Optimization Techniques in Computer Vision
Ill-Posed Problems and Regularization

Authors: Mongi A. Abidi, Andrei V. Gribok, Joonki Paik



Features a comprehensive description of regularization through optimization

Contains a large selection of data fusion algorithms

Includes chapters devoted to video compression and enhancement

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.

Table of contents

Front Matter
Pages i-xv

Part I
Front Matter
Pages 1-1
Ill-Posed Problems in Imaging and Computer Vision
Pages 3-27
Selection of the Regularization Parameter
Pages 29-50

Part II
Front Matter
Pages 51-51
Introduction to Optimization
Pages 53-67
Unconstrained Optimization
Pages 69-92
Constrained Optimization
Pages 93-110

Part III
Front Matter
Pages 111-111
Frequency-Domain Implementation of Regularization
Pages 113-130
Iterative Methods
Pages 131-138
Regularized Image Interpolation Based on Data Fusion
Pages 139-155

Part IV
Front Matter
Pages 157-157
Enhancement of Compressed Video
Pages 159-177
Volumetric Description of Three-Dimensional Objects for Object Recognition
Pages 179-196
Regularized 3D Image Smoothing
Pages 197-218
Multimodal Scene Reconstruction Using Genetic Algorithm-Based Optimization
Pages 219-247

Back Matter
Pages 249-293

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