 53-67
    3. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 69-92
    4. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 93-110
  4. Part III

    1. Front Matter
      Pages 111-111
    2. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 113-130
    3. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 131-138
    4. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 139-155
  5. Part IV

    1. Front Matter
      Pages 157-157
    2. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 159-177
    3. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 179-196
    4. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 197-218
    5. Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 219-247
  6. Back Matter
    Pages 249-293

About this book

Introduction

This book presents practical optimization techniques used in image processing and computer vision problems. Ill-posed problems are introduced and used as examples to show how each type of problem is related to typical image processing and computer vision problems. Unconstrained optimization gives the best solution based on numerical minimization of a single, scalar-valued objective function or cost function. Unconstrained optimization problems have been intensively studied, and many algorithms and tools have been developed to solve them. Most practical optimization problems, however, arise with a set of constraints. Typical examples of constraints include: (i) pre-specified pixel intensity range, (ii) smoothness or correlation with neighboring information, (iii) existence on a certain contour of lines or curves, and (iv) given statistical or spectral characteristics of the solution. Regularized optimization is a special method used to solve a class of constrained optimization problems. The term regularization refers to the transformation of an objective function with constraints into a different objective function, automatically reflecting constraints in the unconstrained minimization process. Because of its simplicity and efficiency, regularized optimization has many application areas, such as image restoration, image reconstruction, optical flow estimation, etc.

Optimization plays a major role in a wide variety of theories for image processing and computer vision. Various optimization techniques are used at different levels for these problems, and this volume summarizes and explains these techniques as applied to image processing and computer vision.

Keywords

regularization parameter selection shape representation in image processing image interpolation algorithms regularization methods for linear inverse problems one dimensional optimization unconstrained optimization methods optimization with linear constraints 3D image smoothing 3D volumetric description

Authors and affiliations

  • Mongi A. Abidi
    • 1
  • Andrei V. Gribok
    • 2
  • Joonki Paik
    • 3
  1. 1.Department of Electrical and Computer EngineeringUniversity of TennesseeKnoxvilleUSA
  2. 2.Department of Human Factors, Controls, and StatisticsIdaho National LaboratoryIdaho FallsUSA
  3. 3.Image Processing and Intelligent Systems LaboratoryChung-Ang UniversitySeoulKorea (Republic of)

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-46364-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-46363-6
  • Online ISBN 978-3-319-46364-3
  • Series Print ISSN 2191-6586
  • Series Online ISSN 2191-6594
  • Buy this book on publisher's site