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Optimization Techniques in Computer Vision

Ill-Posed Problems and Regularization

  • Book
  • © 2016

Overview

Authors:
  1. Mongi A. Abidi

    1. Department of Electrical and Computer Engineering, University of Tennessee, Knoxville, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Andrei V. Gribok

    1. Department of Human Factors, Controls, and Statistics, Idaho National Laboratory, Idaho Falls, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Joonki Paik

    1. Image Processing and Intelligent Systems Laboratory, Chung-Ang University, Seoul, Korea (Republic of)

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    You can also search for this author in PubMed   Google Scholar

  • Features a comprehensive description of regularization through optimization
  • Contains a large selection of data fusion algorithms
  • Includes chapters devoted to video compression and enhancement
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xv
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  2. Part I

    1. Front Matter

      Pages 1-1
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    2. Ill-Posed Problems in Imaging and Computer Vision

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 3-27

    3. Selection of the Regularization Parameter

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 29-50

  3. Part II

    1. Front Matter

      Pages 51-51
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    2. Introduction to Optimization

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 53-67

    3. Unconstrained Optimization

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 69-92

    4. Constrained Optimization

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 93-110

  4. Part III

    1. Front Matter

      Pages 111-111
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    2. Frequency-Domain Implementation of Regularization

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 113-130

    3. Iterative Methods

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 131-138

    4. Regularized Image Interpolation Based on Data Fusion

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 139-155

  5. Part IV

    1. Front Matter

      Pages 157-157
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    2. Enhancement of Compressed Video

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 159-177

    3. Volumetric Description of Three-Dimensional Objects for Object Recognition

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 179-196

    4. Regularized 3D Image Smoothing

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 197-218

    5. Multimodal Scene Reconstruction Using Genetic Algorithm-Based Optimization

      • Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
      Pages 219-247

  6. Back Matter

    Pages 249-293
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Keywords

About this book

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.

Reviews

“The presentation of the problems is accompanied by illustrating examples. The book contains both a great theoretical background and practical applications and is thus self-contained. It is useful for master and doctoral students, as well as for researchers and practitioners dealing with computer vision and image processing, but also working in mathematical optimization.” (Ruxandra Stoean, zbMATH 1362.68003, 2017)

Authors and Affiliations

  • Department of Electrical and Computer Engineering, University of Tennessee, Knoxville, USA

    Mongi A. Abidi

  • Department of Human Factors, Controls, and Statistics, Idaho National Laboratory, Idaho Falls, USA

    Andrei V. Gribok

  • Image Processing and Intelligent Systems Laboratory, Chung-Ang University, Seoul, Korea (Republic of)

    Joonki Paik

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