Numerical methods for image registration

Based on the author's lecture notes and research, this well-illustrated and comprehensive text is one of the first to provide an introduction to image registration with particular emphasis on numerical methods in medical imaging. Ideal for researchers in industry and academia, it is also a suitable study guide for graduate mathematicians, computer scientists, engineers, medical physicists, and radiologists.Image registration is utilised whenever information obtained from different viewpoints needs to be combined or compared and unwanted distortion needs to be eliminated. For example, CCTV ima

CG Type Algorithm for Indefinite Linear Systems

. The conjugate gradient algorithm (CG) is an effective tool for solving a system of linear equation with a positive definite coefficient matrix. We show the reasons for a possible breakdown of the method when applied to a symmetric system with an indefinite coefficient matrix. Although in finite arithmetic a breakdown of the method occurs rather seldom, near breakdowns may slow down the speed of convergence. We propose a look-ahead technique to overcome these near breakdowns. Moreover, we present a modification of the CG algorithm applicable to symmetric indefinite systems (CGI). The CGI algorithm is nearly as efficient as the plain CG algorithm. We compared the CGI algorithm with a modification of the composite step bi-conjugate gradient algorithm of Bank and Chan. Key words. Krylov subspace iteration, symmetric, indefinite matrices, CG algorithm, look-ahead techniques, polynomial iterative method, orthogonal polynomials, formally orthogonal polynomials. AMS(MOS) subject classificati..

A unified approach to fast image registration and a new curvature based registration technique

Image registration is central to many challenges in medical imaging today. It has a vast range of applications. The purpose of this note is twofold. First, we review some of the most promising non-linear registration strategies currently used in medical imaging. We show that all these techniques may be phrased in terms of a variational problem and allow for a unified treatment. Second, we introduce, within the variational framework, a new nonlinear registration model based on a curvature type regularizer. We show that affine linear transformations belong to the kernel of this regularizer. This has the important consequence that an additional pre-registration step is no longer necessary. Furthermore, we develop a stable and fast implementation of the new scheme based on a real discrete cosine transformation. We demonstrate the advantages of the new technique for synthetic data sets and present an application of the algorithm for registering MR-mammography images

Numerical methods for volume preserving image registration

Image registration techniques are used routinely in a variety of today’s medical imaging diagnosis. Since the problem is ill-posed, one may like to add additional information about distortions. This applies, for example, to the registration of contrast enhanced images, where variations of substructures are not related to patient motion but to contrast uptake. Here, one may only be interested in registrations which do not alter the volume of any substructure. In this paper we discuss image registration techniques with a focus on volume preserving constraints. These constraints can reduce the non-uniqueness of the registration problem significantly. Our implementation is based on a constrained optimization formulation. Upon discretization, we obtain a large, discrete, highly nonlinear optimization problem and the necessary conditions for the solution form a discretize nonlinear partial differential equation. To solve the problem we use a variant of Sequential Quadratic Programming method. Moreover, we present results on synthetic as well as on real life data.