Optimal control approach to image registration |
Posted on:2010-03-23 | Degree:Ph.D | Type:Dissertation |
University:The University of Texas at Arlington | Candidate:Salako, Stephen Taiwo | Full Text:PDF |
GTID:1448390002983070 | Subject:Applied Mathematics |
Abstract/Summary: | |
The purpose of this dissertation is twofold: To present a new method of orthogonal grid generation and to investigate certain theoretical aspects of the optimal control approach to the image registration problem.;In the first part of this dissertation, we will present a variational method of orthogonal grid generation which is based on the deformation method and solving Euler-Lagrange equations. Although the concept of grid generation has been studied extensively, the generation of orthogonal grids is still one of the most challenging problems of the grid generation methods.;An orthogonal grid should offer significant advantages in the solution of systems of partial differential equations. Previous work requires a uniform grid to improve the orthogonality of grids. The grid deformation method provides size control via a monitor function but it has no control over gridline orthogonality.;Our approach is to improve orthogonality while providing size distribution by the deformation method.;In the second part, we replace the cost functional in the orthogonality problem with the sum of squared differences known as SSD to solve the Image registration problem.;Image registration is a significant part of image processing. It is a process of finding an optimal geometric transformation between corresponding pixels that minimizes the SSD. In this optimal control approach, we use the grid deformation equations as constraints.;In this dissertation, we prove the existence of optimal solutions using the direct method in the calculus of variations; discuss the non-uniqueness of solutions and the existence of Lagrange multipliers of the optimal control problem for image registration using an abstract theorem concerning the existence of Lagrange multipliers on Banach spaces. |
Keywords/Search Tags: | Optimal control, Image registration, Grid generation, Method, Problem |
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