Optimal Control Approach to Image Registration

Stephen Taiwo Salako

doi:10.13189/ujam.2018.060501

Abstract

We discuss the orthogonality problem of moving grids, where we minimize a cost function with a regularization term and improve the orthogonality of grids by making the angle between grids close to .The initial grid used is obtained by a well-established method known as the grid deformation method. We will then replace the cost function in the orthogonality problem with sum of squared differences (SSD) to discuss the image registration problem. We will discuss the non-uniqueness of solutions, existence of optimal solutions and prove the existence of Lagrange multipliers of the image registration problem using the Direct Method in Calculus of Variation and then derive an optimality system based on the construction of a Lagrangian functional from which optimal transformations can be calculated.

Highlights

In this paper we use the moving grid method
The moving grid method forms the foundation for the optimization of grid orthogonality as well as the image registration problem
The optimization problem for nonlinear registration is ill-posed for reasons which will be discussed in future chapters; we add regularization terms or penalty terms next to the dissimilarity measure term to be minimized, which interconnects the transformation and data to be transformed [38]

Summary

Introduction

In this paper we use the moving grid method. The moving grid method forms the foundation for the optimization of grid orthogonality as well as the image registration problem.1.2. In this paper we use the moving grid method. The moving grid method forms the foundation for the optimization of grid orthogonality as well as the image registration problem. To solve a differential equation numerically by finite difference, finite element or finite volume methods, a good grid is needed for discretization of the physical domain. The idea of this method is to move nodes with correct velocities so that the nodal mapping has a desirable determinant. There are numerous approaches of grid generation as discussed in [8].In this paper we use the moving grid method

Objectives

Methods

Discussion

Conclusion