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Spie Press Book

Singular Value Decomposition for Imaging Applications
Author(s): Christian D. Zuniga
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Book Description

Singular value decomposition (SVD) is one of the most useful results of linear algebra with many applications. However, it is rarely discussed in books and classes. This Spotlight describes SVD, its applications to imaging, and its computation in a single introductory text. Sample code is included for illustration.
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Book Details

Date Published: 22 September 2021
Pages: 47
ISBN:
Volume: SL62

Table of Contents
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1 Introduction
1.1 Matrices in imaging
1.2 Singular value decomposition
1.3 Applications to imaging problems

2 Camera Calibration
2.1 Camera model
2.2 Direct linear transform method

3 Multiple View Geometry
3.1 Image to image projections
3.2 Fundamental matrix
3.3 Triangulation

4 Spectral Clustering

5 Simulation of Partially Coherent Systems
5.1 Optical system simulation
5.2 Partial coherence
5.3 Model-based optical proximity correction

6 Computing the SVD
6.1 Introduction
6.2 Bidiagonalization
6.3 QR algorithm

7 Appendix: Code Listings
7.1 Camera calibration
7.2 Spectral clustering
7.3 Partial coherence

Preface

The singular value decomposition (SVD) is among the most useful results of linear algebra with many applications to imaging. The SVD provides a way to factor any matrix into simpler component matrix. In many cases, keeping the most dominant components is enough to represent a matrix with good accuracy. This Spotlight series book first reviews what is SVD. Then, it covers several common imaging problems where the SVD is applied along with sample Python code. Finally, it outlines a basic algorithm for computing the SVD.

Christian Zuniga
September 2021


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