Optimization Techniques in Computer Vision

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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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.

• 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
• algorithm analysis and problem complexity

“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)

• 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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