Application of Global Optimization to Image Registration Öffentlichkeit

Abstract

Given two images, image registration aims to transform an image into a given reference image so that the two images look alike. This technique is vital in many applications, such as medical imaging and astronomy. Finding the best transformation can be phrased as solving a mathematical optimization problem. Due to the non-convexity of the objective function, commonly employed optimization techniques often generate local minimizers, limiting the accuracy of the registration. This thesis evaluates the applicability of a global optimization method, called DDNCID, for image registration. Direct application of DDNCID in image registration could cause minimizers to be infeasible. Thus, a focus of this thesis is to add a bound constraint by imposing a barrier function into the objective function to extend DDNCID.

Table of Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Optimization in Image Registration 5

2.1 Image Registration . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Double Descent and Color Intermittent Diffusion . . . . . 9

3 Global Optimization with Log Barrier Constraint 15

3.1 Logarithmic Barrier Method . . . . . . . . . . . . . . . . . 15

3.2 Improvements of DDNCID in Image Registration . . . . . 18

4 Numerical Experiments 20

4.1 2D Affine Registration without Boundary Constraints . . . 20

4.2 2D Affine Registration with Boundary Constraints . . . . . 22

4.3 2D Rigid Registration . . . . . . . . . . . . . . . . . . . . 22

5 Conclusion 25

5.1 Current Work . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . 25

A MATLAB Code 26

A.1 Log Barrier Constraint . . . . . . . . . . . . . . . . . . . . 26

A.2 Hessian Approximation . . . . . . . . . . . . . . . . . . . . 28

Bibliography 30

About this Honors Thesis

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School	Emory College
Department	Mathematics and Computer Science
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Mathematics
Stichwort	image registration optimization
Committee Chair / Thesis Advisor	Ruthotto, Lars, Emory University
Committee Members	Manetta, Manuela, Emory University Duffus, Dwight, Emory University Marianne, Lancaster, Emory University

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